9702_s22_qp_22 Question 2

 

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 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 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_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.

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 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_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 14

An unknown mass and a 1.00 kg mass are fixed at opposite ends of a bar. The bar has negligible mass and a length of 30.0 cm. 

The bar balances when supported by a pivot placed 20.0 cm from the unknown mass, as shown. bar pivot 20.0 cm 1.00 kg mass 30.0 cm unknown mass 

What is the unknown mass? 

A 333 g 

B 500 g 

C 667 g 

D 1000 g

ANSWER: B

The Physics behind the answer:

• The second condition of equilibrium is that the sum of clockwise moments equals the sum of counter-clockwise moments.
• The above leads to the equation (1.00 kg)(g)(10.0 cm) = (unknown mass)(g)(20.0 cm).
• After doing the mathematics, the unknown mass is determined i.e. 0.500 kg. This is option B.

9702_s22_qp_13 Question 13

A street lamp is fixed to a wall by a metal rod and a cable. 

 

Which vector triangle could represent the forces acting on the end of the rod at point P?

ANSWER: D

The Physics behind the answer:

• When a system is in equilibrium, the sum of all the forces acting on the system must be equal to zero. This is the first condition of equilibrium.
• The sum of these 3 forces must be zero.
• When forces are drawn using vector arrows using tip-to-tail method, the resultant force or the sum of all forces on an object is found through the straight line distance from the tail of the first arrow drawn to the tip of the last vector arrow.
• When an object is in equilibrium, these vector arrows drawn tip-to-tail returns to its origin, that is, a closed figure where the tail of first and tip of last arrows are at the same point. This shows that resultant force is zero. 
• There are 3 forces acting at point P of the metal rod [the system].
• the downward weight of the lamp
• the tension in the cable directed along the cable itself
• the compressive force of the rod which is directed to the right
• All the options are closed figures. We need to see which one is consistent with the directions mentioned in bullet 3. Thus, the answer is D.

9702_s22_qp_13 Question 12

Which statement describes the two forces in a couple? 

A They act in the same direction. 

B They act through the same point. 

C They produce zero resultant force. 

D They produce zero resultant moment.

ANSWER: C

The Physics behind the answer:

• A couple is a pair of equal, parallel but opposite forces whose effect is to produce a turning effect on a body without giving it linear acceleration. 
• The above means that the forces
• must act in the opposite directions contrary to option A,
• must act at different points contrary to option B, and
• must produce a rotation contrary to option D.
• Furthermore, a zero linear acceleration means zero resultant force. Thus, the answer is C.

9702_s22_qp_13 Question 9

A ball is dropped onto horizontal ground and bounces vertically upwards. When the ball is in contact with the ground, the following forces act: 

● the weight W of the ball 

● the contact force P exerted on the ground by the ball 

● the contact force N exerted on the ball by the ground. 

When the ball is in contact with the ground, the ball is momentarily stationary. At this instant, which relationship is correct? 

A N = P + W 

B N > P + W 

C N = W 

D N > W

ANSWER: D

The Physics behind the answer:

• For the ball moving downwards to eventually move upwards, a resultant force is needed to slow it down to a stop and speeds it up again in the opposite direction.
• In the case of the ball above, the resultant force needed is met when it is in contact with the ground. When it was not in contact yet, the only force acting is gravity or force W.
• When it's already in contact, there are 3 forces given. However, for the resultant force, there are only 2 of those that act on the ball, W and N. The other force P is acting on the ground.
• With only W and N acting, the needed resultant force is the sum of a stronger N and a weaker W.