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# Summary and exercises

## Summary

• Newton's First Law: Every object will remain at rest or in uniform motion in a straight line unless it is made to change its state by the action of an unbalanced force.
• Newton's Second Law: The resultant force acting on a body will cause the body to accelerate in the direction of the resultant force The acceleration of the body is directly proportional to the magnitude of the resultant force and inversely proportional to the mass of the object.
• Newton's Third Law: If body A exerts a force on body B then body B will exert an equal but opposite force on body A.
• Newton's Law of Universal Gravitation: Every body in the universe exerts a force on every other body. The force is directly proportional to the product of the masses of the bodies and inversely proportional to the square of the distance between them.
• Equilibrium: Objects at rest or moving with constant velocity are in equilibrium and have a zeroresultant force.
• Equilibrant: The equilibrant of any number of forces is the single force required to produce equilibrium.
• Triangle Law for Forces in Equilibrium: Three forces in equilibrium can be represented in magnitude and direction by the three sides of a triangle taken in order.
• Momentum: The momentum of an object is defined as its mass multiplied by its velocity.
• Momentum of a System: The total momentum of a system is the sum of the momenta of each of the objects in the system.
• Principle of Conservation of Linear Momentum:: The total linear momentum of an isolated system is constant' or In an isolated system the total momentum before a collision (or explosion) is equal to the total momentum after the collision (or explosion)'.
• Law of Momentum:: The applied resultant force acting on an object is equal to the rate of change of the object's momentum and this force is in the direction of the change in momentum.

## End of Chapter exercises

### Forces and Newton's Laws

1. [SC 2003/11] A constant, resultant force acts on a body which can move freely in a straight line. Which physical quantity will remain constant?
1. acceleration
2. velocity
3. momentum
4. kinetic energy
2. [SC 2005/11 SG1] Two forces, 10 N and 15 N, act at an angle at the same point. Which of the following cannot be the resultant of these two forces?
1. A: 2 N
2. B: 5 N
3. C: 8 N
4. D: 20 N
3. A concrete block weighing 250 N is at rest on an inclined surface at an angle of 20. The magnitude of the normal force, in newtons, is
• A: 250
• B: 250 cos 20
• C: 250 sin 20
• D: 2500 cos 20
4. A 30 kg box sits on a flat frictionless surface. Two forces of 200 N each are applied to the box as shown in the diagram. Which statement best describes the motion of the box?
1. A: The box is lifted off the surface.
2. B: The box moves to the right.
3. C: The box does not move.
4. D: The box moves to the left.
5. A concrete block weighing 200 N is at rest on an inclined surface at an angle of 20. The normal reaction, in newtons, is
• A: 200
• B: 200 cos 20
• C: 200 sin 20
• D: 2000 cos 20
6. [SC 2003/11]A box, mass mm, is at rest on a rough horizontal surface. A force of constant magnitude FF is then applied on the box at an angle of 60to the horizontal, as shown. If the box has a uniform horizontal acceleration of magnitude, aa, the frictional force acting on the box is ......
1. A: Fcos60-maFcos60-ma in the direction of A
2. B: Fcos60-maFcos60-ma in the direction of B
3. C: Fsin60-maFsin60-ma in the direction of A
4. D: Fsin60-maFsin60-ma in the direction of B
7. [SC 2002/11 SG] Thabo stands in a train carriage which is moving eastwards. The train suddenly brakes. Thabo continues to move eastwards due to the effect of
1. A: his inertia.
2. B: the inertia of the train.
3. C: the braking force on him.
4. D: a resultant force acting on him.
8. [SC 2002/11 HG1] A body slides down a frictionless inclined plane. Which one of the following physical quantities will remain constant throughout the motion?
1. A: velocity
2. B: momentum
3. C: acceleration
4. D: kinetic energy
9. [SC 2002/11 HG1] A body moving at a CONSTANT VELOCITY on a horizontal plane, has a number of unequal forces acting on it. Which one of the following statements is TRUE?
1. A: At least two of the forces must be acting in the same direction.
2. B: The resultant of the forces is zero.
3. C: Friction between the body and the plane causes a resultant force.
4. D: The vector sum of the forces causes a resultant force which acts in the direction of motion.
10. [IEB 2005/11 HG] Two masses of mm and 2m2m respectively are connected by an elastic band on a frictionless surface. The masses are pulled in opposite directions by two forces each of magnitude FF, stretching the elastic band and holding the masses stationary. Which of the following gives the magnitude of the tension in the elastic band?
1. A: zero
2. B: 12F12F
3. C: FF
4. D: 2F2F
11. [IEB 2005/11 HG] A rocket takes off from its launching pad, accelerating up into the air. The rocket accelerates because the magnitude of the upward force, FF is greater than the magnitude of the rocket's weight, WW. Which of the following statements best describes how force FF arises?
1. A: FF is the force of the air acting on the base of the rocket.
2. B: FF is the force of the rocket's gas jet pushing down on the air.
3. C: FF is the force of the rocket's gas jet pushing down on the ground.
4. D: FF is the reaction to the force that the rocket exerts on the gases which escape out through the tail nozzle.
12. [SC 2001/11 HG1] A box of mass 20 kg rests on a smooth horizontal surface. What will happen to the box if two forces each of magnitude 200 N are applied simultaneously to the box as shown in the diagram. The box will ...
1. A: be lifted off the surface.
2. B: move to the left.
3. C: move to the right.
4. D: remain at rest.
13. [SC 2001/11 HG1] A 2 kg mass is suspended from spring balance X, while a 3 kg mass is suspended from spring balance Y. Balance X is in turn suspended from the 3 kg mass. Ignore the weights of the two spring balances. The readings (in N) on balances X and Y are as follows:
 X Y (A) 20 30 (B) 20 50 (C) 25 25 (D) 50 50
14. [SC 2002/03 HG1] PP and QQ are two forces of equal magnitude applied simultaneously to a body at X. As the angle θθ between the forces is decreased from 180 to 0, the magnitude of the resultant of the two forces will
1. A: initially increase and then decrease.
2. B: initially decrease and then increase.
3. C: increase only.
4. D: decrease only.
15. [SC 2002/03 HG1] The graph below shows the velocity-time graph for a moving object: Which of the following graphs could best represent the relationship between the resultant force applied to the object and time?
 (a) (b) (c) (d)
16. [SC 2002/03 HG1] Two blocks each of mass 8 kg are in contact with each other and are accelerated along a frictionless surface by a force of 80 N as shown in the diagram. The force which block Q will exert on block P is equal to ...
1. A: 0 N
2. B: 40 N
3. C: 60 N
4. D: 80 N
17. [SC 2002/03 HG1] Three 1 kg mass pieces are placed on top of a 2 kg trolley. When a force of magnitude FF is applied to the trolley, it experiences an acceleration aa. If one of the 1 kg mass pieces falls off while FF is still being applied, the trolley will accelerate at ...
1. A: 15a15a
2. B: 45a45a
3. C: 54a54a
4. D: 5a5a
18. [IEB 2004/11 HG1] A car moves along a horizontal road at constant velocity. Which of the following statements is true?
1. A: The car is not in equilibrium.
2. B: There are no forces acting on the car.
3. C: There is zero resultant force.
4. D: There is no frictional force.
19. [IEB 2004/11 HG1] A crane lifts a load vertically upwards at constant speed. The upward force exerted on the load is FF. Which of the following statements is correct?
1. A: The acceleration of the load is 9,8 m.s-2-2 downwards.
2. B: The resultant force on the load is F.
3. C: The load has a weight equal in magnitude to F.
4. D: The forces of the crane on the load, and the weight of the load, are an example of a Newton's third law 'action-reaction' pair.
20. [IEB 2004/11 HG1] A body of mass MM is at rest on a smooth horizontal surface with two forces applied to it as in the diagram below. Force F1F1 is equal to MgMg. The force F1F1 is applied to the right at an angle θθ to the horizontal, and a force of F2F2 is applied horizontally to the left. How is the body affected when the angle θθ is increased?
1. A: It remains at rest.
2. B: It lifts up off the surface, and accelerates towards the right.
3. C: It lifts up off the surface, and accelerates towards the left.
4. D: It accelerates to the left, moving along the smooth horizontal surface.
21. [IEB 2003/11 HG1] Which of the following statements correctly explains why a passenger in a car, who is not restrained by the seat belt, continues to move forward when the brakes are applied suddenly?
1. A: The braking force applied to the car exerts an equal and opposite force on the passenger.
2. B: A forward force (called inertia) acts on the passenger.
3. C: A resultant forward force acts on the passenger.
4. D: A zero resultant force acts on the passenger.
22. [IEB 2004/11 HG1] A rocket (mass 20 000 kg) accelerates from rest to 40 m··s-1-1in the first 1,6 seconds of its journey upwards into space. The rocket's propulsion system consists of exhaust gases, which are pushed out of an outlet at its base.
1. Explain, with reference to the appropriate law of Newton, how the escaping exhaust gases exert an upwards force (thrust) on the rocket.
2. What is the magnitude of the total thrust exerted on the rocket during the first 1,6 s?
3. An astronaut of mass 80 kg is carried in the space capsule. Determine the resultant force acting on him during the first 1,6 s.
4. Explain why the astronaut, seated in his chair, feels “heavier” while the rocket is launched.
23. [IEB 2003/11 HG1 - Sports Car]
1. State Newton's Second Law of Motion.
2. A sports car (mass 1 000 kg) is able to accelerate uniformly from rest to 30 m··s-1-1in a minimum time of 6 s.
1. Calculate the magnitude of the acceleration of the car.
2. What is the magnitude of the resultant force acting on the car during these 6 s?
3. The magnitude of the force that the wheels of the vehicle exert on the road surface as it accelerates is 7500 N. What is the magnitude of the retarding forces acting on this car?
4. By reference to a suitable Law of Motion, explain why a headrest is important in a car with such a rapid acceleration.
24. [IEB 2005/11 HG1] A child (mass 18 kg) is strapped in his car seat as the car moves to the right at constant velocity along a straight level road. A tool box rests on the seat beside him. The driver brakes suddenly, bringing the car rapidly to a halt. There is negligible friction between the car seat and the box.
1. Draw a labelled free-body diagram of the forces acting on the child during the time that the car is being braked.
2. Draw a labelled free-body diagram of the forces acting on the box during the time that the car is being braked.
3. What is the rate of change of the child's momentum as the car is braked to a standstill from a speed of 72 km.h-1-1 in 4 s. Modern cars are designed with safety features (besides seat belts) to protect drivers and passengers during collisions e.g. the crumple zones on the car's body. Rather than remaining rigid during a collision, the crumple zones allow the car's body to collapse steadily.
4. State Newton's second law of motion.
5. Explain how the crumple zone on a car reduces the force of impact on it during a collision.
25. [SC 2003/11 HG1]The total mass of a lift together with its load is 1 200 kg. It is moving downwards at a constant velocity of 9 m··s-1-1.
1. What will be the magnitude of the force exerted by the cable on the lift while it is moving downwards at constant velocity? Give an explanation for your answer. The lift is now uniformly brought to rest over a distance of 18 m.
2. Calculate the magnitude of the acceleration of the lift.
3. Calculate the magnitude of the force exerted by the cable while the lift is being brought to rest.
26. A driving force of 800 N acts on a car of mass 600 kg.
1. Calculate the car's acceleration.
2. Calculate the car's speed after 20 s.
3. Calculate the new acceleration if a frictional force of 50 N starts to act on the car after 20 s.
4. Calculate the speed of the car after another 20 s (i.e. a total of 40 s after the start).
27. [IEB 2002/11 HG1 - A Crate on an Inclined Plane] Elephants are being moved from the Kruger National Park to the Eastern Cape. They are loaded into crates that are pulled up a ramp (an inclined plane) on frictionless rollers. The diagram shows a crate being held stationary on the ramp by means of a rope parallel to the ramp. The tension in the rope is 5 000 N.
1. Explain how one can deduce the following: “The forces acting on the crate are in equilibrium”.
2. Draw a labelled free-body diagram of the forces acting on the crane and elephant. (Regard the crate and elephant as one object, and represent them as a dot. Also show the relevant angles between the forces.)
3. The crate has a mass of 800 kg. Determine the mass of the elephant.
4. The crate is now pulled up the ramp at a constant speed. How does the crate being pulled up the ramp at a constant speed affect the forces acting on the crate and elephant? Justify your answer, mentioning any law or principle that applies to this situation.
28. [IEB 2002/11 HG1 - Car in Tow] Car A is towing Car B with a light tow rope. The cars move along a straight, horizontal road.
1. Write down a statement of Newton's Second Law of Motion (in words).
2. As they start off, Car A exerts a forwards force of 600 N at its end of the tow rope. The force of friction on Car B when it starts to move is 200 N. The mass of Car B is 1 200 kg. Calculate the acceleration of Car B.
3. After a while, the cars travel at constant velocity. The force exerted on the tow rope is now 300 N while the force of friction on Car B increases. What is the magnitude and direction of the force of friction on Car B now?
4. Towing with a rope is very dangerous. A solid bar should be used in preference to a tow rope. This is especially true should Car A suddenly apply brakes. What would be the advantage of the solid bar over the tow rope in such a situation?
5. The mass of Car A is also 1 200 kg. Car A and Car B are now joined by a solid tow bar and the total braking force is 9 600 N. Over what distance could the cars stop from a velocity of 20 m··s-1-1?
29. [IEB 2001/11 HG1] - Testing the Brakes of a Car A braking test is carried out on a car travelling at 20 m··s-1-1. A braking distance of 30 m is measured when a braking force of 6 000 N is applied to stop the car.
1. Calculate the acceleration of the car when a braking force of 6 000 N is applied.
2. Show that the mass of this car is 900 kg.
3. How long (in s) does it take for this car to stop from 20 m··s-1-1under the braking action described above?
4. A trailer of mass 600 kg is attached to the car and the braking test is repeated from 20 m··s-1-1using the same braking force of 6 000 N. How much longer will it take to stop the car with the trailer in tow?
30. [IEB 2001/11 HG1] A rocket takes off from its launching pad, accelerating up into the air. Which of the following statements best describes the reason for the upward acceleration of the rocket?
1. A: The force that the atmosphere (air) exerts underneath the rocket is greater than the weight of the rocket.
2. B: The force that the ground exerts on the rocket is greater than the weight of the rocket.
3. C: The force that the rocket exerts on the escaping gases is less than the weight of the rocket.
4. D: The force that the escaping gases exerts on the rocket is greater than the weight of the rocket.
31. [IEB 2005/11 HG] A box is held stationary on a smooth plane that is inclined at angle θθ to the horizontal. FF is the force exerted by a rope on the box. ww is the weight of the box and NN is the normal force of the plane on the box. Which of the following statements is correct?
1. A: tanθ=Fwtanθ=Fw
2. B: tanθ=FNtanθ=FN
3. C: cosθ=Fwcosθ=Fw
4. D: sinθ=Nwsinθ=Nw
32. [SC 2001/11 HG1] As a result of three forces F1F1, F2F2 and F3F3 acting on it, an object at point P is in equilibrium. Which of the following statements is not true with reference to the three forces?
1. The resultant of forces F1F1, F2F2 and F3F3 is zero.
2. Forces F1F1, F2F2 and F3F3 lie in the same plane.
3. Forces F3F3 is the resultant of forces F1F1 and F2F2.
4. The sum of the components of all the forces in any chosen direction is zero.
33. A block of mass M is held stationary by a rope of negligible mass. The block rests on a frictionless plane which is inclined at 3030 to the horizontal.
1. Draw a labelled force diagram which shows all the forces acting on the block.
2. Resolve the force due to gravity into components that are parallel and perpendicular to the plane.
3. Calculate the weight of the block when the force in the rope is 8N.
34. [SC 2003/11] A heavy box, mass mm, is lifted by means of a rope R which passes over a pulley fixed to a pole. A second rope S, tied to rope R at point P, exerts a horizontal force and pulls the box to the right. After lifting the box to a certain height, the box is held stationary as shown in the sketch below. Ignore the masses of the ropes. The tension in rope R is 5 850 N.
1. Draw a diagram (with labels) of all the forces acting at the point P, when P is in equilibrium.
2. By resolving the force exerted by rope R into components, calculate the ......
1. magnitude of the force exerted by rope S.
2. mass, m, of the box.
3. Will the tension in rope R, increase, decrease or remain the same if rope S is pulled further to the right (the length of rope R remains the same)? Give a reason for your choice.
35. A tow truck attempts to tow a broken down car of mass 400 kg. The coefficient of static friction is 0,60 and the coefficient of kinetic (dynamic) friction is 0,4. A rope connects the tow truck to the car. Calculate the force required:
1. to just move the car if the rope is parallel to the road.
2. to keep the car moving at constant speed if the rope is parallel to the road.
3. to just move the car if the rope makes an angle of 30 to the road.
4. to keep the car moving at constant speed if the rope makes an angle of 30 to the road.
36. A crate weighing 2000 N is to be lowered at constant speed down skids 4 m long, from a truck 2 m high.
1. If the coefficient of sliding friction between the crate and the skids is 0,30, will the crate need to be pulled down or held back?
2. How great is the force needed parallel to the skids?
37. Block A in the figures below weighs 4 N and block B weighs 8 N. The coefficient of kinetic friction between all surfaces is 0,25. Find the force P necessary to drag block B to the left at constant speed if
1. A rests on B and moves with it
2. A is held at rest
3. A and B are connected by a light flexible cord passing around a fixed frictionless pulley

### Gravitation

1. [SC 2003/11]An object attracts another with a gravitational force FF. If the distance between the centres of the two objects is now decreased to a third (1313) of the original distance, the force of attraction that the one object would exert on the other would become......
1. A: 19F19F
2. B: 13F13F
3. C: 3F3F
4. D: 9F9F
2. [SC 2003/11] An object is dropped from a height of 1 km above the Earth. If air resistance is ignored, the acceleration of the object is dependent on the
1. A: mass of the object
2. B: radius of the earth
3. C: mass of the earth
4. D: weight of the object
3. A man has a mass of 70 kg on Earth. He is walking on a new planet that has a mass four times that of the Earth and the radius is the same as that of the Earth ( MEE = 6 x 102424 kg, rEE = 6 x 1066 m )
1. Calculate the force between the man and the Earth.
2. What is the man's mass on the new planet?
3. Would his weight be bigger or smaller on the new planet? Explain how you arrived at your answer.
4. Calculate the distance between two objects, 5000 kg and 6 x 101212 kg respectively, if the magnitude of the force between them is 3 x 10?8?8 N.
5. Calculate the mass of the Moon given that an object weighing 80 N on the Moon has a weight of 480 N on Earth and the radius of the Moon is 1,6 x 101616 m.
6. The following information was obtained from a free-fall experiment to determine the value of gg with a pendulum. Average falling distance between marks = 920 mm Time taken for 40 swings = 70 s Use the data to calculate the value of gg.
7. An astronaut in a satellite 1600 km above the Earth experiences gravitational force of the magnitude of 700 N on Earth. The Earth's radius is 6400 km. Calculate
1. The magnitude of the gravitational force which the astronaut experiences in the satellite.
2. The magnitude of the gravitational force on an object in the satellite which weighs 300 N on Earth.
8. An astronaut of mass 70 kg on Earth lands on a planet which has half the Earth's radius and twice its mass. Calculate the magnitude of the force of gravity which is exerted on him on the planet.
9. Calculate the magnitude of the gravitational force of attraction between two spheres of lead with a mass of 10 kg and 6 kg respectively if they are placed 50 mm apart.
10. The gravitational force between two objects is 1200 N. What is the gravitational force between the objects if the mass of each is doubled and the distance between them halved?
11. Calculate the gravitational force between the Sun with a mass of 2 x 103030 kg and the Earth with a mass of 6 x 102424 kg if the distance between them is 1,4 x 1088 km.
12. How does the gravitational force of attraction between two objects change when
1. the mass of each object is doubled.
2. the distance between the centres of the objects is doubled.
3. the mass of one object is halved, and the distance between the centres of the objects is halved.
13. Read each of the following statements and say whether you agree or not. Give reasons for your answer and rewrite the statement if necessary:
1. The gravitational acceleration g is constant.
2. The weight of an object is independent of its mass.
3. G is dependent on the mass of the object that is being accelerated.
14. An astronaut weighs 750 N on the surface of the Earth.
1. What will his weight be on the surface of Saturn, which has a mass 100 times greater than the Earth, and a radius 5 times greater than the Earth?
2. What is his mass on Saturn?
15. A piece of space garbage is at rest at a height 3 times the Earth's radius above the Earth's surface. Determine its acceleration due to gravity. Assume the Earth's mass is 6,0 x 102424 kg and the Earth's radius is 6400 km.
16. Your mass is 60 kg in Paris at ground level. How much less would you weigh after taking a lift to the top of the Eiffel Tower, which is 405 m high? Assume the Earth's mass is 6,0 x 102424 kg and the Earth's radius is 6400 km.
1. State Newton's Law of Universal Gravitation.
2. Use Newton's Law of Universal Gravitation to determine the magnitude of the acceleration due to gravity on the Moon. The mass of the Moon is 7,40 ×× 102222 kg. The radius of the Moon is 1,74 ×× 1066 m.
3. Will an astronaut, kitted out in his space suit, jump higher on the Moon or on the Earth? Give a reason for your answer.

### Momentum

1. [SC 2003/11]A projectile is fired vertically upwards from the ground. At the highest point of its motion, the projectile explodes and separates into two pieces of equal mass. If one of the pieces is projected vertically upwards after the explosion, the second piece will ......
1. A: drop to the ground at zero initial speed.
2. B: be projected downwards at the same initial speed at the first piece.
3. C: be projected upwards at the same initial speed as the first piece.
4. D: be projected downwards at twice the initial speed as the first piece.
2. [IEB 2004/11 HG1] A ball hits a wall horizontally with a speed of 15 m··s-1-1. It rebounds horizontally with a speed of 8 m··s-1-1. Which of the following statements about the system of the ball and the wall is true?
1. A: The total linear momentum of the system is not conserved during this collision.
2. B: The law of conservation of energy does not apply to this system.
3. C: The change in momentum of the wall is equal to the change in momentum of the ball.
4. D: Energy is transferred from the ball to the wall.
3. [IEB 2001/11 HG1] A block of mass M collides with a stationary block of mass 2M. The two blocks move off together with a velocity of v. What is the velocity of the block of mass M immediately before it collides with the block of mass 2M?
1. A: v
2. B: 2v
3. C: 3v
4. D: 4v
4. [IEB 2003/11 HG1] A cricket ball and a tennis ball move horizontally towards you with the same momentum. A cricket ball has greater mass than a tennis ball. You apply the same force in stopping each ball. How does the time taken to stop each ball compare?
1. A: It will take longer to stop the cricket ball.
2. B: It will take longer to stop the tennis ball.
3. C: It will take the same time to stop each of the balls.
4. D: One cannot say how long without knowing the kind of collision the ball has when stopping.
5. [IEB 2004/11 HG1] Two identical billiard balls collide head-on with each other. The first ball hits the second ball with a speed of V, and the second ball hits the first ball with a speed of 2V. After the collision, the first ball moves off in the opposite direction with a speed of 2V. Which expression correctly gives the speed of the second ball after the collision?
1. A: V
2. B: 2V
3. C: 3V
4. D: 4V
6. [SC 2002/11 HG1] Which one of the following physical quantities is the same as the rate of change of momentum?
1. A: resultant force
2. B: work
3. C: power
4. D: impulse
7. [IEB 2005/11 HG] Cart X moves along a smooth track with momentum pp. A resultant force FF applied to the cart stops it in time tt. Another cart Y has only half the mass of X, but it has the same momentum pp. In what time will cart Y be brought to rest when the same resultant force FF acts on it?
1. A: 12t12t
2. B: tt
3. C: 2t2t
4. D: 4t4t
8. [SC 2002/03 HG1] A ball with mass mm strikes a wall perpendicularly with a speed, vv. If it rebounds in the opposite direction with the same speed, vv, the magnitude of the change in momentum will be ...
1. A: 2mv2mv
2. B: mvmv
3. C: 12mv12mv
4. D: 0mv0mv
9. Show that impulse and momentum have the same units.
10. A golf club exerts an average force of 3 kN on a ball of mass 0,06 kg. If the golf club is in contact with the golf ball for 5 x 10-4-4 seconds, calculate
1. the change in the momentum of the golf ball.
2. the velocity of the golf ball as it leaves the club.
11. During a game of hockey, a player strikes a stationary ball of mass 150 g. The graph below shows how the force of the ball varies with the time.
1. What does the area under this graph represent?
2. Calculate the speed at which the ball leaves the hockey stick.
3. The same player hits a practice ball of the same mass, but which is made from a softer material. The hit is such that the ball moves off with the same speed as before. How will the area, the height and the base of the triangle that forms the graph, compare with that of the original ball?
12. The fronts of modern cars are deliberately designed in such a way that in case of a head-on collision, the front would crumple. Why is it desirable that the front of the car should crumple?
13. A ball of mass 100 g strikes a wall horizontally at 10 m··s-1-1and rebounds at 8 m··s-1-1. It is in contact with the wall for 0,01 s.
1. Calculate the average force exerted by the wall on the ball.
2. Consider a lump of putty also of mass 100 g which strikes the wall at 10 m··s-1-1and comes to rest in 0,01 s against the surface. Explain qualitatively (no numbers) whether the force exerted on the putty will be less than, greater than of the same as the force exerted on the ball by the wall. Do not do any calculations.
14. Shaun swings his cricket bat and hits a stationary cricket ball vertically upwards so that it rises to a height of 11,25 m above the ground. The ball has a mass of 125 g. Determine
1. the speed with which the ball left the bat.
2. the impulse exerted by the bat on the ball.
3. the impulse exerted by the ball on the bat.
4. for how long the ball is in the air.
15. A glass plate is mounted horizontally 1,05 m above the ground. An iron ball of mass 0,4 kg is released from rest and falls a distance of 1,25 m before striking the glass plate and breaking it. The total time taken from release to hitting the ground is recorded as 0,80 s. Assume that the time taken to break the plate is negligible.
1. Calculate the speed at which the ball strikes the glass plate.
2. Show that the speed of the ball immediately after breaking the plate is 2,0 m··s-1-1.
3. Calculate the magnitude and give the direction of the change of momentum which the ball experiences during its contact with the glass plate.
4. Give the magnitude and direction of the impulse which the glass plate experiences when the ball hits it.
16. [SC 2004/11 HG1]A cricket ball, mass 175 g is thrown directly towards a player at a velocity of 12 m··s-1-1. It is hit back in the opposite direction with a velocity of 30 m··s-1-1. The ball is in contact with the bat for a period of 0,05 s.
1. Calculate the impulse of the ball.
2. Calculate the magnitude of the force exerted by the bat on the ball.
17. [IEB 2005/11 HG1] A ball bounces to a vertical height of 0,9 m when it is dropped from a height of 1,8 m. It rebounds immediately after it strikes the ground, and the effects of air resistance are negligible.
1. How long (in s) does it take for the ball to hit the ground after it has been dropped?
2. At what speed does the ball strike the ground?
3. At what speed does the ball rebound from the ground?
4. How long (in s) does the ball take to reach its maximum height after the bounce?
5. Draw a velocity-time graph for the motion of the ball from the time it is dropped to the time when it rebounds to 0,9 m. Clearly, show the following on the graph:
1. the time when the ball hits the ground
2. the time when it reaches 0,9 m
3. the velocity of the ball when it hits the ground, and
4. the velocity of the ball when it rebounds from the ground.
18. [SC 2002/11 HG1] In a railway shunting yard, a locomotive of mass 4 000 kg, travelling due east at a velocity of 1,5 m··s-1-1, collides with a stationary goods wagon of mass 3 000 kg in an attempt to couple with it. The coupling fails and instead the goods wagon moves due east with a velocity of 2,8 m··s-1-1.
1. Calculate the magnitude and direction of the velocity of the locomotive immediately after collision.
2. Name and state in words the law you used to answer question Item 306
19. [SC 2005/11 SG1] A combination of trolley A (fitted with a spring) of mass 1 kg, and trolley B of mass 2 kg, moves to the right at 3 m··s-1-1 along a frictionless, horizontal surface. The spring is kept compressed between the two trolleys. While the combination of the two trolleys is moving at 3 m··s-1-1 , the spring is released and when it has expanded completely, the 2 kg trolley is then moving to the right at 4,7 m··s-1-1 as shown below.
1. State, in words, the principle of conservation of linear momentum.
2. Calculate the magnitude and direction of the velocity of the 1 kg trolley immediately after the spring has expanded completely.
20. [IEB 2002/11 HG1] A ball bounces back from the ground. Which of the following statements is true of this event?
1. The magnitude of the change in momentum of the ball is equal to the magnitude of the change in momentum of the Earth.
2. The magnitude of the impulse experienced by the ball is greater than the magnitude of the impulse experienced by the Earth.
3. The speed of the ball before the collision will always be equal to the speed of the ball after the collision.
4. Only the ball experiences a change in momentum during this event.
21. [SC 2002/11 SG] A boy is standing in a small stationary boat. He throws his schoolbag, mass 2 kg, horizontally towards the jetty with a velocity of 5 m··s-1-1. The combined mass of the boy and the boat is 50 kg.
1. Calculate the magnitude of the horizontal momentum of the bag immediately after the boy has thrown it.
2. Calculate the velocity (magnitude and direction) of the boat-and-boy immediately after the bag is thrown.

### Torque and levers

1. State whether each of the following statements are true or false. If the statement is false, rewrite the statement correcting it.
1. The torque tells us what the turning effect of a force is.
2. To increase the mechanical advantage of a spanner you need to move the effort closer to the load.
3. A class 2 lever has the effort between the fulcrum and the load.
4. An object will be in equilibrium if the clockwise moment and the anticlockwise moments are equal.
5. Mechanical advantage is a measure of the difference between the load and the effort.
6. The force times the perpendicular distance is called the mechanical advantage.
2. Study the diagram below and determine whether the seesaw is balanced. Show all your calculations.
3. Two children are playing on a seesaw. Tumi has a weight of 200 N and Thandi weighs 240 N. Tumi is sitting at a distance of 1,2 m from the pivot.
1. What type of lever is a seesaw?
2. Calculate the moment of the force that Tumi exerts on the seesaw.
3. At what distance from the pivot should Thandi sit to balance the seesaw?
4. An applied force of 25 N is needed to open the cap of a glass bottle using a bottle opener. The distance between the applied force and the fulcrum is 10 cm and the distance between the load and the fulcrum is 1 cm.
1. What type of lever is a bottle opener? Give a reason for your answer.
2. Calculate the mechanical advantage of the bottle opener.
3. Calculate the force that the bottle cap is exerting.
5. Determine the force needed to lift the 20 kg load in the wheelbarrow in the diagram below.
6. A body builder picks up a weight of 50 N using his right hand. The distance between the body builder's hand and his elbow is 45 cm. The distance between his elbow and where his muscles are attached to his forearm is 5 cm.
1. What type of lever is the human arm? Explain your answer using a diagram.
2. Determine the force his muscles need to apply to hold the weight steady.

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