11.14 Summary and exercises  (Page 2/2)

Gravitation

1. [SC 2003/11]An object attracts another with a gravitational force $F$ . If the distance between the centres of the two objects is now decreased to a third ( $\frac{1}{3}$ ) of the original distance, the force of attraction that the one object would exert on the other would become $...$
   1. A $\frac{1}{9}F$
   2. B $\frac{1}{3}F$
   3. C $3F$
   4. D $9F$
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 $\cdots$
   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 ( M ${}_E$ = 6 x 10 ${}^{24}$ kg, r ${}_E$ = 6 x 10 ${}^6$ 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 10 ${}^{12}$ kg respectively, if the magnitude of the force between them is 3 x 10 ${}^{?8}$ 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 10 ${}^{16}$ m.
6. The following information was obtained from a free-fall experiment to determine the value of $g$ with a pendulum. Average falling distance between marks = 920 mmTime taken for 40 swings = 70 s Use the data to calculate the value of $g$ .
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 10 ${}^{30}$ kg and the Earth with a mass of 6 x 10 ${}^{24}$ kg if the distance between them is 1,4 x 10 ${}^8$ 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 10 ${}^{24}$ 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 10 ${}^{24}$ kg and the Earth's radius is 6400 km.
17. 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 $\times$ 10 ${}^{22}$ kg. The radius of the Moon is 1,74 $\times$ 10 ${}^6$ 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 ${}^{-1}$ . It rebounds horizontally with a speed of 8 m $·$ s ${}^{-1}$ . 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 $p$ . A resultant force $F$ applied to the cart stops it in time $t$ . Another cart Y has only half the mass of X, but it has the same momentum $p$ .

   

   In what time will cart Y be brought to rest when the same resultant force $F$ acts on it?
   1. A $\frac{1}{2}t$
   2. B $t$
   3. C $2t$
   4. D $4t$
8. [SC 2002/03 HG1] A ball with mass $m$ strikes a wall perpendicularly with a speed, $v$ . If it rebounds in the opposite direction with the same speed, $v$ , the magnitude of the change in momentum will be ...
   1. A $2mv$
   2. B $mv$
   3. C $\frac{1}{2}mv$
   4. D $0mv$
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 ${}^{-4}$ 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 ${}^{-1}$ and rebounds at 8 m $·$ s ${}^{-1}$ . 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 ${}^{-1}$ and 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 ${}^{-1}$ .
    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 ${}^{-1}$ . It is hit back in the opposite direction with a velocity of 30 m $·$ s ${}^{-1}$ . 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 ${}^{-1}$ , 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. 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 [link]
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 ${}^{-1}$ 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 ${}^{-1}$ , 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 ${}^{-1}$ 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 ${}^{-1}$ . 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.