9702_s22_qp_22 Question 4

 

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_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_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 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 11

Skaters of masses 80 kg and 40 kg move directly towards each other and collide. 

Before the collision, the heavier skater is moving to the right at a speed of 2.0 m s⁻¹ and the lighter skater is moving to the left at a speed of 1.0 m s⁻¹. 

After the collision, the heavier skater moves to the right at a speed of 0.80 m s⁻¹. 

What is the relative speed of separation of the two skaters? 

A 0.6 m s⁻¹ 

B 1.4 m s⁻¹ 

C 2.2 m s⁻¹ 

D 2.6 m s⁻¹ 

ANSWER: A

The Physics behind the answer:

• Momentum is conserved in this situation. The total momentum before collision and the total momentum after are equal.
• This conservation gives: (80)(2.0) + (40)(-1.0) = (80)(0.80) + 40x where x is the velocity of 40-kg skater after collision.
• After doing the mathematics, x = 1.4 m s⁻¹.
• But the answer is not B as what is being asked is the relative speed of separation e.g. the speed of one skater as seen by the other.
• Relative speed is calculated by taking the difference between speeds when objects are moving in the same direction or taking the sum of the speed when moving in the opposite directions.
• We therefore should do 1.4 - 0.80.... the answer is 0.6 m s⁻¹ [A].

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.