St. Joseph s AngloChinese School


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1 Time allowed:.5 hours Take g = 0 ms  if necessary. St. Joseph s AngloChinese School First Term Examination Form 6 ASL Physics Section A (40%) Answer ALL questions in this section. Write your answers in the answer sheets provided.. ms  8 m Passengers enter the loop Passengers leave the loop Figure On one particular ride in an amusement park, passengers looptheloop in a vertical circle, as shown in Figure. The loop has a radius of 8 m and a passenger of mass 60 kg is traveling at a speed of ms  when he is at the highest point of the loop. The passenger is now at the highest point. (a) Draw the free body diagram of the passenger. Label all the forces. (b) Calculate the centripetal acceleration of the passenger. (c) Calculate the force the seat exerts on the passenger. ( marks) ( mark) ( marks) (d) Operators of this ride must ensure that the speed at which the passengers enter the loop (see Figure ) is above a certain value. (i) Suggest a reason for this. ( marks) (ii) Assume that there is no friction between the track and the cart, find the minimum speed at which the passengers enter the loop. (4 marks). Suppose the force acting on a tennis ball of mass kg is given by Figure below as a function of time. F/N t/s Figure Assuming the ball is being served so it is nearly at rest initially, estimate (a) the total impulse given to the ball, and (b) the velocity of the ball just after being struck. ( marks) ( marks)
2 3. A 0.4 kg mass rests on a frictionless surface and is connected by springs to two supports as shown in Figure 3. Each spring is at its natural length. The force constant of each spring is 30 N m . The mass is pulled to one side along the line of the springs through a distance of 0. m. On release, the mass performs simple harmonic motion. Figure 3 (a) Find the period of oscillation. (3 marks) (b) Calculate the energy stored at the moment of release, and calculate the speed of the mass when it has traveled 0.05 m. (4 marks) (c) Sketch a graph showing the kinetic energy of the mass varies with time for one complete oscillation after the mass is released. (3 marks)
3 Section B (35%) There are 3 questions in this section. Answer ALL questions. ALL the answers should be marked on the M.C. answer sheet.. Q R 30 X P A uniform metre rule of mass 0. kg is hinged to a wall at P and the other end R is connected by a wire attached to the wall at Q, vertically above P as shown in the diagram above. A block X of mass 0. kg is hung from the rule 5 cm from R. The metre rule is horizontal. Find the tension in the wire. A..5 N B. 3.5 N C. 4.0 N D. 7.0 N. Which of the following is/are examples of zero resultant force acting on an object? () A mass at rest on the table. () A metal ball falling with terminal velocity in water. (3) A basketball after shoot by a sportsman. A. () only B. () and () only C. () and (3) only D. (), () and (3) 3. Two wooden blocks A and B of the same mass are connected by a string which passes over a smooth fixed pulley as shown. The blocks are at rest. The maximum friction between any two surfaces is N. If a force F parallel to the plane is applied to A, find its minimum value for moving A. A. N B. 4 N C. 6 N D. cannot be determined because the mass of each block and the angle of inclination are not given. 4. A bullet of velocity u can just penetrate into a wooden board by cm. If the velocity of the bullet were doubled, it could penetrate the same wooden board by A. 4 cm. B. 6 cm. C. 8 cm. D. 0 cm. 3
4 5. F / N t / s The graph shows the time variation of the net force, F, acting on an object of mass kg. The object is initially at rest and its subsequent motion is along a straight line. Which of the following statements is/are correct? () The final speed of the object is not equal to zero. () The maximum speed of the object is less than 5 m s . (3) The object is decelerating in the first 6 seconds. A. () only B. (3) only C. () and () only D. (), () and (3) 6. Balls X and Y are projected from the same point on the ground at the same time. X is projected vertically upwards at a speed of 0 m s  while Y is projected at an angle of 30 to the horizontal at a speed of 0 m s . Which of the following is/are correct? () X and Y reach their respective highest positions at the same time. () X and Y have the same acceleration throughout the flight in air. (3) X and Y have zero speed at their highest positions. A. () only B. () and () only C. () and (3) only D. (), () and (3) 7. A particle is projected horizontally from a table with an initial speed u and attains a speed v just before hitting the ground. What is the time of flight of the particle? (Neglect air resistance.) A. v g B. C. D. v u g v u g v g u 8. For no spilling of water, the minimum speed of a bucket of water at the highest point when whirled in a vertical circle is ms . The radius of the circle is A. 0. m B. 0. m C. 0.4 m D. 0.8 m 4
5 9. The maximum frictional force between the road surface and the wheels of a car is halved when the road is wet. If the maximum safety speed for rounding an unbanked corner is 0 m s  when the road is dry, what is the maximum safety speed when the road is wet? A. 7. m s  B. 8.4 m s  C. 0. m s  D..3 m s  0. A mass m slides on a frictionless horizontal surface at speed u. It strikes a light spring of force constant k attached to a rigid wall as shown. After a completely elastic encounter with the spring the mass moves in the opposite direction. In terms of k, m and u, how long is the mass m in contact with the spring? A. B. C. D. π π π π mu k m k m k k mu m u. An object is suspended from a light spring and produces an extension of.5 cm in the spring. The object is now set to oscillate in simple harmonic motion vertically. The period of oscillation is A. 0.π s B. 0.5π s C..0π s D..5π s. A simple pendulum is displaced an angle θ and is released from rest. If T is the tension in the string and m is the mass of the bob, which of the following statements is/are correct? () When the bob passes through its lowest position, the tension T is equal to mg. () At the moment just after the bob is released, T cos θ = mg. (3) The restoring force of the harmonic motion is mg sin θ. A. (3) only B. C. () and () only () and (3) only T D. (), () and (3) mg 3. The graph in the figure shows how the displacement x of a particle performing SHM varies with time t. x 0 t t t Which of the following statements is incorrect? A. The speed is maximum at time t. B. The restoring force is maximum at time t. C. The kinetic energy of the particle has a maximum value at time t. D. The acceleration is zero at time t. 5
6 Section C (5%) Answer any ONE question from this section. Write your answers in the answer sheets provided.. (a) State Newton s laws of motion. (4 marks) (b) State the principle of conservation of linear momentum and show that it can be derived from Newton s laws of motion. (4 marks) (c) An object placed on a turntable may curve outwards to the edge if the turntable rotates at a high speed. A student says that there is an outward force acting on the object to push it outward. Explain whether the student is correct or incorrect. (4 marks) A small ball is projected horizontally with a certain speed from a height of m above a smooth horizontal floor. The ball falls under gravity, hit the ground and bounces up. (a) Assuming that no energy is lost in the process, sketch graphs to show how the vertical component of the velocity and the acceleration of the ball vary with time to the point when the ball bounces up to the original level. Take downward direction as positive. Label the axes wherever possible. Describe the force(s) acting on the ball and briefly explain the shape of the graphs. (6 marks) (b) State the change(s), if any, to the graphs in (a) (i) for the following cases. Briefly explain your answer. (i) A ball of greater mass is used. (ii) The projection speed is increased. (iii) Some kinetic energy is lost when the ball hits the ground. (4.5 marks) (c) Discuss whether the momentum of the ball is conserved when it hits the ground. (.5 marks) END OF PAPER Useful Formulae in Advanced Supplementary Level Physics A. v a= = ω r r centripetal acceleration A. a= ω x simple harmonic motion 6
7 St. Joseph s AngloChinese School Section A. (a) First Term Examination Form 6 ASL Physics Solution Reaction form the seat Weight (b) centripetal acceleration v a= r = = 8 ms  8 v (c) R + mg = m r R = 60(8) (d) (i) R = 480 N The force exerted on the passenger from the seat is 480 N. If the speed of the cart is too low, the reaction acting on the passenger will drop to zero. Ensuring that the speed at which the passengers enter the loop above a certain value can prevent them from dropping out of the cart. (ii) For looping the loop with minimum speed v at the highest position, v mg = m r v = gr Let u be the minimum speed at which the passengers enter the loop. By conservation of energy, mu mv = mg(r) mu mgr = mgr u= 5gr = 5 (0)(8) = 0ms  the minimum speed at which the passengers enter the loop is 0 ms . (a) Impulse = area under Ft graph = ( 50)( 0.04) = 5 Ns (b) Ft = mv mu 5 = 0.06v 0.06(0) v = 83.3 ms  7
8 3. (a) effective force constant k = x 30 = 60 N m  Period of oscillation = m π k 0.4 = π =0.53 s 60 (b) energy stored when the mass is released (c) = ( 30)( 0.) = 0.3 J By conservation of energy gain in kinetic energy = loss in elastic potential energy v ( 0.4) = 0.3 ( 30)( 0.05) v =.06 ms  K.E. / J t / s 3 Section B B B 3 C 4 C 5 C 6 B 7 D 8 C 9 A 0 B A A 3 D 8
9 9
10 0
11 Section C. (a) Newton s st law of motion states that everybody continues to be in a state of rest or moves with uniform velocity unless a resultant force acts on it. Newton s nd law of motion states that the acceleration / rate of change of momentum of a body is directly proportional to the resultant force acting on the body and occurs in the direction of this force. + Newton s 3 rd law of motion states that to every action there is an equal and opposite reaction. Action and reaction are acting on two different bodies. + (b) The principle of the conservation of linear momentum states that the momentum of a system is conserved if no external resultant force acts on the system. Suppose an object A of mass m A and velocity u A, collides with another object B of mass m B and velocity u B. Assume that the final velocities of A and B are respectively v A and v B. By Newton s nd law of motion, force acting on A by B, force acting on B by A, F F BA AB ma ( v A u A ) = and t mb ( vb u B ) = during collision. t Moreover, by Newton s 3 rd law, F BA = F AB m ( v A u A ) mb ( vb u = t t A B ) Rearranging the terms, we have m A u A + m B u B = m A v A + m B v B i.e. the linear momentum of the system is conserved. (c) The student is incorrect. There is not an outward force to push the object outward. A centripetal force is required to keep an object moving in a circle of radius r. This is provided by the friction between the object and the turntable. If the limiting friction is smaller than the required centripetal force, the object would maintain its velocity by its inertia and would be moving in a straight line. Therefore, it seems to curve outwards.
12 (a) By v = u + as, = ( )( 0) v = 4.5 ms  y ( ) By s = ut + at t = 0 = 0.45 s 0.45 a / ms During the flight of the ball when it is not in contact with the ground, only gravitational force (weight) is acting on the ball. When the ball is in contact with the ground, the reaction force from the ground also acts on it. Before the rebound, the acceleration is constant as the ball is falling freely and so its vertical velocity increases uniformly from zero to 4.5 ms  before hitting the ground. When the ball is in contact with the ground, the acceleration of the ball is very large and directed upward as the upward reaction force is greater than the weight of the ball. The vertical velocity of the ball changes abruptly from downward (+ ve) to upward ( ve). During the upward flight, the acceleration of the ball is constant and its vertical velocity increases uniformly from 4.5 ms  (upwards) to zero at the highest point. (b) (i) As the acceleration due to gravity is independently of the mass of the ball, the accelerationtime graph and hence the vertical velocitytime graph remain the same. (ii) The acceleration due to gravity is not affected by the horizontal speed of the ball, both accelerationtime and vertical velocitytime graph remain the same. (iii) The magnitude of the vertical velocity decreases after the rebound and hence the time taken for the upward flight decreases. (Accept graphical explanation) The shape of the accelerationtime graph remains unchanged. (c) The momentum of the ball is not conserved when it hits the ground since there is a resultant external force acting the ball reaction force minus gravitational force. (Remark: However, if the ball and the earth are considered as a single system, the total momentum of the system is conserved since the gravitational forces and reaction forces acting on them are now internal forces.)
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