Forces and Dynamics Worksheet 1. A block rests on a rough surface. Two forces P and Q act on the block, parallel to the surface. A friction force F between the block and the surface keeps the block in equilibrium. Which vector diagram best represents the three forces? A. P F B. P Q F Q C. P Q D. P F F Q 2. If the resultant external force acting on a particle is zero, the particle A. must have constant speed. B. must be at rest. C. must have constant velocity. D. must have zero momentum. Page 1 of 44
3. The weight of a mass is measured on Earth using a spring balance and a lever balance, as shown below. spring balance lever balance What change, if any, would occur in the measurements if they were repeated on the Moon s surface? Spring balance Lever balance A. same same B. same decrease C. decrease same D. decrease decrease 4. A mass is suspended from the roof of a lift (elevator) by means of a spring balance, as illustrated below. lift (elevator) mass Page 2 of 44
The lift (elevator) is moving upwards and the readings of the spring balance are noted as follows. Accelerating: Constant speed: Slowing down: R a R c R s Which one of the following is a correct relationship between the readings? A. R a > R c B. R a = R s C. R c = R s D. R c < R s 5. A body of weight 2W hangs vertically from a string attached to a body of weight W. Weight W is released and both bodies fall vertically. W 2W Air resistance may be neglected. What is the tension in the string during the fall? A. Zero B. W C. 2W D. 3W Page 3 of 44
6. A ball of weight W slides along a frictionless surface as shown below. P E Q At time T, the ball has moved from point P to the edge E of the surface. The ball then falls freely to point Q. Which graph best shows the variation with time t of the resultant upward vertical force F acting on the ball between point P and point Q? A. F +W B. F +W 0 0 T t 0 0 T t - W - W C. F +W D. F +W 0 0 T t 0 0 T t - W - W Page 4 of 44
7. A fireman is holding a hosepipe so that water leaves the pipe horizontally. The hosepipe has a constant cross-sectional area. The magnitude of the force that the fireman exerts to hold the hosepipe stationary is F. The volume of water delivered by the hose per second doubles, the force that the fireman must now exert is A. 2F. B. 2F. C. 4F. D. 8F. 8. A frictionless trolley of mass m moves down a slope with a constant acceleration a. A second similar frictionless trolley has mass 2m. The acceleration of the second trolley as it moves down the slope is A. 1 a. 2 B. a. C. 2a. D. 4a. Page 5 of 44
9. A ball of weight W is dropped on to the pan of a top pan weighing balance and rebounds off the pan. pan 00.00 At the instant that the ball has zero velocity when in contact with the pan, the scale will read A. zero. B. a value less than W but greater than zero. C. W. D. a value greater than W. Page 6 of 44
10. A stone of mass m is attached to a string. The stone is made to rotate in a vertical circle of radius r, as shown. v r At the point where the stone is vertically above the centre of the circle, the stone has speed v. Which of the following expressions gives the tension in the string? A. B. mv mg r mv 2 r 2 C. mv r 2 mg D. 2 mv + mg r Page 7 of 44
11. A light inextensible string has a mass attached to each end and passes over a frictionless pulley as shown. pulley string mass M mass m The masses are of magnitudes M and m, where m < M. The acceleration of free fall is g. The downward acceleration of the mass M is ( ) ( ) M m g A.. M + m ( ) M m g B.. M ( ) ( ) M + m g C.. M m Mg D.. M + m ( ) Page 8 of 44
12. Mandy stands on a weighing scale inside a lift (elevator) that accelerates vertically upwards as shown in the diagram below. The forces on Mandy are her weight W and the reaction force from the scale R. The reading of the scale is A. R + W. B. W. C. R. D. R W. 13. A general expression for Newton s second law of motion is p F =. t What condition is applied so that the law may be expressed in the form F = ma? A. The mass m is constant. B. The acceleration a is constant. C. The force F is constant. D. The direction of the force F is constant. Page 9 of 44
14. A bird of weight W lands at the midpoint of a horizontal wire stretched between two poles. The magnitude of the force exerted by each pole on the wire is F. F F W The bird will be in equilibrium if A. 2F > W. B. 2F = W. C. 2F < W. D. F = W. 15. The momentum of a system is conserved if A. no external forces act on the system. B. no friction forces act within the system. C. no kinetic energy is lost or gained by the system. D. the forces acting on the system are in equilibrium. Page 10 of 44
16. An object of mass m is initially at rest. An impulse I acts on the object. The change in kinetic energy of the object is A. B. 2 I. 2m 2 I. m C. I 2 m. D. 2I 2 m. 17. Two spheres of masses m 1 and m 2 are moving towards each other along the same straight-line with speeds v 1 and v 2 as shown. positive direction m 1 v 1 v 2 m 2 The spheres collide. Which of the following gives the total change in linear momentum of the spheres as a result of the collision? A. 0 B. m 1 v 1 + m 2 v 2 C. m 1 v 1 m 2 v 2 D. m 2 v 2 m 1 v 1 Page 11 of 44
18. A ball of mass 2.0 kg falls vertically and hits the ground with speed 7.0 ms 1 as shown below. 7.0 ms 1 1 3.0 ms before after The ball leaves the ground with a vertical speed 3.0 ms 1. The magnitude of the change in momentum of the ball is A. zero. B. 8.0 Ns. C. 10 Ns. D. 20 Ns. 19. Which of the following quantities are conserved in an inelastic collision between two bodies? Total linear momentum of the bodies Total kinetic energy of the bodies A. yes yes B. yes no C. no yes D. no no Page 12 of 44
20. A constant force is applied to a ball of mass m. The velocity of the ball changes from v 1 to v 2. The impulse received by the ball is A. m(v 2 + v 1 ). B. m(v 2 v 1 ). C. m(v 2 2 + v 1 2 ). D. m(v 2 2 v 1 2 ). 21. The engine of a rocket ejects gas at high speed, as shown below. rocket high speed gas direction of motion of rocket The rocket accelerates forwards because A. the momentum of the gas is equal but opposite in direction to the momentum of the rocket. B. the gas pushes on the air at the back of the rocket. C. the change in momentum of the gas gives rise to a force on the rocket. D. the ejected gas creates a region of high pressure behind the rocket. Page 13 of 44
22. A small ball P moves with speed v towards another identical ball Q along a line joining the centres of the two balls. Ball Q is at rest. Kinetic energy is conserved in the collision. v P Q at rest Which one of the following situations is a possible outcome of the collision between the balls? A. v v B. v = 0 v P Q P Q C. v 3v D. 4 4 P Q P v v 2 2 Q 23. A rocket is fired vertically. At its highest point, it explodes. Which one of the following describes what happens to its total momentum and total kinetic energy as a result of the explosion? Total momentum Total kinetic energy A. unchanged increased B. unchanged unchanged C. increased increased D. increased unchanged Page 14 of 44
24. This question is about an experiment designed to investigate Newton s second law. In order to investigate Newton s second law, David arranged for a heavy trolley to be accelerated by small weights, as shown below. The acceleration of the trolley was recorded electronically. David recorded the acceleration for different weights up to a maximum of 3.0 N. He plotted a graph of his results. heavy trolley acceleration pulley weight (a) Describe the graph that would be expected if two quantities are proportional to one another....... Page 15 of 44
(b) David s data are shown below, with uncertainty limits included for the value of the weights. Draw the best-fit line for these data. 1.40 acceleration / ms 2 1.20 1.00 0.80 0.60 0.40 0.20 0.00 0.00 0.50 1.00 1.50 2.00 2.50 weight / N (c) Use the graph to (i) explain what is meant by a systematic error......... (ii) estimate the value of the frictional force that is acting on the trolley... Page 16 of 44
(iii) estimate the mass of the trolley......... (Total 9 marks) 25. Block on an inclined plane A block is held stationary on a frictionless inclined plane by means of a string as shown below. string block inclined plane (a) (i) On the diagram draw arrows to represent the three forces acting on the block. (3) (ii) The angle θ of inclination of the plane is 25. The block has mass 2.6 kg. Calculate the force in the string. You may assume that g = 9.8 m s 2. Page 17 of 44
(b) The string is pulled so that the block is now moving at a constant speed of 0.85 m s 1 up the inclined plane. (i) Explain why the magnitude of the force in the string is the same as that found in (a)(ii). (ii) Calculate the power required to move the block at this speed. (iii) State the rate of change of the gravitational potential energy of the block. Explain your answer. (Total 11 marks) 26. Kinematics (a) State the principle of conservation of energy....... Page 18 of 44
(b) An aircraft accelerates from rest along a horizontal straight runway and then takes-off. Discuss how the principle of conservation of energy applies to the energy changes that take place while the aircraft is accelerating along the runway............. (3) (c) The mass of the aircraft is 8.0 10 3 kg. (i) The average resultant force on the aircraft while travelling along the runway is 70 kn. The speed of the aircraft just as it lifts off is 75 m s 1. Estimate the distance travelled along the runway. (3) (ii) The aircraft climbs to a height of 1250 m. Calculate the potential energy gained during the climb. Page 19 of 44
When approaching its destination, the pilot puts the aircraft into a holding pattern. This means the aircraft flies at a constant speed of 90 m s 1 in a horizontal circle of radius 500 m as shown in the diagram below. 500 m (d) For the aircraft in the holding pattern, (i) calculate the magnitude of the resultant force on the aircraft; (ii) state the direction of the resultant force. (Total 11 marks) 27. This question is about linear motion. A car moves along a straight road. At time t = 0 the car starts to move from rest and oil begins to drip from the engine of the car. One drop of oil is produced every 0.80 s. Oil drops are left on the road. The position of the oil drops are drawn to scale on the grid below such that 1.0 cm represents 4.0 m. The grid starts at time t = 0. direction of motion 1.0cm (a) (i) State the feature of the diagram above which indicates that, initially, the car is accelerating... Page 20 of 44
(ii) On the grid above, draw further dots to show where oil would have dripped if the drops had been produced from the time when the car had started to move. (iii) Determine the distance moved by the car during the first 5.6 s of its motion..... (b) Using information from the grid above, determine for the car, (i) the final constant speed....... (ii) the initial acceleration....... (Total 8 marks) Page 21 of 44
28. This question is about momentum. (a) Define (i) linear momentum..... (ii) impulse..... (b) In a ride in a pleasure park, a carriage of mass 450 kg is travelling horizontally at a speed of 18 m s 1. It passes through a shallow tank containing stationary water. The tank is of length 9.3 m. The carriage leaves the tank at a speed of 13 m s 1. carriage, mass 450 kg 18 m s 1 water-tank 13 m s 1 9.3m As the carriage passes through the tank, the carriage loses momentum and causes some water to be pushed forwards with a speed of 19 m s 1 in the direction of motion of the carriage. (i) For the carriage passing through the water-tank, deduce that the magnitude of its total change in momentum is 2250N s..... Page 22 of 44
(ii) Use the answer in (b)(i) to deduce that the mass of water moved in the direction of motion of the carriage is approximately 120 kg....... (iii) Calculate the mean value of the magnitude of the acceleration of the carriage in the water......... (3) (c) For the carriage in (b) passing through the water-tank, determine (i) its total loss in kinetic energy......... (3) (ii) the gain in kinetic energy of the water that is moved in the direction of motion of the carriage..... Page 23 of 44
(d) By reference to the principles of conservation of momentum and of energy, explain your answers in (c)............. (3) (Total 15 marks) 29. Momentum (a) State the law of conservation of momentum.......... (b) An ice hockey puck collides with the wall of an ice rink. The puck is sliding along a line that makes an angle of 45 to the wall. wall 45 45 ice rink direction of puck before collision direction of puck afte r collision The collision between the wall and the puck is perfectly elastic. (i) State what is meant by an elastic collision. Page 24 of 44
(ii) Discuss how the law of conservation of momentum applies to this situation. (c) The diagram below is a scale diagram that shows the vector representing the momentum of the puck before collision. Scale: 1.0 cm = 0.10 N s By adding appropriate vectors to the diagram, deduce that the magnitude of the change in momentum of the puck as a result of the collision is 0.71 N s. (4) Page 25 of 44
(d) The sketch-graph below shows the variation with time t of the force F exerted by the wall on the puck. F 0 0 t The total contact time is 12 ms. Estimate, explaining your reasoning, the maximum force exerted by the wall on the puck................ (3) (Total 12 marks) 30. This question is about momentum and energy. (a) Define impulse of a force and state the relation between impulse and momentum. definition:...... relation:...... Page 26 of 44
(b) By applying Newton s laws of motion to the collision of two particles, deduce that momentum is conserved in the collision......................... (5) (c) In an experiment to measure the speed of a bullet, the bullet is fired into a piece of plasticine suspended from a rigid support by a light thread. bullet speed V 24cm plasticine The speed of the bullet on impact with the plasticine is V. As a result of the impact, the bullet embeds itself in the plasticine and the plasticine is displaced vertically through a height of 24 cm. The mass of the bullet is 5.2 10 3 kg and the mass of the plasticine is 0.38 kg. Page 27 of 44
(i) Ignoring the mass of the bullet, calculate the speed of the plasticine immediately after the impact......... (ii) Deduce that the speed V with which the bullet strikes the plasticine is about 160 m s 1......... (Total 11 marks) Page 28 of 44
31. Electric motor (a) In an experiment to measure the efficiency of a small dc electric motor, the motor is clamped to the edge of a bench. The motor is used to raise a small weight that is attached to a pulley wheel by cotton thread. The pulley wheel is rotated by the motor. The thread wraps around the pulley wheel, so raising the weight. axel motor pulley wheel cotton thread Side view weight End-on-view The time taken for the motor to raise the weight through a certain height is measured. It is assumed that the weight accelerates uniformly whilst being raised. The weight of the cotton thread is negligible. (i) Draw a labelled free-body force diagram of the forces acting on the accelerating weight. (3) Page 29 of 44
(ii) The weight has a mass of 15 g and it takes 2.2 s to raise it from rest through a height of 0.84 m. Calculate the tension in the thread as the weight is being raised. (Acceleration of free fall g = 10 m s 2.) (4) (b) In a second experiment, the current is adjusted so that the weight of mass 15 g is raised at constant speed. The motor is connected to a 6.0 V supply and it now takes the motor 3.4 s to raise the weight through 0.84 m. (i) Suggest how it might be determined that the weight is being raised at constant speed. (ii) Determine the power delivered to the weight by the motor. (Acceleration of free fall g = 10 m s 2.) Page 30 of 44
(iii) The current in the motor is 45 ma. Estimate the efficiency of the motor. (Total 13 marks) 32. This question is about conservation of momentum and conservation of energy. (a) State Newton s third law.......... (b) State the law of conservation of momentum....... The diagram below shows two identical balls A and B on a horizontal surface. Ball B is at rest and ball A is moving with speed V along a line joining the centres of the balls. The mass of each ball is M. v Before collision A B During the collision of the balls, the magnitude of the force that ball A exerts on ball B is F AB and the magnitude of the force that ball B exerts on ball A is F BA. Page 31 of 44
(c) On the diagram below, add labelled arrows to represent the magnitude and direction of the forces F AB and F BA. During the collision A B (3) The balls are in contact for a time t. After the collision, the speed of ball A is +v A and the speed of ball B is +v B in the directions shown. v A v B After the collision A B As a result of the collision, there is a change in momentum of ball A and of ball B. (d) Use Newton s second law of motion to deduce an expression relating the forces acting during the collision to the change in momentum of (i) ball B..... (ii) ball A..... Page 32 of 44
(e) Apply Newton s third law and your answers to (d), to deduce that the change in momentum of the system (ball A and ball B) as a result of this collision, is zero................ (4) (f) Deduce, that if kinetic energy is conserved in the collision, then after the collision, ball A will come to rest and ball B will move with speed V................ (3) (Total 17 marks) 33. This question is about the kinematics of an elevator (lift). (a) Explain the difference between the gravitational mass and the inertial mass of an object................ (3) Page 33 of 44
An elevator (lift) starts from rest on the ground floor and comes to rest at a higher floor. Its motion is controlled by an electric motor. A simplified graph of the variation of the elevator s velocity with time is shown below. velocity / m s 1 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 time / s (b) The mass of the elevator is 250 kg. Use this information to calculate (i) the acceleration of the elevator during the first 0.50 s....... (ii) the total distance travelled by the elevator....... Page 34 of 44
(iii) the minimum work required to raise the elevator to the higher floor....... (iv) the minimum average power required to raise the elevator to the higher floor....... (v) the efficiency of the electric motor that lifts the elevator, given that the input power to the motor is 5.0 kw....... (c) On the graph axes below, sketch a realistic variation of velocity for the elevator. Explain your reasoning. (The simplified version is shown as a dotted line) velocity / m s 1 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 time / s Page 35 of 44
The elevator is supported by a cable. The diagram below is a free-body force diagram for when the elevator is moving upwards during the first 0.50 s. tension weight (d) In the space below, draw free-body force diagrams for the elevator during the following time intervals. (i) 0.5 to 11.50 s (ii) 11.50 to 12.00 s (3) A person is standing on weighing scales in the elevator. Before the elevator rises, the reading on the scales is W. Page 36 of 44
(e) On the axes below, sketch a graph to show how the reading on the scales varies during the whole 12.00 s upward journey of the elevator. (Note that this is a sketch graph you do not need to add any values.) reading on scales W 0.00 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 time / s (3) (f) The elevator now returns to the ground floor where it comes to rest. Describe and explain the energy changes that take place during the whole up and down journey................... (4) (Total 25 marks) Page 37 of 44
34. Momentum (a) State the law of conservation of linear momentum.......... (b) A toy rocket of mass 0.12 kg contains 0.59 kg of water as shown in the diagram below. high-pressure air water nozzle, radius 1.4mm The space above the water contains high-pressure air. The nozzle of the rocket has a circular cross-section of radius 1.4 mm. When the nozzle is opened, water emerges from the nozzle at a constant speed of 18 m s 1. The density of water is 1000 kg m 3. (i) Deduce that the volume of water ejected per second through the nozzle is 1.1 10 4 m 3. Page 38 of 44
(ii) Deduce that the upward force that the ejected water exerts on the rocket is approximately 2.0 N. Explain your working by reference to Newton s laws of motion. (4) (iii) Calculate the time delay between opening the nozzle and the rocket achieving lift-off. (Total 10 marks) Page 39 of 44
35. Linear motion At a sports event, a skier descends a slope AB. At B there is a dip BC of width 12 m. The slope and dip are shown in the diagram below. The vertical height of the slope is 41 m. A (not to scale) 41m slope B C D 1.8m dip 12m The graph below shows the variation with time t of the speed v down the slope of the skier. 25.0 20.0 v / ms 1 15.0 10.0 5.0 0.0 0.0 1.0 2.0 3.0 4.0 t / s 5.0 6.0 7.0 8.0 The skier, of mass 72 kg, takes 8.0 s to ski, from rest, down the length AB of the slope. (a) Use the graph to (i) calculate the kinetic energy E K of the skier at point B. Page 40 of 44 (ii) determine the length of the slope.
(4) Page 41 of 44
(b) (i) Calculate the magnitude of the change E P in the gravitational potential energy of the skier between point A and point B. (ii) Use your anwers to (a)(i) and (b)(i) to determine the ratio ( EP EK ). E P (iii) Suggest what this ration represents. Page 42 of 44
(c) At point B of the slope, the skier leaves the ground. He flies across the dip and lands on the lower side at point D. The lower side C of the dip is 1.8 m below the upper side B. (i) Calculate the time taken for an object to fall, from rest, through a vertical distance of 1.8 m. Assume negligible air resistance. (ii) The time calculated in (c)(i) is the time of flight of the skier across the dip. Determine the horizontal distance travelled by the skier during this time, assuming that the skier has the constant speed at which he leaves the slope at B. (Total 15 marks) 36. This question is about driving a metal bar into the ground. Large metal bars can be driven into the ground using a heavy falling object. object 3 mass = 2.0 10 kg bar mass = 400 kg Page 43 of 44
In the situation shown, the object has a mass 2.0 10 3 kg and the metal bar has a mass of 400 kg. The object strikes the bar at a speed of 6.0 m s 1. It comes to rest on the bar without bouncing. As a result of the collision, the bar is driven into the ground to a depth of 0.75 m. (a) Determine the speed of the bar immediately after the object strikes it................... (4) (b) Determine the average frictional force exerted by the ground on the bar................ (3) (Total 7 marks) Page 44 of 44