The Physics Behind: 2022-09-04

Friday, September 9, 2022

NOTICE

The explanations and working for the rest of the questions in the June 2022 Series,

will be published in concurrence with the corresponding classes I will be having in Term 2.

Thursday, September 8, 2022

9702_s22_qp_12 Question 20

A wire is being stretched by a tensile force.

Which statement about the elastic limit must be correct?

A The deformation is plastic after the elastic limit has been reached.

B The deformation is plastic until the elastic limit is reached.

C The extension is proportional to the tensile force after the elastic limit has been reached.

D The extension is proportional to the tensile force until the elastic limit is reached.

ANSWER: A

The Physics Behind

If you apply a small force to a wire [or spring] and then release it, it will return to its original length (this is elastic deformation.). However, if you apply a large force, the wire [spring] may not return to its original length; the spring has become permanently deformed (this is plastic deformation.).
The force beyond which the wire [spring] becomes permanently deformed is known as the elastic limit.
This is also to say that beyond the elastic limit, the wire will have permanent deformation which is called plastic.

9702_s22_qp_12 Question 19

A metal wire obeys Hooke’s law and has a Young modulus of 2.0 x 10¹¹ Pa. The wire has an original length of 1.6 m and a diameter of 0.48 x 10^-3 m.

What is the spring constant of the wire?

A 7.2 x 10³ N m–1

B 2.3 x 10⁴ N m–1

C 2.9 x 10⁴ N m–1

D 9.0 x 10⁴ N m–1

ANSWER: B

The Physics Behind

The spring constant can be derived from the spring version of the Hooke's Law, that is, force F is directly proportional to extension x as

k = F/x

The other version of the Hooke's Law states that the stress [that is F/A] is directly proportional to strain [that is x/L]. The proportionality constant here is the Young modulus Y.

Y = F/A / x/L

Rearranging the second equation above, you should see that

Y = FL / Ax

Y = (F/x) (L/A)

Note that F/x is the spring constant k that you need. So,

Y = k (L/A)

k = AY/L

k = 1/4 πd²Y/L

Substituting the given data, k is

k = ((0.25) π (0.48 x 10^-3 m)² (2.0 x 10¹¹ P))/ (1.6 m)

k = 23000 N m–1

A student attempts to derive the formula for kinetic energy E_K. She begins by considering an object of mass m which is initially at rest. A constant force F applied to the object causes it to accelerate to final velocity v in displacement s. The kinetic energy gained by the object is equal to the work done on the object by the force F.

Which equation would the student not need in order to derive the formula for E_K?

A F = ma

B W = Fs

C E = 1/2 Fs

D v² = u² + 2as

ANSWER: C

The Physics Behind

E_K is derived by the above mentioned student, likely, as follows.

E_K = W
E_K = Fs since W = Fd
E_K = mas since F = ma
E_K = m(1/2 (v² -u²) since v² = u² + 2as

The resulting equation can therefore be simplified by considering that u = 0 as the object was initially at rest.

E_K = 1/2 mv².

You should notice that all equations in the options except that in option C are used.

Wednesday, September 7, 2022

9702_s22_qp_12 Question 17

Researchers have developed a new type of filament lamp with an efficiency of 40%. Old-type filament lamps have an efficiency of 5.0%. The two types of lamp produce the same useful output power.

What is the ratio

input power to new type of lamp / input power to old type of lamp?

A 0.13

B 0.63

C 1.6

D 8.0

ANSWER: A

The Physics Behind

Efficiency e is

e = useful power / input power.

input power = useful power / e

The ratio r which is input power to new type of lamp / input power to old type of lamp therefore is

r = (useful power / 0.4) ÷ (useful power / 0.05)

r = 0.05 / 0.4 because useful power is the same

r = 0.125

r = 0.13

[rounded off to following the proper number of significant figures]

9702_s22_qp_12 Question 16

Which product of two quantities is equal to power?

A force x distance

B force x velocity

C work done x time

D work done x velocity

ANSWER: B

The Physics Behind

Power is defined as the rate of doing work.
In equation form, power is work done divided by time.

P = W / t

but W = F x d

so P = F x d / t

but d/t = v

so P = F x v.

9702_s22_qp_12 Question 15

A closed U-shaped tube contains a stationary liquid of density ρ. One side of the tube contains a gas at pressure p₁ and the other side contains a gas at pressure p₂, as shown.

The acceleration of free fall is g. Which equation is correct?

A p₁ = ρgy

B p₂ = ρg(x – z)

C p₁ – p₂ = ρg(y – z)

D p₁ + p₂ = ρgx

ANSWER: C

The Physics Behind

Fluid pressure must be the same at same levels.
At that level, that is, the surface of liquid at the left side of the U-shaped tube, the pressure is p₁.
The pressure at the same level at the right side of tube is the combined pressure p₂ and the pressure due to the liquid above that liquid
In equation form, the above gives

p₁ = p₂ + M

where M is the pressure due to the liquid above the level.

M = ρgh

where h is the length of the column of liquid above the level

Therefore, p₁ = p₂ + ρgh

where h = y - z.

9702_s22_qp_12 Question 14

A granite rock at the surface of the Earth has density ρ. The rock is transported to the surface of another planet.

The acceleration of free fall on the surface of the other planet is twice that on the surface of the Earth.

What is the density of the rock on the other planet?

A 0.5ρ

B ρ

C 2ρ

D 4ρ

ANSWER: B

The Physics Behind

Transporting the granite rock to another planet does not change the

mass of the rock
volume of the rock

Therefore, the density which is mass divided by volume doesn't change as well.

9702_s22_qp_12 Question 13

A diving board of length 5.0 m is hinged at one end and supported 2.0 m from this end by a spring of spring constant 10 kN m^–1. A child of mass 40 kg stands at the far end of the board.

What is the extra compression of the spring caused by the child standing on the end of the board?

A 1.0 cm

B 1.6 cm

C 9.8 cm

D 16 cm

ANSWER: C

The Physics Behind

To determine the compression x of the spring, Hooke's Law will be used.

x = F / k

where F is the force experienced by spring and k is the spring constant.

The force F can be calculated using the second condition of equilibrium.

(weight) (5.0 m) = (F) (2.0 m)

F' = ((40 kg) (9.81 N kg-1) (5.0 m)) / (2.0 m)

F' = 980 N

F' is the force of the spring, contrary to the F which is the force on spring.

These two, however, are Third Law force pair and must have equal magnitudes.

The compression x [based on Hooke's Law] therefore is

x = 980 N / 10000 N m^–1

x = 0. 098 m

[or 9.8 cm]

Further Physics behind

"Why isn't the weight given in this question? when obviously diving board's weight is not negligible?"

At the beginning when the child wasn't standing at one end, the force at hinge is already adjusted together with the force on spring to deal with the weight.
In the above, it is initially in equilibrium with the spring having compressed already.
Now that the child is standing on one end, the force at hinge has to increase and the force by the spring must also increase.
This increase in the spring's force is equal to the F [or F'] and that the corresponding additional compression is the x being asked in this question.
In summary, you really do not need to know the weight of the diving board.

9702_s22_qp_12 Question 12

A uniform rod is attached by a hinge at one end to a wall. The other end of the rod is supported by a wire so that the rod is horizontal and in equilibrium.

Which arrow shows the direction of the force on the rod from the hinge?

ANSWER: D

The Physics Behind

The first condition of equilibrium states that the sum of all forces on object is zero.
This means that

the sum of forces along the vertical is zero
the sum of forces along the horizontal is also zero

Along the vertical, the weight is cancelled by the vertical component of the tension in the wire and upward component of the force from the hinge [let's call it Y]. You can realize that this indeed the case when you use the second condition of equilibrium.
Along the horizontal, the horizontal component of tension is cancelled by the horizontal force exerted by the hinge [let's call it X].
These upward Y and rightward X gives us the idea that the direction should be that in D.

9702_s22_qp_12 Question 11

Two forces form a couple.

Which statement describes the two forces?

A They are in the same direction.

B They are perpendicular to each other.

C They have the same magnitude.

D They pass through the same point.

ANSWER: C

The Physics Behind

A pair of forces known as a couple must be:

equal in magnitude
parallel, but opposite in direction
separated by a distance d.

The turning effect or moment of a couple is known as its torque [torque of a couple].

9702_s22_qp_12 Question 10

Two balls X and Y are moving towards each other with speeds of 5 m s^–1 and 15 m s^–1 respectively.

They make a perfectly elastic head-on collision and ball Y moves to the right with a speed of 7 m s^–1.

What is the speed and direction of ball X after the collision?

A 3 m s^–1 to the left

B 13 m s^–1 to the left

C 3 m s^–1 to the right

D 13 m s^–1 to the right

ANSWER: B

The Physics Behind

In a perfectly elastic collision,

the kinetic energy is conserved, and
the momentum is conserved.

Combining these two conservation principles in this type of collision reveals that

u_X - u_Y ₌v_Y- v_X

"the relative speed of approach equals the relative speed of separation"

where u stands for before-collision velocities and v as after-collision velocities

Using the above equation,

(+5 m s^–1) - (-15 m s^–1) | = (+7m s^–1) - v_X

20 m s^–1 = 7 m s^–1 - v_X

v_X = - 13 m s^–1

Answer: 27 m s^–1, the negative sign means to the left

9702_s22_qp_12 Question 9

A stone S and a foam rubber ball R are identical spheres of equal volume. They are released from rest at time t = 0 and fall vertically through the air. Both reach terminal velocity.

Which graph best shows the variation with time t of the speed v of the stone and of the rubber ball?

ANSWER: B

The Physics Behind

The terminal velocity is reached by an object that are released from rest is reached when the resultant force has already become zero which means that

the acceleration is also zero [Newton's 2nd Law of Motion] and
the velocity remains the same [from definition of acceleration, that is, no more change in velocity].

The resultant force is the sum of the forces acting on objects.

One force is the downward gravity [weight]
The other is air resistance dependent on both the surface area and speed of object

As the object moves down, it speeds up and therefore the air resistance is getting stronger and stronger. The resultant force then is becoming smaller and smaller. However, there is a difference between the objects S and R as though the air resistance on them is same at same speed, stone R is heavier than rubber R.
The above means that R can have resultant force of 0 [or zero acceleration or terminal velocity] faster than S.
Option B is the answer.

9702_s22_qp_12 Question 8

A child of mass 20 kg stands on the rough surface of a sledge of mass 40 kg. The sledge can slide on a horizontal frictionless surface.

One end of a rope is attached to the sledge. The rope passes around a fixed frictionless pole, and the other end of the rope is held by the child, as shown.

The rope is horizontal. The child pulls on the rope with a horizontal force of 12 N. This causes the child and the sledge to move with equal acceleration towards the pole.

What is the frictional force between the child and the sledge?

A 4.0 N

B 6.0 N

C 8.0 N

D 12 N

ANSWER: A

The Physics Behind

From the statement/given information "This causes the child and the sledge to move with equal acceleration towards the pole.", the following should be satisfied:

For the sledge

a = F_s / m_T

where F_s = 12 N + 12 N and m_T = 60 kg

F_s is the resultant force on sledge

m_T is the total mass

For the child

a = F_c / m_c

where F_c = 12 - f and m_c = 20 kg

F_c is the resultant force on the child

m_c is the mass of the child

f is the frictional force

The accelerations are equal so

0.40 N kg-1 = (12 N - f) / 20 kg

8.0 N = 12 N - f

f = 8.0 N - 12 N

f = 4.0 N

9702_s22_qp_12 Question 7

Which statement is not a requirement of a pair of forces that obey Newton’s third law of motion?

A The forces act in opposite directions.

B The forces act on different objects.

C The forces act on objects in contact.

D The forces are of equal magnitude.

ANSWER: C

The Physics Behind

The law applies in all cases where there interaction is present, may it be by contact or not.
Non-contact interaction are those we see with masses, with charges, and magnets/moving charges.

9702_s22_qp_12 Question 6

The water surface in a deep well is 78.0 m below the top of the well. A person at the top of the well drops a heavy stone down the well.

Air resistance is negligible. The speed of sound in the air is 330 m s^–1.

What is the time interval between the person dropping the stone and hearing it hitting the water?

A 3.75 s

B 3.99 s

C 4.19 s

D 4.22 s

ANSWER: D

The Physics Behind

The time interval x between the person dropping the stone and hearing it hitting the water can be determined by calculating

the time t₁ when the stone hits the water and produce sound
the time t₂ when sound travels upwards and reach the person's ear
adding t₁ and t₂.

For time t₁, the motion is freefall/at uniform acceleration so use the equation of motion s = ut₁ + 1/2 at₁²

78.0 = 0 + 1/2 (9.8) t₁²

t₁² =15.92

t₁ = 3.99 s

For time t₂, sound is a wave unaffected by gravity so use the constant speed formula v = d/t₂

t₂ = 78.0 / 330
t₂ = 0.236 s

Therefore, answer is D.

9702_s22_qp_12 Question 5

A car travels anticlockwise along a horizontal circular road of radius 12 m, as shown.

The car takes a time of 4.0 s to move from position P to position Q.

What is the magnitude of the average velocity of the car for the journey from P to Q?

A 4.2 m s^–1

B 4.7 m s^–1

C 6.0 m s^–1

D 14 m s^–1

ANSWER: A

The Physics Behind

Average velocity v of an object that has moved a displacement d in time t is

v = d / t

The time t is given [4.0 s]. The displacement d however needs to be calculated first and this is the straight line distance from P to Q.

You should see that you can have a right triangle with the sides measuring 12 m each.
The hypotenuse is the d. Using Pythagorean Theorem you should get d = 17 m.
For the v, divide 17 m by 4.0 s.

The answer therefore is A.

9702_s22_qp_12 Question 4

An object is moving with an initial velocity of 4.0 m s^–1 to the right. The velocity of the object changes so that its final velocity is 3.0 m s^–1 downwards, as shown.

Which arrow represents the change in velocity of the object?

ANSWER: B

The Physics Behind

The key idea here is vector addition.

When adding quantities with direction e.g. velocities, a tip-to-tail method can be used.
Represent each vector by an arrow with its magnitude proportional to length of arrow and direction represented by direction of arrow itself.
With same scale, start drawing one starting from the tip of the previous [tip-to-tail].
When done drawing all arrows, tip-to-tail, connect the tail of the first arrow drawn and tip of the last arrow using a straight arrow.

its length is proportional to magnitude of the resultant or vector sum
its direction is given by the arrow

A change in a quantity e.g. change in velocity Δv, means final velocity v minus initial velocity u.

You can rewrite Δv = v - u as Δv = v + (- u).
Then use the tip-to-tail, that is, draw an arrow representing one vector and draw the next vector from its tip [consider the negative as you are adding a negative as suggested by the above formula].
Your diagram should look like final velocity drawn downward with initial velocity drawn leftward i.e. + (-v).

9702_s22_qp_12 Question 3

Which statement about systematic errors is not correct?

A A systematic error can be caused by using an incorrectly calibrated instrument.

B One particular type of systematic error can affect all the measurements by the same amount.

C The effect of a systematic error can be reduced by repeating and averaging the measurements.

D Zero error is a type of systematic error.

ANSWER: C

The Physics Behind

Systematic error is an error associated with uncalibrated or faulty equipment or incorrect measurement practice which tend to affect all data in an investigation or experiment.
Options A, B and C are all correct.

9702_s22_qp_12 Question 2

What is the symbol for the SI base unit of temperature?

A C

B K

C °C

D °K

ANSWER: B

The Physics Behind

C is the symbol used for coulomb, a unit of charge. So option A cannot be the answer.
°C is a unit of temperature but not its SI unit. So option C is not the answer either.
Temperature is a scalar quantity and in a sense must have a lowest possible value of zero unit just as other scalars like length, mass, time.... there are no negative magnitudes for these, the lowest magnitude is zero.
In Celsius scale, Fahrenheit scale, Rankine scale, and others, the degree symbol in corresponding units °C, °F and °R implies a "degree" or a comparison. These scales can have "negative magnitude of a scalar".
The SI unit of temperature is kelvin.

Temperature expressed in kelvins is also called the absolute temperature or thermodynamic temperature.
The lowest temperature in this scale is zero [absolute zero].
The symbol is K and not °K in relation to explanation given in bullet 4 above.

9702_s22_qp_12 Question 1

Which estimate is reasonable?

A 1 x 10^–3 kg for the mass of a grain of sand

B 1 x 10^–2 m³ for the volume of a tennis ball

C 1 x 10⁰ J for the work done lifting an apple from waist height to head height

D 1 x 10⁴W for the power of a light bulb in a house

ANSWER: C

The Physics Behind

Imagine normal apples being sold in stores. The masses differ between 70 and 200 grams [estimate].
The corresponding weights therefore ranges from 0.7 N to 2 N.
For the distance between the waist and head is about a little less than 1 metre.
Option C therefore is reasonable.

Tuesday, September 6, 2022

9702_s22_qp_11 Question 20

Which statement about elastic and plastic deformation must be correct?

A Elastic deformation and plastic deformation are proportional to the applied force.

B Elastic deformation and plastic deformation cause no change in volume.

C Elastic deformation causes heating of the material but plastic deformation does not.

D Elastic deformation is reversible but plastic deformation is not.

ANSWER: D

The Physics Behind

Definitions are important.

9702_s22_qp_11 Question 19

Two wires, P and Q, are made from the same metal and hang vertically from a steel girder.

Wire Q has half the length and twice the diameter of wire P.

Identical masses are attached to the bottom of each wire. Both wires obey Hooke’s law as they are stretched by the weight of the masses.

What is the ratio extension of wire Q / extension of wire P?

A 8 / 1

B 4 / 1

C 1 / 1

D 1 / 2

ANSWER: A

The Physics Behind

One version of Hooke's Law is given by the following equation

Y = stress / strain

where Y is constant called Young modulus,

stress = force F / area A, and strain = extension x / original length L

Substituting all the other equation to Hooke's Law equation,

Y = FL/Ax

x = FL/AY

Assume that x is the extension of wire Q. For the extension X of wire P which has half L and 2D,

X = F(0.5)L/4AY

[where F and Y are same in both wires]

X = 8 FL/AY

X = 8x

Therefore, the ratio being asked is

8x/x

[or option A]

9702_s22_qp_11 Question 18

Objects with different masses are placed on the horizontal surface of a table. The objects are then raised to different heights above the table. The gain in gravitational potential energy of each object is the same.

Which graph best shows the variation of the height h of the objects above the table with their mass m?

ANSWER: A

The Physics Behind

The change in gravitational potential energy is the weight of the object multiplied by the change in height.

ΔE_p = mg Δh

E_p = mgh when initial height is set as reference point

In the above question, the following are held the same / constant.

E_p
g

With these 2 quantities unchanged, we can see from the equation that h is inversely proportional to m. This is shown graphically in option A.

9702_s22_qp_11 Question 17

The total energy supplied to an electric motor is E. Energy Q is wasted and the remaining energy does useful work.

What is the efficiency of the motor?

A Q/E

B (Q/E) - 1

C 1 - (Q/E)

D (1 - Q) / E

ANSWER: C

The Physics Behind

Efficiency is the useful work or energy divided by the input energy or the total energy supplied.
Let E be the total energy and W be the remaining energy or work.

E = W + Q

With efficiency as e, the above can then be written mathematically as

e = W / (W + Q)

e = (E - Q) / (W + Q)

e = E/(W + Q) - Q/(W + Q)

but E = W + Q

so, e = E/E - Q/E

e = 1 - Q/E

9702_s22_qp_11 Question 16

A box slides down a rough ramp.

The change in the gravitational potential energy of the box is 16 J as it moves between positions X and Y. The box has 24 J of kinetic energy at X and 35 J of kinetic energy at Y.

How much work is done against the frictional force?

A 5 J

B 19 J

C 27 J

D 43 J

ANSWER: A

The Physics Behind

Energy is conserved. The total energy at X must be equal to the total energy at Y.
At X,

16 J of potential energy
24 J of kinetic energy

At Y,

0 J of potential energy [at reference point]
35 J of kinetic energy
energy lost

The energy lost is due to work done against friction.

9702_s22_qp_11 Question 15

In a large container in an oil refinery, three oils of different densities are mixed. No chemical activity occurs.

The mixture consists of:

1200 kg of oil of density 1100 kgm^–3
1500 kg of oil of density 860 kgm^–3
4000 kg of oil of density 910 kgm^–3.

What is the density of the mixture?

A 927 kgm^–3

B 933 kgm^–3

C 957 kgm^–3

D 1045 kgm^–3

ANSWER: A

The Physics Behind

Density of the mixture is equal to the combined masses over the total volume of the mixture.
The total mass is 6700 kg.
The total volume equivalent to each given mass can be calculated by dividing the given mass by the corresponding density.
The total volume or the volume of the mixture, then, should be 7.23 m³.
Now, the density is

6700 kg / 7.23 m³

927 kgm^–3

9702_s22_qp_11 Question 14

A solid block has sides of length L, 2L and 4L. The block is submerged in water of uniform density so that the faces with the largest area are horizontal, as shown.

The upthrust acting on the block is U.

The block is now rotated to a new position so that the faces with the smallest area are horizontal. The block remains fully submerged in the water.

What is the upthrust acting on the block in its new position?

A U/4

B U

C 2U

D 4U

ANSWER: B

The Physics Behind

Archimedes Principle states that the upthrust acting on a body is equal in magnitude to the weight of the liquid or gas that it displaces.
In the question above, regardless of the orientation of the block, it will displace the same amount of volume of water.
This means that the weight of the displaced water remains the same. So, the answer is B.

9702_s22_qp_11 Question 13

A uniform diving board is held by two fixed rods at points P and Q. A person stands at end R of the diving board, as shown.

The forces exerted by the rods on the board are vertical. The board remains in equilibrium as the person slowly moves towards point Q from end R.

Which row describes the changes to the magnitudes of the forces exerted by the rods on the board?

ANSWER: A

The Physics Behind

With reference to the conditions of equilibrium,

the upward force at Q cancels the sum of downward forces [i.e. force at P and weight] , and
the clockwise moment due to weight cancels the counterclockwise moment at P.

When the person moves towards point Q [pivot],

the moment of weight decreases because the perpendicular distance decreases as the person moves closer to pivot,
the force at P decreases as it needs to produce a turning effect that cancels the decreasing moment of weight, and
since the force at P decreases, then the force at Q which is equal in magnitude to the sum of 2 downward forces also decreases.

9702_s22_qp_11 Question 12

When must an object be in equilibrium?

A when no resultant force acts on the object

B when no resultant force and no resultant torque act on the object

C when no resultant torque acts on the object

D when the upward force on the object is equal and opposite to its weight

ANSWER: B

The Physics Behind

Equilibrium is meet only after 2 conditions are satisfied.

The sum of all forces on the object is zero.
The sum of clockwise moments equals the sum of the anti-clockwise moments.

Option B has statement / phrases equivalent to the above.

Monday, September 5, 2022

9702_s22_qp_11 Question 11

A horizontal wooden plank is pivoted at one end, as shown.

The plank has a mass of 100 kg and a length of 10 m. The centre of gravity of the plank is a distance of 4 m from the pivot.

What is the moment of the weight of the plank about the pivot?

A 4 × 10² N m

B 5 × 10² N m

C 4 × 10³ N m

D 5 × 10³ N m

ANSWER: C

The Physics Behind

The moment of a force = force × perpendicular distance of the pivot from the line of action of the force.
The moment of weight which is our force in this question is the product of

mass which is 100 kg
acceleration due to gravity
perpendicular distance of 4 m

The answer therefore is C.

9702_s22_qp_11 Question 10

What is a statement of the principle of conservation of momentum?

A A force is equal to the rate of change of momentum of the object upon which it acts.

B In a perfectly elastic collision, the relative momentum of the objects before impact is equal to their relative momentum after impact.

C The momentum of an object is the product of the mass of the object and its velocity.

D The total momentum of a system of interacting objects remains constant, providing no resultant external force acts on the system.

ANSWER: D

The Physics Behind

Just like any other conservation laws / principle, conservation of momentum means the total momentum before an interaction equals the total momentum after objects interact.
This holds true in a closed system, that is, there is no external forces applied on the system.
Momentum is always conserved as there is no other form of momentum unlike in other quantities like energy where we can say that there are instances that kinetic energy is conserved and in others it is not conserved [as there are other energy forms].

9702_s22_qp_11 Question 9

A projectile is launched at an angle above horizontal ground and travels through the air.

Assume that no upthrust acts on the projectile.

Which diagram shows the directions of the force or forces acting on the projectile at position X?

ANSWER: B

The Physics Behind answer

Before reaching peak or point X,

a velocity-dependent drag acts on the projectile, opposing the motion,
this can be pictured as two drag components acting in the opposite directions of the vertical and horizontal velocities,
downward gravity also acts on the projectile.

When the projectile is at point X,

the air resistance along the horizontal remains as the horizontal velocity is maintained along the horizontal [zero resultant force along horizontal so no change is velocity],
the air resistance along the vertical is gone as it is velocity-dependent i.e. vertical velocity is zero at X, but the gravity is remains acting on the projectile's mass
there are 2 forces and can be represented by vector arrows in option B.

9702_s22_qp_11 Question 8

Water flows out of a pipe and hits a wall.

When the jet of water hits the wall, it has horizontal velocity v and cross-sectional area A.

The density of the water is ρ. The water does not rebound from the wall.

What is the force exerted on the wall by the water?

A ρv/A

B ρv/A²

C ρAv

D ρAv²

ANSWER: D

The Physics Behind answer

The work done on the wall by a volume of water is equal to the change in kinetic energy of water that volume during collision.
The following are some formulas and other concepts needed:

change in kinetic energy ΔE_k = 1/2 mv² - 0
work done W = average F x d = 1/2 Fd
density ρ = m/V
volume V = Ad
Note that we use W = Fd only when the F is constant. However, in the case of the water described above, the force varies at constant rate. So we take the average.

Based on bullet 1 and the formulas in bullet 2,

ΔE_k = W

1/2 mv² = 1/2 Fd

mv² = Fd

ρVv² = Fd

Therefore, F = ρAvv²

9702_s22_qp_11 Question 7

An object is moving along the ground in a straight line at a constant speed.

Which statement about the resultant force acting on the object is correct?

A The resultant force acting on the object is equal to its weight.

B The resultant force acting on the object is equal to the product of its mass and its velocity.

C The resultant force acting on the object is equal to the resistive force.

D The resultant force acting on the object is equal to zero.

ANSWER: D

The Physics Behind

Newton's 2nd Law of Motion [or the Law of Acceleration] states that an object's acceleration is directly proportional to the resultant force on it when mass is unchanged.
A movement along a straight line at constant speed means that the acceleration is zero.
Therefore, by virtue of the 2nd Law, resultant force on the object must also be zero.

9702_s22_qp_11 Question 6

A ball is thrown horizontally with a speed of 10.0 m s^–1 above horizontal ground. The ball hits the ground after a time of 3.0 s.

Air resistance is negligible.

What is the speed of the ball just before it hits the ground?

A 10 m s^–1

B 29 m s^–1

C 31 m s^–1

D 39 m s^–1

ANSWER: C

The Physics Behind

The speed is the magnitude of the velocity of ball just before it hits the ground.
This can be calculated using the Pythagorean Theorem

v² = v_x² + v_y²

where v_x is the horizontal speed and v_yis the vertical speed

The vertical speed v_y can be calculated using the equation of motion [from definition of acceleration],

v_y = u + at

where u is initial vertical speed [zero] and t is 3.0 s.

9702_s22_qp_11 Question 5

The curved line PQR is the velocity–time graph for a car starting from rest.

What is the average acceleration of the car over the first 5 s?

A the area below the curve PQ

B the area of the triangle PQS

C the gradient of the straight line PQ

D the gradient of the tangent at Q

ANSWER: C

The Physics Behind

Options A and B give distance.
Option D tells the instantaneous acceleration.
Average acceleration is the gradient of the line PQ. This means that the instantaneous acceleration varies with time from 0 to 5 s, that is from a lower value changing at constant rate to a higher value. The gradient of line PQ gives the average of these acceleration values within this time interval.

9702_s22_qp_11 Question 4

Two cables are attached to a bracket and exert forces as shown.

What are the magnitudes of the horizontal and vertical components of the resultant of the two forces?

ANSWER: C

The Physics Behind

Trigonometry i.e. sine and cosine functions are needed.
For the 15.0 N,

x-component is 15.0 cos(20.0°)
y-component is 15.0 sin(20.0°)

For the 6.00 N,

x-component is 6.00 sin(40.0°)
y-component is 6.00 cos(40.0°)

The magnitude of the components of the resultant force can be determined by vector adding the corresponding components of each given force.
The answer, therefore, is C.

9702_s22_qp_11 Question 3

A value for the acceleration of free fall on Earth is given as (10 ± 2) m s^–2.

Which statement is correct?

A The value is accurate but not precise.

B The value is both precise and accurate.

C The value is neither precise nor accurate.

D The value is precise but not accurate.

ANSWER: A

The Physics Behind

Accuracy is the term used to refer to how close a measurement is to the true or accepted value.
Precision refers to how close measurements of the same item are to each other.
By stating (10 ± 2) m s^–2, it means that

the acceleration, 10 m s^–2, is measured representing how close it is to the accepted value of g, and
this acceleration can vary from 8.0 to 12 [± 2 m s^–2] implying closeness of measurements when experiment / method of determining g is repeated.

The above implies accuracy and precision respectively. Thus, the answer is B.

9702_s22_qp_11 Question 2

Which two units are identical when expressed in terms of SI base units?

A J C^–1 and kgm² A^–1s^–2

B J s and kg m²s^–1

C N m and kgm³s^–2

D Ns and kgm s^–3

ANSWER: B

The Physics Behind

The following are some SI derived units and where they are based from.

1 J = 1 Nm
1 N = 1 kg m s^–2

Using the above,

1 J s = 1 Nm s

1 J s = 1 kg m s^–2 m s

1 J s = 1 kg m²s^–1

9702_s22_qp_11 Question 1

Which term represents a physical quantity?

A metre

B percentage uncertainty

C quark flavour

D spring constant

ANSWER: D

The Physics Behind

Spring constant is the measured by dividing the restoring force [a physical quantity] by the extension of the spring [another physical quantity].
Operating with these 2 physical quantities yields another physical quantity.

Sunday, September 4, 2022

9702_s22_qp_13 Question 8

A car accelerates from rest. The graph shows the variation of the momentum of the car with time.

What is the meaning of the gradient of the graph at a particular time?

A the kinetic energy of the car

B the rate of change of kinetic energy of the car

C the resultant force on the car

D the velocity of the car

ANSWER: C

The Physics behind the answer:

The gradient is the steepness of a line that is measured by dividing the change along y-axis by the change along the x-axis.
In the case of the above graph, gradient is determined by dividing a Δ momentum by a corresponding Δ time.
This Δ momentum per Δ time is our definition of force.

Other Physics concepts related to the question:

Since the graph is a curve, there is a need for us to draw a tangent line at the time value in question, if we are to calculate actual values. The [resultant] force on the object at that time is the gradient of the tangent line.

9702_s22_qp_13 Question 6

Two projectiles, X and Y, are fired into the air from the same place on level ground and reach the same maximum height, as shown.

Projectile X is fired vertically upwards and projectile Y is fired at an angle to the horizontal.

Air resistance is negligible.

Which statement is correct?

A X and Y are at rest at their maximum heights.

B X and Y are fired with the same speed.

C X and Y take the same time to return to the ground.

D X and Y travel the same distance.

ANSWER: C

The Physics behind the answer:

A projectile motion can be split into 2 motions - one along the vertical and the other along the horizontal. Assuming that air resistance is negligible, the projectile

experiences a force [gravity] along the vertical and so it will accelerate at rate 9.81 m s^-2.
experiences no force along the horizontal i.e. zero acceleration and travels at constant horizontal velocity.

You can say therefore that the motion of Y is the same as the motion of X along the vertical plus a constant velocity motion along the horizontal.
This means that when sent up at the same time with the velocity of X the same as the vertical component of velocity of Y [which should be as seen in the graph], they will return to the ground at the same time as they have the same acceleration [9.81 m s^-2].
The only difference is that Y has moved horizontally due to its horizontal velocity/motion.

9702_s22_qp_13 Question 7

A small glider moves along a horizontal air track as shown.

At each end of the air track, the glider has a perfectly elastic collision with a fixed buffer.

The glider moves at a constant speed between collisions.

Which graph represents the variation with time t of the velocity v of the glider as it moves between the two buffers?

ANSWER: D

The Physics behind the answer:

By "has a perfectly elastic collision" it means that the kinetic energy of the glider is conserved.

This means further that, for each collision, the speed of the glider remains the same.
It is only the direction of the glider that changes at every collision.

Since the options A, B, C and D are all velocity-time graph i.e. speed plus the directions, following the Cartesian plane conventions it is D that tells that speed [or magnitude of velocity] doesn't change while directions do every collision with the fixed buffers.

9702_s22_qp_13 Question 5

Forces of magnitudes 2N, 4 N and 7 N combine to produce a resultant force.

The magnitudes of the three forces are fixed, but the forces may act in any direction in the same plane.

What is not a possible magnitude of the resultant force?

A 0 N

B 5 N

C 8 N

D 13 N

ANSWER: A

The Physics behind the answer:

To answer this question, you must recognize that these combination of forces yields different possible magnitudes ranging from 1 N to 13 N.

The maximum possible value is determined by assuming that they all are in the same direction.
The minimum possible value is determined by assuming that 2 N and 6 N are in the same direction while 7 N is acting opposite to that.

Within this range, all options are possible except for option A.

9702_s22_qp_13 Question 3

The drag coefficient C_d is a number with no units. It is used to compare the drag on different cars at different speeds. C_d is given by the equation

Cd = 2F / vⁿρA

where F is the drag force on the car, ρ is the density of the air, A is the cross-sectional area of the car and v is the speed of the car.

What is the value of n?

A 1

B 2

C 3

D 4

ANSWER: B

The Physics behind the answer:

The key idea here is to do dimensional analysis i.e. see what exponent n must be so that the units of 2F is the same as the unit of vⁿρA.
For the 2F,

the unit is N
which is defined as kg m s^-2

For the vⁿρA,

the unit of v is (m s^-1)ⁿ, ρ is kg m^-3, and A is m²
simplifying the above gives (m s^-1)ⁿ kg m^-1

Combining the above 2 sets of units, we will have

the kgs cancel each other
leading to m² s^-2/ (m s^-1)ⁿ

Now, it is clear that n = 2 for these 2 sets of units cancel each other i.e. to be unitless.

9702_s22_qp_13 Question 4

A micrometer screw gauge is used to measure the diameter of a small uniform steel sphere. The measurement of the diameter is 5.00 mm ± 0.01 mm.

What is the percentage uncertainty in the calculated volume of the sphere, using these values?

A 0.2%

B 0.4%

C 0.6%

D 1.2%

ANSWER: C

The Physics behind the answer:

By volume, you should know that it considers 3 dimensions. This is implied in the formulas for volume, (4/3)πr3 where r is the radius for the sphere in particular.
The uncertainty of a result of multiplication/division is the sum of percentage uncertainties of the dimensions [quantities] used in the calculations.

Since you are given absolute uncertainty, this must be converted to percentage uncertainty first. The diameter 5.00 mm ± 0.01 mm is same as 5.00 mm ± 0.2%.
Because radius [or half of diameter] is multiplied to itself a couple of times, then the uncertainty as explained above should be 0.2% + 0.2% + 0.2%.

The answer therefore is C, 0.6%.

9702_s22_qp_13 Question 21

The extension of a copper wire is measured for different forces applied to the wire. A graph is plotted to show the variation of the force on the wire against extension. The maximum force is applied at point P.

Which statement must be correct?

A Point R is the limit of proportionality.

B The elastic potential energy of the wire at point S is given by the area under the graph between points T and S.

C There is no plastic deformation between points Q and P.

D The wire obeys Hooke’s law up to a point between R and Q.

ANSWER: B

The Physics Behind answer

The limit of proportionality is point S, contrary to option A.
The statement in option C is incorrect.
The wire obeys Hooke's Law only till the limit of proportionality S, in contrary to option D.
The correct answer is C as explained below.

The elastic potential energy, as long as the limit of proportionality is not exceeded is equal to the work done, W = average force x extension [W = 0.5Fx].
This is just the same as the area under the graph.

9702_s22_qp_13 Question 2

Which list of unit prefixes decreases in magnitude from left to right?

A centi, deci, milli

B deci, milli, centi

C pico, kilo, milli

D kilo, milli, pico

ANSWER: D

The Physics behind the answer:

The options all have 3 prefixes with power of 10 magnitudes.
However, the only option that has descending order of magnitudes is D.

kilo means 10³
milli means 10^-3
pico means 10^-9

9702_s22_qp_13 Question 1

Which pair of quantities are physical quantities?

A charge and ampere

B efficiency and kilogram

C pascal and strain

D period and potential difference

ANSWER: D

The Physics behind the answer:

Physical quantities are those properties that we may be able to measure. A unit on the other hand is the one quantity where we compare any other quantities.
For example, saying that "my sister is 5 Physics books tall" you are describing a quantity i.e. height and comparing it with the unit Physics book. This is to say that if you know the length of a Physics book, then the height of the sister is 5 times of that. In everyday usage, however, we do not use the Physics book as a unit. Instead, we use a metre, centimetre, inches, feet, etc.. We say 5 metre or 5 cm or 5 feet, and others.
You should see that units are written after the number describing a physical quantity.
Among the options, only D has both physical quantities - period and potential difference - of units second and volts, respectively.