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Formulas:
Speed or velocity = change in distance/change in time, v = d/t [Units: m/s]
Acceleration = change in velocity/change in time, a= (vf - vi)/t [Units: m/s/s or m/s2]
For acceleration under gravity (starting from rest at time t = 0s)
Acceleration due to gravity at the surface of a planet, g = GM/r2
Four longer questions. Each question is worth 5 points. (Total points = 20.)
Show all calculations!!
1. A 1000kg car is heading North at a speed of 2m/s.
a) What is the car's kinetic energy?
KE = 0.5mv2 = 0.5x1000(2)2 = 2000 J
b) If the driver slams on the brakes and the car comes to a stop over a distance of 10m how much work does the frictional force do in bring the car to a stop?
Work = 2000 J by conservation of energy.
c) Determine the magnitude of the frictional force which slows the car down?
Work = Fd
F = Work/d = 2000/10 = 200 N
c) In which direction is this frictional force acting (i.e. is it pointing North, South, East, or West)?
South
2. A crane lifts a 20kg concrete slab onto a section of scaffolding 5m above the ground.
a) Determine the work done by the crane?
Work = Fd = mgd = 20x10x5 = 1000 J
b) What form of energy does the concrete possess when at this height?
Gravitational potential energy (GPE)
c) If the slab of concrete falls, what is its kinetic energy just before it strikes the ground ? (Neglect friction.)
KE = 1000 J
d) How fast is the slab moving just before it hits the ground?
KE = 0.5mv2
1000 = 0.5x20v2
v2 = 100
v = 10 m/s
e) After the slab hits the ground, what happens to the energy?
The energy is converted to heat and sound energy.
3. If an explosion between a 2kg mass and a 1kg mass causes the 1kg mass to move at 2m/s, North how fast and in what direction does the 2kg mass move? (Hint: Use conservation of total momentum.)
Ptot(before) = (m1 + m2)v = (m1 + m2)0 = 0
Ptot(after) = m1v1 + m2v2 = 2v1 + 1x2 = 2v1 + 2
By conservation of momentum Ptot(before) = Ptot(after) therefore
0 = 2v1 + 2
v1 = -1m/s, North = 1m/s, South.
4. A toy train weighing 4kg is traveling at 3m/s and collides with a stationary railway car weighing 2kg.
a) After the collision the train and car stick together. Use conservation of momentum to determine their speed after the collision.
Ptot(before) = m1v1 + m2v2 = 4x3 + 2x0 = 12
Ptot(after) = (m1 + m2)v = (4 + 2)v = 6v
By conservation of momentum Ptot(before) = Ptot(after) therefore
12 = 6v
v = 2m/s
b) Determine the total KE (kinetic energy) before the collision.
Twenty short answer questions. Each question is worth 4 points. (Total points = 80.)
5. When a stone hits the ground it loses all of its kinetic energy. Where does this energy go?
It is converted into heat and sound energy.
6. The weight W = mg is just the force due to gravity acting on a mass m. The force due to gravity can also be represented by F = GMm/r2. Clearly explain the conditions under which each formula is valid.
W = mg is valid for objects near the surface of a planet.
F = GMm/r2 is valid for all separations r between two objects.
7. If the mass of the earth doubled and nothing else changed, would your weight also increase?
Yes
If yes, how much would it increase by?
Your weight would double.
8. Which requires more work – lifting a 50kg sack a vertical distance of 2m or lifting a 25kg sack a vertical distance of 4m?
They both require the same amount of work.
9. In the diagram I have drawn a car which is driving around a sharp bend at constant speed.
a) At point A draw an arrow indicating the direction in which an acceleration is acting on the car.
The arrow points towards the center of the circle.
b) At point B the car slips on some ice and slides off the road. Draw an arrow indicating the direction in which the car will slide.
The arrow points to the left.
10. What does the word conserve mean in physics?
To keep constant.
11. During a collision airbags are used in cars to
a) increase the momentum.
b) decrease the interaction time and hence decrease the force.
c) increase the interaction time and hence decrease the force.
d) decrease the total energy.
12. For a pendulum bob which swings in a vertical arc, as shown,
a) the kinetic energy is constant throughout the motion.
b) the total energy (= KE + GPE) is constant throughout the motion.
c) the kinetic energy is a maximum at its highest point.
d) the gravitational potential energy is a maximum at its lowest point.
13. A satellite which is moving in a circular orbit around the Earth has an acceleration which
a) is equal to 0m/s2.
b) points away from the Earth.
c) points towards the Earth.
d) points in the direction of the velocity.
14. If the distance between the Earth and the Moon were doubled, the force of gravity between these two objects would
a) increase by a factor of 2.
b) decrease by a factor of 2.
c) increase by a factor of 4.
d) decrease by a factor of 4.
15. The Earth and Moon are attracted to each other by a gravitational force. The more massive Earth attracts the less massive moon with a force that is greater, smaller, or the same as the force with which the moon attracts the Earth?
The same force.
16. In all collisions ______________total momentum_________________ and ________________total energy__________________ are conserved.
17. A golf ball and a Ping Pong ball both move with the same kinetic energy. Circle the true statement.
a) Both balls have the same speed.
b) The golf ball has the greater speed.
c) The Ping Pong ball has the greater speed.
d) You cannot determine which ball has the greatest speed from the information given.
18. a) For the same force, which cannon imparts the greater speed to a cannonball – a long cannon or a short one?
A longer cannon.
b) Explain.
For a longer cannon, the force is applied for a longer period of time which imparts a greater speed to the cannonball.
19. a) Describe the difference between an elastic collision and an inelastic collision.
Inelastic collision – the objects stick together.
Elastic collision – the objects bounce off each other.
b) For which types of collision is momentum conserved?
Momentum is conserved for all types of collisions.
20. In a demonstration I whirled a bucket of water, which was on a short string, in a vertical circle. The water did not fall out of the bucket during this motion. What would happen to the water and the bucket if the string broke at the highest point of the circle? Immediately after the string broke
a) the bucket would move upwards and the water would fall downwards.
b) both the bucket and water would continue in a horizontal direction.
c) both the bucket and water would move in a downward direction.
d) the bucket would move in an arbitrary direction but the water would always fall downwards.
21. A person is walking towards the train station. He sees a train approaching and doubles his speed. His kinetic energy increases by a factor of
a) 2
b) 4
c) 0.5
d) 0.25
22. High and low tides on the Earth are caused by
a) the Sun's gravitational force and the rotation of the Earth about it's axis.
b) the moon's gravitational force and the rotation of the Earth about it's axis.
c) the motion of the Earth around the Sun.
d) the very high rotational motion of the Earth about it's axis.
23. Consider a planet which has the same mass as the Earth but twice the radius of the Earth. The acceleration due to gravity (g) on this planet would be
a) 2.5 m/s2
b) 5 m/s2
c) 20 m/s2
d) 40 m/s2
24. You throw a rock vertically into the air. Initially the rock possesses kinetic energy. However, at the top of its flight, the rock is motionless and therefore has zero kinetic energy. Does this mean that, in fact, energy is not conserved?
No, energy is conserved.
If energy is conserved, explain what has happened to the kinetic energy.
The kinetic energy is converted to gravitational potential energy (GPE).
