TEST #1

Energy, Force & Acceleration

1. If the speed of an object doubles, by what factor is its kinetic energy increased? (1)
2. An electric motor is rated at 500 Watts. Assuming that it is 100%
   efficient, how much work could it do in 10 seconds? (1)
3. How much kinetic energy does 0.5 kg of water have if it is flowing with a
   velocity of 0.8 m/s? (1)
4. An oscillating spring has a mass of 500 g bobbing up and down on
   its end. The mass travels 30cm between its lowest point and its
   highest point during a cycle.
   a) Relative to its lowest point in the cycle, what is the
   gravitational potential energy of the bob at its highest point? (2)
   b) Relative to the highest point of the bob in the cycle, how
   much elastic potential energy is stored in the spring when
   the bob is at its lowest point? (1)
5. A pendulum consisting of a metal ball at the end of a piece of light
   string. The pendulum oscillates in such a way that the difference in height
   between the highest and lowest points of the bob is 35 cm. Estimate the
   maximum speed of the bob as it passes its lowest point. (2)
6. The water pressure in a pipe at the outlet of a pump is 300,000
   Pascals. How much force does the water exert on 0.005 square
   meters of the inside surface of the pipe? (2)
7. An object on a flat surface has 2 forces acting on it. The forces are
   parallel to the surface but in different directions as shown in the
   diagram below. What is the resultant force on the object? (3)
8. 
9. A steel ball is dropped from a point that is 20 meters above ground
   level. How fast will it be traveling 0.5 seconds after being dropped? (2)
10. A steel ball is dropped from a point that is 20 meters above ground
    level. How far will it have dropped 1 second after being dropped? (2)
11. A metal ball is fired vertically from ground level at a velocity of
    50 m/s. Estimate the maximum height that the ball will reach and
    the time taken to reach the ground. (4)
12. A racing car travels at a constant speed of 35 m/s in a circular
    track that has a radius of 40 m.
    What is the car’s centripetal acceleration? (2)
13. Write a brief description of intermolecular forces and explain how
    these contribute to molecular potential energy. (5)

TOTAL = 28

TEST #1

Energy, Force & Acceleration

1. By a factor of 4. The kinetic energy is proportional to the velocity²
2. 5000 Joules. 1 Watt = 1 J/s
3. KE = ½mv² : KE = 0.5 x 0.5 x 0.8² = 0.16 J
4. a) PE = mgh PE = 0.5 x 9.81 x 0.3 = 1.47 J
   b) 1.47 J All of the gravitational potential energy is converted to
5. kinetic energy and then elastic potential energy as the bob moves down to its lowest point.
6. PE = KE. mgh = ½mv² . m x 9.81 x 0.35 = ½mv² .
   v² = 2 x 9.81 x 0.35. v = 2.62 m/s
7. 300 000 N/m² x 0.005 m² = 1500 N
8. Resultant² = 20² + 50² therefore Resultant = Ö 2900 = 53.85 N
9. v = gt velocity = 9.81 x 0.5 = 4.905 m/s
10. Average velocity = (0 + 9.81)/2 = 4.905 m/s.
    d = vt. Distance = 4.905 x 1 = 4.905 m
11. Time to reach max height = v₀/g = 50/9.81 = 5.1s.
    Maximum height, d_max = ½gt_max = ½ x 9.81 x 5.1 = 25m
    Time to reach ground = 2 x 5.1s = 10.2 seconds.
12. a_c = v²/r = 35² / 40 = 30.63 m/s².
13. All materials consist of atomic, ionic or molecular particles. There are forces of attraction and repulsion between particles that are known as intermolecular forces. When the normal position of a particle is changed as a result of an applied force (when work is done), the change in position results in an increase in molecular potential energy.

TEST #2

Inertia, Vectors & Pressure

Questions

1. What is the difference between inertia, mass and volume? (3)
2. State Newton’s first law of motion. (2)
3. What does the gravitational force between two objects depend upon? (1)
4. What is the weight of 1 kilogram at the Earth’s surface? (1)
5. Use the diagram below to determine the resultant of 2 forces acting at less than 90º to
   each other. Force 1 has a magnitude of 4.26 Newtons and force 2 has a magnitude of 6 N.
   Complete the parallelogram, use a ruler to measure the length of the resultant and
   estimate the magnitude of the resultant. (3)
6. 
   
   If a cannonball is fired at an angle of 36.87º to the horizontal with a velocity of 100 m/s,
   use the vector diagram below to estimate
   a) The vertical component of its velocity? and (1)
   b) The horizontal component of its velocity? (1)
   
7. 

   
   What is the sum of the vertical components of the forces shown in Diagram 5.1 below? (2)
   

8. 
   
   What is the sum of the horizontal components of the forces shown in Diagram 1.5 above? (1)
   
9. What is the pressure exerted on the floor by a person who weighs 50 kg and rests all
   of her weight on a stiletto heel with an area of 0.9 square centimeters? (3)
   
10. What is the pressure (above atmospheric pressure) at a depth of 20 meters in salt
    water with a density of 1100 kilograms per cubic meter? (3)
    
11. If nearly the earth’s entire atmosphere is located in a region that is roughly 30 kilometers
    deep, why is the pressure at 15 km above the earth’s surface not roughly half of that at the
    earth’s surface? (2)
    
12. A hydraulic jack has a small piston with a diameter of 1cm and a larger piston with a
    diameter of 3.5cm. How much force is exerted on the circular surface of the larger piston
    if the smaller piston exerts a force of 200 N on the oil connecting the circular surfaces of
    the two pistons? (Assume that the surfaces of the pistons are at the same depth in the oil) (4)

TOTAL = 27

TEST #2

Inertia, Vectors & Pressure

1. Inertia is a measure of an object’s mass or tendency to oppose acceleration. Mass is a measure of the amount of matter in an object or body. Volume is a measure of the amount of space an object or body occupies.
2. Newton’s First Law: An object that is at rest will tend to stay at rest and an object that is in motion will tend to continue its motion in the same direction with the same speed unless a force or set of unbalanced forces acts upon it.
3. The mass of each object and their distance apart.
4. The force that the earth’s gravity exerts on 1 kg is 9.81 N.
5. Using the diagram in the test paper, draw the resultant as shown in the diagram below. Measuring the lines on the original diagram, 43mm is equivalent to 6 N. The length of the resultant is 75mm.
   This is equivalent to 75/43 x 6 = 10.47 N.
   
6. 
   Vertical component = 6 grid marks. 1 grid mark = 10 m/s.
   Vertical component = 60 m/s.
   Horizontal component = 80m/s
   
7. The horizontal components are 5, -3 and –1 which add up to 1.
   
8. The vertical components are 2, 1 and –2. These add up to 1.
   
9. 50 kg has a weight of 50 x 9.81 N = 490.5 N
   0.9 square cm has an area of 0.9/(100 x 100) = 0.00009 m².
   The pressure is thus 490.5 / 0.00009 = 5,450,000 Pa.
   
10. 1100 x 9.81 x 20 = 215,820 Pa.
    
11. The density of the air drops with pressure. It varies as the air pressure varies.
    
12. The area of a circle = p x r² or p x (d/2)² Where r is the radius and d is the diameter.
    Area of small piston in contact with the oil = p x (1/2)² = 0.7854 cm²
    Area of larger piston in contact with the oil = p x (3.5/2)² = 9.62 cm²
    The force on the larger surface will be multiplied by the ratio of the areas:
    Force = (9.62/0.7854) x 200N = 2449.7 N.

TEST #3

Friction, Projectiles, Reaction & Momentum

Questions

1. What is the coefficient of friction between two surfaces if the friction force is 700 N when
   the force pushing the two surfaces together is 1500 N? (3)
2. The coefficient of friction between the runners of a sled and the ground is 12.
   What force will be needed to pull the sled if it has a mass of 800 kg? (2)
3. Why does an arrow that is shot upwards (vertically) hit the ground at almost the same speed
   as it left the bow? (2)
4. An arrow is fired horizontally with a velocity of 6 m/s from a point 10 meters above the ground.
   a) How long will it take to reach the ground? (2)
   b) How far will it travel relative to the ground before hitting the ground? (1)
5. An arrow is fired from a point 2 meters above the ground with a velocity of 5 m/s at an
   angle of 30º to the horizontal:
   a) What are the vertical and horizontal components of it’s velocity? (2)
   b) How long will it take to reach the ground? (2)
   c) How far will it travel relative to the ground before hitting the ground? (1)
6. A person steps onto a pier from a boat that is tied to the pier. Describe the forces between
   the person’s foot and the boat and the forces in the rope between the boat and the pier. (3)
7. In a tug-of-war, two teams each exert a force of 1000 N on their end of the rope.
   What is the tension in the rope? (1)
8. Which has the greater momentum: A bullet with a mass of 40 grams traveling at 350 m/s
   or a cannon ball with a mass of 4 kg traveling at 10 m/s? (2)
9. Why does a bullet fired from a rifle travel further than the same type of bullet fired
   from a revolver? (1)
10. One golfer hits a ball with an average force of 100 N with the club in contact with the ball
    for 0.05 seconds. Another golfer hits the ball with an average force of 120 N and the ball
    remains in contact with the club for 0.04 seconds. Which ball will travel further? Why? (3)
11. A bowling ball with a mass of 2.5 kg rolls along a smooth wooden floor at a velocity of 4 m/s.
    Will more momentum be transferred if it hits a wall and bounces back than if it hits a second
    ball and stops as a result of the collision? Explain. (2)

TOTAL = 26

TEST #3

Friction, Projectiles, Reaction & Momentum

1. 700N / 1500N = 0.467
2. The weight of 500 kg = 9.81 x 800 = 7848 N.
   The friction force would be = 12 x 7848 = 122625 N
3. As the arrow travels upwards, it gains gravitational potential energy and loses kinetic energy. Apart from some loss of energy due to friction, the kinetic energy of the arrow is converted to gravitational potential energy. This is converted back to kinetic energy on the way down.
4. The time to drop to the ground from 10 m :
   Rearrange the equation d = ½gt² (g is the acceleration in place of a)
   ..............____ ......___________
   (a) t = Ö 2d/g = Ö 2 x 10 ¸ 9.81 = 1.428 seconds.
   
   (b) The distance covered = 6 x 1.428 = 8.57 m.
   
5. The vertical component of its velocity = 5m/s x sin 30º = 2.5 m/s
   The horizontal component of its velocity = 5 x cos 30º = 4.33 m/s
   Time to reach maximum height (above 2m): ) t_max = v₀ /g = 2.5 / 9.81 = 0.255 seconds.
6. The maximum height (above 2m) : d_max = ½g t_max ² = 0.5 x 9.81 x (0.255)² = 0.32 meters.

   The maximum height = 2 m + 0.32 m = 2.32 meters.

   The time to drop to the ground from 2.32 m :

   Rearrange the equation d = ½gt² (g is the acceleration in place of a)

   .......____ .....___________
   t = Ö 2d/g = Ö 2 x 2.32 / 9.81 = 0.688 seconds.

   The total time that thearrow is in the air is 0.255s + 0.688 = 0.943 seconds.

   With a horizontal velocity of 4.33 m/s it can reach a distance of 4.33 x 0.943 = 4.08 meters in this time.
   

7. The boat doesn’t move because the pier doesn’t move. The tension in the rope from the pier acts on the boat. The opposite tension in the rope acts on the pier. (Other forces keep the pier from moving relative the ground.) The tension in the rope balances the force from the person’s foot. The reaction from the boat propels the person forwards.
8. 1000 N in both directions.
9. Momentum of bullet = 0.04kg x 350 m/s = 14 kg-m/s
   Momentum of cannon ball = 4kg x 10 m/s = 40 kg-m/s
   The cannon ball has the greater momentum.
10. The longer barrel enables the high-pressure gasses that propel the bullet to exert a force on the bullet for a longer period of time. The impulse provided is therefore greater.
11. The impulse from the club of Golfer 1 = 100N x 0.05s = 5 N-s
    The impulse from the club of Golfer 2 = 120N x 0.04s = 4.8 N-s.
    The first golfer should hit the ball further.
12. The ball transfers more momentum in its original direction if it needs to reverse its direction

TEST #4

Collisions, Stability, Machines & Rotation

Questions

1. A marble with a mass of 15 grams moving at 2 m/s collides with an identical marble that
   is at rest. After the collision, the first marble is at rest. What is the speed of the second
   marble after the collision? (1)
2. A marble with a mass of 15 grams swinging on the end of a piece of string and moving
   at 2.5 m/s collides with a lump of putty that is attached to the end of a second piece of
   string. The putty has a mass of 20 grams and is stationary prior to the collision.
   What is the combined momentum of the putty and marble after the collision? (2)
3. What is the difference between the center of gravity and the center of mass?
   Under what conditions do these differ? (3)
4. Under what conditions will a floating object become unstable and tend to capsize? (2)
5. If someone lifts a rock weighing 75 N using a lever and the downward force needed to do
   this at the other end of the lever is 10 N, What is the mechanical advantage of the lever? (2)
6. How far should the downward force need to move for the rock to be lifted 200 cm? (1)
7. Sketch three common types of levers showing the fulcrum, load and applied force
   in each case. (3)
8. Sketch a system in which a single pulley can be used to lift an object with a mechanical
   advantage of 2. (2)
9. Why is there a difference between the theoretical mechanical advantage and the actual
   mechanical advantage of a machine? (2)
10. 
11. The diagram shows a ruler that is balanced at point A.
    Neglecting the weight of the ruler, what is the clockwise moment acting on the ruler? (2)
    What is the mass suspended on the left
    hand side of the ruler? (2)
12.  
13. A Scottish hammer thrower swings a steel ball with a mass of 20kg in a circular path. The path has a radius of 1.5 meters and the ball rotates around the thrower at a rate of 0.7 revolutions per second.
    What is the tangential velocity of the ball? (3)
    What is the angular momentum of the ball? (2)

TOTAL = 27

TEST #4

Collisions, Stability, Machines & Rotation

1. 2 m/s. All of the momentum from the first marble will have been transferred to the second marble.
2. Momentum before collision = 0.015kg x 2.5 m/s = 0.0375 kg-m/s. The momentum of the system after collision must be the same. The combined mass is 0.015kg + 0.02kg = 0.035 kg.
   The velocity just after impact will be = 0.0375 / 0.035 = 1.07 m/s
3. The center of mass is a point at the center of an object’s distribution of mass. The mass of the body can often be regarded as being concentrated at that point. The center of gravity is a point at the center of an object’s distribution of weight. Unless the object is very large, the center of mass is located at the same point as the center of gravity.
4. If the center of mass moves to above the center of buoyancy.
5. 7.5
6. The mechanical advantage of the system (lever) is 7.5. The effort – or downward force – needs to move 7.5 times as far as the load moves. If the load moves 200cm, the other end of the lever must move 7.5 x 200cm = 1500cm or 1.5 meters.
7. 
8. 
9.  
10.  
11. The actual mechanical advantage is always a bit less as a result of energy losses due to friction.
12. The weight of 5 kg is 5 x 9.81 = 49.05 N. The clockwise moment = 49.05 x 0.2 = 9.81 N-m.
    The force on the left-hand side should be 9.81 / 0.35 = 28.03 N.
    This is equivalent to the weight of 28.03 / 9.81 = 2.86 kg.
13. The circumference of the circular path is 2p x 1.5 = 9.43 m. At 0.7 revolutions per second, the tangential speed is 0.7 x 9.43 = 6.6 m/s.
    The angular momentum = mvr = 20 x 6.6 x 1.5 = 198 kg-m² /s.