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Answer all the questions.
1 In space, Asteroid A, called Dimorphos travels at constant speed in a circle around a larger
Asteroid B, called Didymos. The diagram shows Asteroid A at position P.
Asteroid B
Didymos
Asteroid A
Dimorphos P
r0 = 1.19 km
The distance r0 between Asteroid A and Asteroid B is 1.19 km.
The time T0 for Asteroid A to travel once around Asteroid B is 4.29 × 104 s (11 hours 55 minutes).
(a) Calculate the average speed v, in m s–1, of Asteroid A.
v = ................................................. m s–1 [2]
(b) Explain one similarity and one difference between the velocity of Asteroid A at P and its velocity
six hours later.
similarity ...........................................................................................................................................
..........................................................................................................................................................
difference .........................................................................................................................................
..........................................................................................................................................................
[2]
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(c) In 2022, the NASA DART mission impact caused Asteroid A to follow a different circular path
round Asteroid B.
The new time TN for Asteroid A to travel once around Asteroid B was reduced by 30 minutes.
(i) Show that the ratio
new time to travel around Asteroid B TN
original time to travel around Asteroid B T0
is approximately 0.958.
[1]
(ii) The relationship between the distance r from the centre of Asteroid B to the centre of Asteroid A
and the time T for Asteroid A to travel around Asteroid B is
r3 ∝ T2
Calculate the new distance rN from the centre of Asteroid B to the centre of Asteroid A.
Give your answer in km and to 3 significant figures.
rN = .................................................... km [3]
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2 In ice hockey, players use a stick to hit an object called a puck, across the surface of the ice.
Assume that the frictional force between the ice and the puck is negligible.
The mass of each puck is 0.16 kg.
(a) State Newton’s second law of motion.
..........................................................................................................................................................
..................................................................................................................................................... [1]
(b) A player hits a single, stationary, puck. The stick is in contact with the puck for a time of 0.033 s
and the puck moves at a velocity of 20 m s–1 across the ice.
Calculate:
(i) the impulse of the force applied to the puck. Include an appropriate unit.
impulse = ................................... unit ............... [2]
(ii) the average force F that the stick exerts on the puck.
F = ...................................................... N [1]
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5
(c) A mass m is stuck on top of a second puck B. Puck B is stationary. The single puck travels
across the surface of the ice towards B as shown in the diagram.
m
single puck 20 m s–1
ice
B
The single puck collides elastically head-on with B.
(i) Explain what is meant by a perfectly elastic collision.
..........................................................................................................................................................
..................................................................................................................................................... [1]
(ii) After the collision B travels across the surface of the ice with a velocity of 8.0 m s–1.
The velocity of the single puck after the collision is –12 m s–1.
Determine m.
m = ..................................................... kg [3]
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