Further mechanicsEdexcel A-Level Physics: Topic test

20 questions, 54 marks

Edexcel A-Level Physics

Further mechanics topic test

Total 54 marks

Name

Class

Date

1
A cricket ball of mass 0.16 kg is travelling horizontally at 30 m s⁻¹ when a batter hits it straight back along the same line. It leaves the bat at 25 m s⁻¹ and the contact with the bat lasts 4.0 ms.
(a)
What is the magnitude of the impulse that the bat exerts on the ball?
[1 mark]
A0.80 N s
B8.8 N s
C4.8 N s
D4.0 N s
(b)
What is the magnitude of the average force that the bat exerts on the ball?
[1 mark]
A2.0 × 10² N
B1.2 × 10³ N
C1.0 × 10³ N
D2.2 × 10³ N
(c)
A fielder catches a similar ball and draws his hands backwards as he catches it. Explain why this reduces the force on his hands.
[2 marks]
Total for question 1: 4 marks
2
Two identical ice hockey pucks, each of mass 0.17 kg, slide on frictionless ice. Puck A, moving at 5.0 m s⁻¹, collides with puck B, which is at rest. After the collision puck A moves at 4.0 m s⁻¹ at 37° to its original direction of motion, and puck B moves off on the other side of that original direction.
(a)
What is the magnitude of the component of puck A's momentum after the collision that is perpendicular to its original direction?
[1 mark]
A0.41 kg m s⁻¹
B0.54 kg m s⁻¹
C0.68 kg m s⁻¹
D0.85 kg m s⁻¹
(b)
What is the speed of puck B immediately after the collision?
[1 mark]
A1.0 m s⁻¹
B2.4 m s⁻¹
C3.0 m s⁻¹
D4.0 m s⁻¹
(c)
Show that this collision is elastic.
[2 marks]
Total for question 2: 4 marks
3
A satellite moves in a circular orbit of radius 6.77 × 10⁶ m about the centre of the Earth. It completes one orbit in 92 minutes.
(a)
Calculate the angular velocity of the satellite and its orbital speed.
[3 marks]
(b)
Calculate the centripetal acceleration of the satellite. Explain why the satellite is accelerating even though its speed is constant, and state the direction of this acceleration.
[4 marks]
Total for question 3: 7 marks
4
A ball of mass 0.20 kg is attached to a light inextensible string of length 0.80 m. The other end of the string is fixed to a ceiling. The ball moves at constant speed in a horizontal circle, with the string making an angle of 30° to the vertical.
(a)
Calculate the radius of the circle, the tension in the string and the speed of the ball.
[6 marks]
(b)
For the ball in part (a), calculate the average resultant force on the ball during half a revolution. Explain why this is smaller than the magnitude of the resultant force at any instant, and state the average resultant force over one complete revolution.
[6 marks]
Total for question 4: 12 marks
5
A small rocket of initial mass 80 kg is launched vertically from rest. Its motor expels burnt fuel downwards at a steady rate of 0.50 kg s⁻¹, at a speed of 2400 m s⁻¹ relative to the rocket. Assume that the loss of mass of the rocket in the first second is negligible, and ignore air resistance.
(a)
What is the force that the rocket exerts on the expelled gas?
[1 mark]
A4.8 × 10³ N
B2.4 × 10³ N
C1.2 × 10³ N
D1.2 × 10² N
(b)
What is the initial acceleration of the rocket?
[1 mark]
A5.2 m s⁻²
B9.8 m s⁻²
C15 m s⁻²
D25 m s⁻²
(c)
Explain, in terms of momentum, why the expulsion of the gas produces an upward force on the rocket.
[2 marks]
Total for question 5: 4 marks
6
A firework shell of mass 2.0 kg is at rest on a smooth horizontal surface. It explodes into three fragments that all move horizontally. One fragment of mass 0.50 kg moves east at 40 m s⁻¹ and another of mass 0.90 kg moves north at 30 m s⁻¹.
(a)
What is the magnitude of the momentum of the third fragment?
[1 mark]
A7.0 kg m s⁻¹
B20 kg m s⁻¹
C47 kg m s⁻¹
D34 kg m s⁻¹
(b)
In which direction does the third fragment move?
[1 mark]
A37° south of west
B53° south of west
C53° south of east
D45° south of west
(c)
Calculate the kinetic energy of the third fragment.
[2 marks]
Total for question 6: 4 marks
7
A ball of mass 0.25 kg on a light string is swung in a vertical circle of radius 0.80 m at a constant speed of 3.0 m s⁻¹ by a student.
(a)
Calculate the tension in the string when the ball is at the top of the circle.
[3 marks]
(b)
Calculate the angular velocity of the ball and the tension in the string when the ball is at the bottom of the circle. State where in the circle the string is most likely to break.
[4 marks]
Total for question 7: 7 marks
8
A bullet of mass 0.010 kg travelling horizontally at 400 m s⁻¹ strikes a block of mass 2.00 kg that hangs at rest from a light inextensible string of length 1.50 m. The bullet embeds in the block, and the string stays taut as the block and bullet begin to swing together.
(a)
Calculate the speed of the block and bullet immediately after the impact. Show that the collision is inelastic and state what happens to the kinetic energy that is lost.
[6 marks]
(b)
Calculate the tension in the string immediately after the impact and the magnitude of the impulse that the bullet exerts on the block. Explain why the tension must be greater than the weight of the block and bullet.
[6 marks]
Total for question 8: 12 marks

End of questions

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).