9702_s22_qp_22 Question 2

 

9702_s22_qp_12 Question 18

 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.

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_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 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_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 19

The diagram shows the variation of a quantity y with a quantity x for objects in a uniform gravitational field. 

What could x and y represent?

ANSWER: B

The Physics Behind answer:

• A direct square proportionality relationship i.e. y ∝ x resembles a parabolic curve.
• This is the kind of curve in the diagram.
• The quantities in options A, C, and D are all having direct proportionality relationships.
• Only in B that a direct square proportionality is involved, that is,

kinetic energy ∝ square of speed.

9702_s22_qp_13 Question 18

A car of weight 15 000 N is travelling along a horizontal road. 

At one instant, the thrust force acting on the car from the engine is 12 000 N and the resistive force acting on the car is 3 000 N. The velocity of the car at this instant is 24 m s^–1. 

What is the power output from the engine? 

A 72 kW 

B 220 kW 

C 290 kW 

D 360 kW

ANSWER: C

The Physics Behind answer:

• Power at an instant is the product of force and speed at that instant.
• Since the power being asked is the output from the engine, then the answer is the product of 12 000 N and 24 m s^–1.
• The product is rounded off to 2 significant figures following the number of significant figures of the speed.

9702_s22_qp_13 Question 17

What is meant by the efficiency of a system? 

A the difference between the useful energy output from the system and the total energy input 

B the difference between the useful energy output from the system and the wasted energy output 

C the ratio of the useful energy output from the system to the total energy input 

D the ratio of the useful energy output from the system to the wasted energy output

Answer: D

The Physics behind the answer:

• Efficiency, by definition, is option D.