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3.4.1.5 Newton’s laws of motion

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Time: 446

Marks: 373

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Q1. An object of mass 3.2 kg is acted on by two forces which are at right angles to each other. The resultant force is 11.5 N. (a) Calculate the acceleration of the object. (2) (b) One of the forces has a magnitude of 6.0 N. Using a scale diagram or otherwise, find: (i) the magnitude of the other force; (2) (ii) the angle between the resultant force and the 6.0 N force. (2) (Total 6 marks) Q2. To determine the force and power involved when a football is kicked, a student suspended a ball from the roof of a gymnasium by a long string as shown in Figure 1. Figure 1 When the ball of mass 0.45 kg was kicked it rose to a maximum height of 9.0 m. The student measured the contact time between the ball and the boot as 0.12 s. the acceleration of free fall, g = 9.8 m s–^2 (a) Assume that air resistance was negligible so that all the initial kinetic energy given to

(i) Calculate the velocity of the ball in this position. (2) (ii) In one test the string broke when the ball was in the position shown in Figure 2. Explain why the ball reached a lower maximum height on this occasion than it did when the string did not break. (2) (Total 15 marks) Q3. A horizontal force of 1.5 kN acts on a motor car of mass 850 kg that is initially at rest. (a) Calculate: (i) the acceleration of the motor car; (1) (ii) the speed of the motor car after 15 s; (2) (iii) the distance travelled by the motor car in the first 7.5 s of the motion; (2) (iv) the distance travelled by the motor car in the first 15 s of the motion. (1) (b) The diagrams below show the graph of force against time together with three incomplete sets of axes. Sketch on these axes the corresponding graphs for acceleration, speed and distance travelled for the first 15 seconds of the car’s motion. You should include labels for the axes and any known numerical values.

(4) (c) In practice the resultant force exerted on the motor car will not be constant with time as suggested by the force-time graph. Air resistance is one factor that affects the resultant force acting on the vehicle. (i) Suggest how the force-time graph will change when air resistance is taken into account. Explain your answer. You may wish to sketch a graph to illustrate your answer. ...............................................................................................................

Maximum acceleration........................ Minimum acceleration...................... (3) (Total 6 marks) Q5. A fairground ride ends with the car moving up a ramp at a slope of 20° to the horizontal as shown in the diagram 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) (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 m s–^2. (2) (c) The car enters the ramp at 22 m s–^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.

Minimum length ............................................... (2) (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. Stopping time ........................................ (3) (Total 9 marks) Q6. Figure 1 shows a graph of velocity against time for an aircraft of mass 2.8 × 104 kg landing on a stationary aircraft-carrier.

(b) A steam catapult is used to enable aircraft to take off from the ship. The catapult accelerates the aircraft from rest to its take-off speed of 71 m s–^1 in a distance of 62 m. Calculate the acceleration of the aircraft. Acceleration ......................................................... (2) (c) In level flight, the pilot sets the course to be 80 m s–^1 due north. There is a wind blowing from east to west at 20 m s–^1. Find, by scale drawing or otherwise, the resultant velocity of the aircraft. Velocity of aircraft: magnitude ............................. direction ................................

(3) (Total 12 marks) Q7. (a) The diagram below shows part of a precipitation system used to collect dust particles in a chimney. It consists of two large parallel vertical plates maintained at potentials of +25 kV and – 25 kV. The diagram below also shows the electric field lines between the plates. (i) Add arrows to the diagram to show the direction of the electric field. (1) (ii) Explain what is meant by an equipotential surface. ...............................................................................................................

Acceleration ...................................................... (1) (ii) the force on the spacecraft produced by the thrusters. Force on spacecraft ...................................................... (2) (b) Calculate the magnitude of the resultant velocity after 25 s. Magnitude of resultant velocity ...................................................... (2) (c) Calculate the angle between the initial and final directions of travel. Angle ...................................................... (1) (Total 6 marks) Q9. Figure 1 shows a skier being pulled by rope up a hill of incline 12° at a steady speed. The total mass of the skier is 85 kg. Two of the forces acting on the skier are already shown.

Figure 1 (a) Mark with arrows and label on Figure 1 a further two forces that are acting on the skier. (2) (b) Calculate the magnitude of the normal reaction on the skier. gravitational field strength, g = 9.8 N kg-^1 Normal reaction = ................................ (3) (c) Explain why the resultant force on the skier must be zero. ........................................................................................................................ ........................................................................................................................ (1) (Total 6 marks) Q10. The figure below shows a cable car being pulled up a 35° slope of length 120 m.

(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 × 10^3 N. Calculate: (i) the acceleration of the cable car down the slope; acceleration ............................................. (3) (ii) the speed of the cable car when it reaches the bottom of the slope; speed ....................................................... (2) (iii) the time taken for the cable car to reach the bottom of the slope. time taken ............................................... (2) (Total 9 marks)

Q11. The figure below shows how the velocity of a motor car increases with time as it accelerates from rest along a straight horizontal road. (a) The acceleration is approximately constant for the first five seconds of the motion. Show that, over the first five seconds of the motion, the acceleration is approximately 2.7 m s–^2. (3) (b) Throughout the motion shown in the figure above there is a constant driving force of 2.0 kN acting on the car. (i) Calculate the mass of the car and its contents mass ................................... (ii) What is the magnitude of the resistive force acting on the car after 40 s?

(b) After 1.5 s the motor is switched off and the car decelerates uniformly until it stops. The deceleration is 0.60 m s–^2. (i) Calculate the resistive force acting on the car. resistive force ..................................................... (ii) Assuming that the resistive force was constant throughout the motion, calculate the thrust from the motor when the car was accelerating. thrust .................................................................... (2) (c) Calculate the total distance travelled by the car. total distance travelled ....................................... (2) (Total 8 marks) Q13. Most cars manufactured in recent years have been fitted with air bags as a safety feature. In a collision the bag inflates automatically to protect the driver as air is released from a compressed air cylinder.

(a) Explain why the driver would be less seriously injured in a collision if the air bag inflates than he would be if unrestrained. ........................................................................................................................ ........................................................................................................................ ........................................................................................................................ ........................................................................................................................ ........................................................................................................................ ........................................................................................................................ ........................................................................................................................ ........................................................................................................................ (5) (b) Why is the driver of a car fitted only with seat belts more likely to be injured than if an air bag was fitted? Ignore the different deceleration times and the difference in the materials used. ........................................................................................................................ ........................................................................................................................ ........................................................................................................................ ........................................................................................................................ (2) (c) With reference to pressure, volume and temperature, discuss what happens to the air as the bag inflates. ........................................................................................................................ ........................................................................................................................ ........................................................................................................................ ........................................................................................................................ ........................................................................................................................ ........................................................................................................................ (3) (Total 10 marks)