Download 2.05 AQA F = ma - extra questions

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AQA PAST PAPER: NEWTON’S LAWS OF MOTION – EXTRA QUESTIONS
Q1. The figure below shows the path of a toy parachute which is bundled into a tight ball and thrown
over a wall from ground level at an angle of 50° to the ground.
(a) The toy parachute is thrown with an initial horizontal speed of 9.0 ms–1. Calculate the initial vertical
speed.
(2 marks)
(b) The wall is a horizontal distance of 12 m from the point at which the toy parachute is thrown. You
may ignore air resistance in this part of the question.
(i)
Calculate the time taken for the toy parachute to reach the wall.
(ii)
The toy parachute just clears the wall. Calculate the height of the wall.
(4 marks)
(c) The parachute opens when it reaches its maximum height at point A on the figure above and it
stops moving horizontally. Describe the vertical motion of the parachute as it falls, in terms of the
forces that act on it.
(4 marks)
Q2. The figure below shows a spacecraft that initially moves at a constant velocity of 890 ms-1
towards A.
To change course, a sideways force is produced by firing thrusters. This increases the velocity
towards B from 0 to 60 ms-1 in 25 s.
(a) The spacecraft has a mass of 5.5 × 104 kg. Calculate:
(i)
the acceleration of the spacecraft towards B;
(ii)
the force on the spacecraft produced by the thrusters.
(b) Calculate the magnitude of the resultant velocity after 25 s.
(c) Calculate the angle between the initial and final directions of travel.
(1 mark)
(2 marks)
(2 marks)
(1 mark)
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Q3. The following data were obtained when two students performed an experiment to determine the
acceleration of free fall. One student released a lump of lead the size of a tennis ball from a window in
a tall building and the other measured the time for it to reach the ground.
distance fallen by the lump of lead = 35m
time to reach the ground = 2.7 s
(a) Calculate a value for the acceleration of free fall, g, from these observations.
(2 marks)
(b) State and explain the effect on the value of g obtained by the students if a tennis ball were used
instead of the lump of lead.
(3 marks)
(c) The graph below shows how the velocity changes with time for the lump of lead from the time of
release until it hits the ground. Sketch on the same axes a graph to show how the velocity would
change with time if a tennis ball were used by the students instead of the lump of lead.
(2 marks)
Q4. A skydiver steps out of an aircraft that is moving horizontally. The skydiver has no initial vertical
speed.
(a)
(i)
Assume that the skydiver has a constant vertical acceleration of 9.8 ms -2. Calculate the
minimum time taken for the skydiver’s vertical speed to reach 35 ms -1.
(ii)
When the skydiver’s vertical speed has reached 35 ms-1, his horizontal speed is 50 ms-1.
Use a scale diagram to determine the resultant velocity of the skydiver.
(5 marks)
(b) In practice, the acceleration is not constant. The figure below shows the graph of vertical
acceleration against time for the first 10 s of the motion of the skydiver. Use the graph to estimate the
time taken for the skydiver to reach a vertical speed of 35 ms-1.
(3 marks)
(c) In terms of the weight and drag forces acting on the skydiver, explain the shape of the
acceleration-time graph shown above.
(4 marks)
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Q5. The figure below shows a cable car being pulled up a 35° slope of length 120 m.
The cable car has a weight of 1.5 × 104 N. The total frictional force resisting motion is 3.0 × 103 N.
(a)
(i)
Show that the component of the weight of the cable car parallel to the slope is 8600 N.
(1 mark)
(ii)
Calculate the tension in the cable when the cable car is moving at a constant speed up
the slope.
(1 mark)
(b) The cable snaps when the cable car is at rest at the top of the slope. The frictional force remains
constant at 3.0 × 103 N.
Calculate:
(i)
the acceleration of the cable car down the slope;
(3 marks)
(ii)
the speed of the cable car when it reaches the bottom of the slope;
(2 marks)
(iii)
the time taken for the cable car to reach the bottom of the slope.
(2 marks)
Q6. Galileo is reported to have dropped a heavy cannon ball and a lighter, smaller musket ball from a
tower at the same time. He observed that they both hit the ground at the same time.
However, a musket ball and a table tennis ball dropped simultaneously would not hit the ground
together. Explain these two sets of observations.
(5 marks)