Download 7 A ball bearing is released into a tall cylinder of clear oil

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AQA PAST PAPER: NEWTON’S LAWS OF MOTION
Q1. A ball bearing is released into a tall cylinder of clear oil. The ball bearing initially accelerates but
soon reaches terminal velocity.
(a) By considering the forces acting on the ball bearing, explain its motion.
(3 marks)
(b) How would you demonstrate that the ball bearing had reached terminal velocity?
(2 marks)
Q2(a) A cricketer throws a ball vertically upwards so that the ball leaves his hands at a speed of
25ms-1. If air resistance can be neglected, calculate
(i)
the maximum height reached by the ball,
(ii)
the time taken to reach maximum height,
(iii)
the speed of the ball when it is at 50% of the maximum height.
(4 marks)
(b) When catching the ball, the cricketer moves his hands for a short distance in the direction of travel
of the ball as it makes contact with his hands. Explain why this technique results in less force being
exerted on the cricketer’s hands.
(2 marks)
Q3. A girl kicks a ball along the ground at a wall 2.0 m away. The ball strikes the wall normally at a
velocity of 8.0ms-1 and rebounds in the opposite direction with an initial velocity of 6.0ms -1. The girl,
who has not moved, stops the ball a short time later.
(a) Explain why the final displacement of the ball is not 4.0 m.
(1 mark)
(b) Explain why the average velocity of the ball is different from its average speed.
(2 marks)
(c) The ball has a mass of 0.45 kg and is in contact with the wall for 0.10 s. For the period of time the
ball is in contact with the wall,
(i)
calculate the average acceleration of the ball.
(ii)
calculate the average force acting on the ball.
(iii)
state the direction of the average force acting on the ball.
(5 marks)
Q4. An apple and a leaf fall from a tree at the same instant. Both apple and leaf start at the same
height above the ground but the apple hits the ground first.
Use Newton’s laws of motion to explain why
(i)
the leaf accelerates at first then reaches a terminal velocity,
(ii)
the apple hits the ground first.
(5 marks)
Q5. An aircraft accelerates horizontally from rest and takes off when its speed is 82 ms-1. The mass of
the aircraft is 5.6 × 104 kg and its engines provide a constant thrust of 1.9 × 105 N.
(a) Calculate
(i)
the initial acceleration of the aircraft,
(ii)
the minimum length of runway required, assuming the acceleration is constant. (3 marks)
(b) In practice, the acceleration is unlikely to be constant. State a reason for this and explain what
effect this will have on the minimum length of runway required.
(2 marks)
(c) After taking off, the aircraft climbs at an angle of 22° to the ground. The thrust from the engines
remains at 1.9 × 105 N. Calculate
(i)
the horizontal component of the thrust,
(ii)
the vertical component of the thrust.
(2 marks)
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Q6. The figure below shows a stationary metal block hanging from the middle of a stretched wire
which is suspended from a horizontal beam. The tension in each half of the wire is 15 N.
(a) Calculate for the wire at A,
(b)
(i)
the resultant horizontal component of the tension forces,
(ii)
the resultant vertical component of the tension forces.
(i)
State the weight of the metal block.
(ii)
Explain how you arrived at your answer, with reference to an appropriate law of motion.
(3 marks)
(3 marks)
Q7. The figure below shows a sledge moving down a slope at constant velocity. The angle of the
slope is 22°.
The three forces acting on the sledge are weight, W, friction, F, and the normal reaction force, R, of
the ground on the sledge.
(a) With reference to an appropriate law of motion, explain why the sledge is moving at constant
velocity.
(2 marks)
(b) The mass of the sledge is 4.5 kg. Calculate the component of W,
(i)
parallel to the slope,
(ii)
perpendicular to the slope,
(2 marks)
(c) State the values of F and R.
(2 marks)
Q8. A car of mass 1500 kg accelerates uniformly from rest to 23 ms-1 in a time of 9.4 s.
(a) Calculate the average resultant force that acts on the car during the acceleration.
(3 marks)
(b) Calculate the distance covered during the acceleration.
(2 marks)
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Q9. The figure below shows an aircraft of mass 14 300 kg in flight. The aircraft has been travelling at
a constant velocity and a constant height. At the instant shown, the thrust is increased and the aircraft
starts to climb. The lift, thrust, drag and weight are indicated on the figure.
(a)
(b)
(i)
(ii)
Show that the upward acceleration of the aircraft is approximately 0.5 ms-2.
Calculate the increase in height as the aircraft climbs for 3 minutes.
(i)
(ii)
Calculate the resultant horizontal force acting on the aircraft.
Calculate the magnitude and direction of the resultant force acting on the aircraft.
(5 marks)
Q10. A radio-controlled model car has a mass of 0.65 kg.
(a) The car accelerates uniformly from rest to 3.5ms-1 in 1.5 s.
Calculate:
(i)
the acceleration of the car,
(ii)
the resultant force acting on the car during this acceleration.
(6 marks)
(4 marks)
(b) After 1.5 s the motor is switched off and the car decelerates uniformly until it stops. The
deceleration is 0.60 ms-2.
(i)
Calculate the resistive force acting on the car.
(ii)
Assuming that the resistive force was constant throughout the motion, calculate the
thrust from the motor when the car was accelerating.
(2 marks)
(c) Calculate the total distance travelled by the car.
(2 marks)
Q11. A fairground ride ends with the car moving up a ramp at a slope of 20° to the horizontal as
shown below:
(a) The car carrying its maximum load of passengers has a total weight of 6.8 kN. Show that the
component of the weight acting parallel to the ramp is about 2.3 kN.
(2 marks)
(b) The mass of the fully loaded car is 690 kg. Show that the force in part (a) will decelerate the car at
about 3.3 ms-2.
(2 marks)
(c) The car enters the ramp at 22 ms-1. Calculate the minimum length that the ramp must be in order
for the car to stop before it reaches the end. Neglect the length of the car.
(2 marks)
(d) The ride owner decides to use a shorter ramp and to install brakes on the car. The additional
decelerating force provided by these brakes is 4600 N. Calculate the new stopping time.
(3 marks)