A-Level Physics Exampro: Scalars and Vectors Exercises, Exercises of Physics

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Exampro A-level Physics

3.4.1.1 Scalars and vectors

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Time: 634

Marks: 523

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Q1. (a) State the conditions necessary for a body to be in equilibrium. ........................................................................................................................ ........................................................................................................................ ........................................................................................................................ ........................................................................................................................ (2) (b) The boat shown in the figure below is being towed at constant velocity. The tension force ( F T) in the towing rope is 2800 N. The forces resisting the motion can be assumed to be the force of the water on the keel ( F K) and the force of the water on the rudder ( F R). By calculation or by scale drawing, find the size of the force, F R, needed to keep the boat in equilibrium. (6) (Total 8 marks) Q2. (a) Define gravitational field strength at a point in a gravitational field. ........................................................................................................................ ........................................................................................................................ (1) (b) Tides vary in height with the relative positions of the Earth, the Sun and the moon which change as the Earth and the Moon move in their orbits. Two possible configurations are shown in Figure 1.

(2) (c) Calculate the magnitude of the gravitational force experienced by 1 kg of sea water on the Earth’s surface at P , due to the Sun ’s gravitational field. radius of the Earth’s orbit = 1.5 × 10^11 m mass of the Sun = 2.0 × 10^30 kg universal gravitational constant, G = 6.7 × 10−11^ Nm^2 kg− (3) (Total 9 marks) Q3. A skier unfortunately breaks a bone in the lower part of the leg whilst attempting a jump. While the bone is healing, a steady force is applied to the leg. This is called traction. Unless this is done the muscles would pull the fractured parts together so tightly that the leg, when healed, would be shorter than it was before the injury. The diagram below shows one arrangement for providing the traction. The pulley system is in equilibrium in the position shown. (a) State fully the conditions that must be satisfied for a system to be in translational and rotational equilibrium.

(3) (b) In the diagram all the pulleys are frictionless so that the tension in the rope is the same everywhere. acceleration of free fall, g = 9.8 m s− (i) Determine the magnitude of the total horizontal force exerted on the leg by the system. (2) (ii) Determine the total upward force exerted on the leg by the system. (1) (iii) Explain briefly why the force calculated in (i) does not move the patient towards the bottom of the bed. ............................................................................................................... ............................................................................................................... ............................................................................................................... ............................................................................................................... ............................................................................................................... (2) (Total 8 marks) Q4. A pivoted metre rule is supported in equilibrium horizontally by a thread inclined at 30° to the vertical.

(Total 1 mark) Q6. Which one of the following pairs contains one vector and one scalar quantity? A Displacement Acceleration B Force Kinetic energy C Power Speed D Work Potential energy (Total 1 mark) Q7. The figure below shows a person of weight 800 N, crossing the gap between two buildings on a nylon rope.

Before the crossing commenced the rope was horizontal and just taut. When the person is halfway across the rope sags by 5.0°. (a) Explain briefly why, however taut the rope is, the rope must sag when the person is on it. ........................................................................................................................ ........................................................................................................................ ........................................................................................................................ (1) (b) By calculation or scale drawing, determine the tension in the rope when the person is half way across. (3) (c) The nylon rope has an ultimate tensile stress of 7.0 × 10^7 Pa. Calculate the minimum diameter of the rope that could be used. (3) (Total 7 marks) Q8. 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)

(ii) on each of the student’s feet. (1) (c) Another student attempts the same exercise but with the forearms at an angle of 30° to the ground, as shown in Figure 2. Figure 2 (i) The directions of some of the forces acting on the hands have been indicated. Indicate, on Figure 2 , any other forces acting on the hands (1) (ii) State the cause of these additional forces. ............................................................................................................... (1) (iii) The reaction force at each hand is 210 N. Calculate the magnitude of the compression force in each forearm in this position. (1) (Total 8 marks) Q11. Coplanar forces of 5 N, 4 N and 3 N act on an object. Which force, in N, could not possibly be the resultant of these forces? A 0 B 4 C

D

(Total 1 mark) Q12. (a) State the difference between a vector quantity and a scalar quantity. ........................................................................................................................ ........................................................................................................................ (1) (b) Give one example of a vector quantity. ........................................................................................................................ (1) (Total 2 marks) Q13. The diagram below shows three ropes attached to a ring. The ropes and the ring all lie in a horizontal plane and are in equilibrium. The tension in rope A is shown in the diagram below. Calculate the tension in ropes B and C. Tension in rope B = .............................................. Tension in rope C = .............................................. (Total 3 marks) Q14. (a) State the difference between vector and scalar quantities.

(2) (ii) Use your scale diagram or a calculation to determine the resultant speed of the raindrop when the wind is blowing. Speed of raindrop ................................... (1) (b) The mass of the raindrop is 4.5 × 10–8^ kg. Calculate its kinetic energy. Kinetic energy ........................................ (3) (c) Calculate the work done by the raindrop as it falls through a vertical distance of 5. m in still air. Gravitational field strength, g = 9.8 N kg– Work done .....................................

(3) (d) Explain why a raindrop falling vertically through still air eventually reaches a constant speed. Two of the 6 marks in this question are available for the quality of your written communication. ........................................................................................................................ ........................................................................................................................ ........................................................................................................................ ........................................................................................................................ ........................................................................................................................ ........................................................................................................................ ........................................................................................................................ ........................................................................................................................ (6) (Total 15 marks) Q16. 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) Q17. Complete the following table. Quantity Vector or Scalar S.I. Unit Displacement Vector m Velocity Weight Energy (Total 3 marks) Q18. The diagram below shows a spacecraft that initially moves at a constant velocity of 890 m s–1^ towards A. To change course, a sideways force is produced by firing thrusters. This increases the velocity towards B from 0 to 60 m s–1^ in 25 s. (a) The spacecraft has a mass of 5.5 × 10^4 kg. Calculate: (i) the acceleration of the spacecraft towards B ;

By resolving forces, calculate: (a) the angle θ ; Angle θ ...................................................... (2) (b) the magnitude of the force F. Magnitude of the force F ...................................................... (1) (Total 3 marks) Q20. 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- Normal reaction = ................................ (3) (c) Explain why the resultant force on the skier must be zero. ........................................................................................................................ ........................................................................................................................ (1) (Total 6 marks) Q21. The figure below shows a cable car being pulled up a 35° slope of length 120 m.