# PHYSICS A 2821 Forces and Motion

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2 Data 2 speed of light in free space, c = ms 1 permeability of free space, 0 = Hm 1 permittivity of free space, 0 = Fm 1 elementary charge, the Planck constant, unified atomic mass constant, rest mass of electron, rest mass of proton, e = C h = Js u = kg m e = kg m p = kg molar gas constant, R = 8.31 J K 1 mol 1 the Avogadro constant, N A = mol 1 gravitational constant, G = Nm 2 kg 2 acceleration of free fall, g = 9.81 m s 2

3 Formulae 3 uniformly accelerated motion, s = ut at 2 refractive index, n = v 2 = u 2 + 2as 1 sinc capacitors in series, 1 C = 1 C C capacitors in parallel, C = C 1 + C capacitor discharge, x = x 0 e t/cr pressure of an ideal gas, p = 1 Nm 3 V <c 2 > radioactive decay, x = x 0 e λt t = λ critical density of matter in the Universe, ρ 0 = 3H G relativity factor, = (1 v 2 c 2 ) current, I = nave nuclear radius, r = r 0 A 1/3 sound intensity level, = 10 lg ( I I 0 ) Turn over

4 4 Answer all the questions. 1 (a) State the difference between a vector and a scalar quantity [1] (b) In the following list underline all the scalar quantities. displacement kinetic energy mass power velocity weight [1] (c) Fig. 1.1 shows a climber on a vertical rock face supported by a rope. The climber is in equilibrium. P 20 rock face T R W Fig. 1.1

5 5 The weight of the climber and her equipment is 650 N. The rope is attached to the climber and fixed to a point P where it makes an angle of 20 to the vertical. The contact force R acts on the climber at right angles to the rock face. (i) Use a vector triangle or resolve forces to calculate 1 the tension T in the rope T =... N 2 the contact force R. R =... N [3] (ii) The climber moves down the rock face and the angle the rope makes with the vertical decreases. Explain why the magnitude of the tension decreases.... [1] [Total: 6] Turn over

6 6 2 Fig. 2.1 shows a skier during a speed skiing competition. Speed skiing is skiing downhill in a straight line as fast as possible. start 400 m section 1 skier 100 m section 2 Fig. 2.1 In section 1 the skier started from rest and travelled at constant acceleration of 3.90 m s 2 for a distance of 400 m. Section 2 is 100 m long and this is where the skier is timed for the competition. The time recorded was 1.82 s. (a) Calculate (i) the time taken for section 1 (ii) the speed of the skier at the end of section 1 time =... s [2] (iii) the average speed for section 2. speed =... m s 1 [1] average speed =... m s 1 [1]

7 7 (b) Explain two methods the skier could adopt to increase the average speed for section [2] [Total: 6] Turn over

8 3 Fig. 3.1 shows a stair lift that takes a woman up a flight of stairs. 8 wall 3.40m 2.20m Fig. 3.1 The total weight of the woman and the chair is 930 N. The height gained is 2.20 m and the distance travelled by the woman is 3.40 m. (a) Calculate the gain in gravitational potential energy of the woman and the chair. (b) Define power. potential energy =... J [2] [1] (c) The lift travels up a slope at an angle of 40.3 to the horizontal in a time of 42.0 s. Calculate (i) the component of the weight of the woman and chair down the slope component =... N [1] (ii) the power required to lift the woman and chair to the top of the stairs. power =... unit... [3] [Total: 7]

9 4 In this question, two marks are available for the quality of written communication. (a) Fig. 4.1 shows a graph of the velocity v against time t for a moving object. 9 v t /s Fig. 4.1 Use the graph to describe and explain how the velocity and acceleration of the object change with time. Use the values on the time axis as reference for your description [3] Turn over

10 (b) Fig. 4.2 shows the displacement s against time t for a second object. 10 s Fig t /s (i) Use the graph to describe and explain how the velocity for this object changes with time. Use the time values on the graph as a reference for your description.... [5]

11 (ii) 11 Sketch on Fig. 4.3 a possible shape for variation of the velocity v against time t for this object. v t /s Fig. 4.3 [2] Quality of Written Communication [2] [Total: 12] Turn over

12 12 5 (a) Fig. 5.1 shows ropes X and Y that provide two equal and opposite forces of 120 N. These forces act vertically at the ends of a uniform horizontal rod of length 2.0 m and weight W of 240 N. The rod is pivoted at its centre. 2.0 m pivot support 240 N 120 N rope Y 120 N rope X W = 240 N Fig. 5.1 pivot rod (i) Calculate the torque on the rod. torque =... N m [2] (ii) Explain why the rod is not in equilibrium.... [1] (b) Fig. 5.2 shows the rod taken off the pivot and supported by ropes X and Y. The tension in rope X and rope Y is 120 N. 120 N 120 N 2.0 m rope X rope Y W = 240 N rod Fig. 5.2 Explain how this rod is in equilibrium [1]

13 13 (c) Fig. 5.3 shows rope X moved, to a point P, 0.50 m from the end towards the centre of the rod. The tensions in the ropes change to maintain equilibrium. rope X 1.50 m rope Y 0.50 m P W = 240 N Fig. 5.3 Calculate the new tension in rope Y by taking moments about P. tension =... N [3] [Total: 7] Turn over

14 6 (a) Define 14 (i) stress... (ii) strain [2] (b) A wire of length 1.75 m and cross-sectional area m 2 is extended by a force of 15.0 N. The material of the wire has a Young modulus of Pa. (i) Calculate the extension of the wire. extension =... m [3] (ii) A second wire made from the same material has the same volume. This wire has twice the original length and is extended by the same force. State and explain whether the extension of the second wire is greater, the same or less than the first wire.... [2] [Total: 7]

15 7 Fig. 7.1 shows how the force F for a spring varies with the compression x F / N x / mm Fig. 7.1 (a) Show that the spring constant for the spring is 25 N m 1. [1] (b) Fig. 7.2 shows the spring being used in a buffer to stop a moving toy train. toy train buffer spring Fig. 7.2 Turn over

16 16 The train of mass 0.45 kg was moving at a speed v when it hit the buffer. The train was brought to rest by the spring as it compresses 12 mm. (i) Show that the work done compressing the spring is J. [2] (ii) Calculate the speed of the train just before it hits the buffer. Assume that the work done compressing the spring is equal to the initial kinetic energy of the train. speed =... m s 1 [3] (c) State and explain the effect on the compression of the spring if the speed of the train is doubled [2] [Total: 8]

17 17 8 (a) A car of mass 850 kg is travelling at a constant speed of 16 m s 1 on a dry, level road when the driver reacts to a problem ahead. The car travels 12 m before the driver applies the brakes. The car then stops in a braking distance of 28 m. (i) Calculate the average deceleration of the car when braking. deceleration =... m s 2 [2] (ii) Calculate the average braking force required to bring the car to rest. braking force =... N [2] (b) (i) Explain how the road surface enables a car to come to rest when braking.... [2] (ii) Hence explain why the braking distance of a car increases if the road is wet.... [1] [Total: 7] END OF QUESTION PAPER

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