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Exploration 1: Work and Energy
WorkExample Table
Name of Force / sign of work (+/- or 0)weight (FG)
normal (n)
friction (f)
Net work
For each situation described below:
- Draw a free body diagram of the object
- Identify all forces acting on the object
- Determine if the work done by each force is positive, negative or zero.
- Make a neat table beside the fbd showing every force and the sign of its work (example below).
- Determine the sign of the net work done on the object
1. An elevator moves upward at constant speed:
2. Adescending elevator slows down and stops:
3. You push a box across a rough floor at constant speed:
4. You slide down a steep hill with friction, increasing your speed:
5. A ball is thrown straight up. Consider the ball from 1 nanosecond after it leaves your hand until it reaches its high point:
6. a box slides up an incline with friction until it stops.
7. Does effort necessarily result in physical work? Suppose two people are in an evenly matched tug-of-war. They are obviously expending effort to pull on the rope, but according to the definition are they doing any physical work? Explain your reasoning.
8. Consider the definition of work that you developed and that was formally introduced in this chapter. Describe a situation in which:
a. a force is applied to an object and positive work is done on the object.
b. a force is applied to an object and negative work is done on the object.
c. a force is applied to an object but no work is done on that object.
9. An elevator has a total mass of 6020.41 kg. The elevator travels 6.0 meters down to the nextfloor. The cable exerts a force of 70,000 N on the elevator.
How much work is done by each of the external forces acting on the elevator?
Determine the net work done on the elevator.
10. A cable is used to lower a log (22,000 N) 10 meters down a hill. The cable is parallel to the hill. The tension in the cable is 7,000 N and a 4,000 N frictional force opposes the motion.
How much work is done by each of the external forces acting on the logr?
Determine the net work done on the log.
11. Ranking Task 1: Equal Forces on Boxes
In the figures below, identical boxes of mass 10 kg are moving at the same initial velocity to the right on a flat surface. The same magnitude force, F, is applied to each box for the distance, d, indicated in the figures.
Rank these situations in order of the work done on the box by F while the box moves the indicated distance to the right. Negative values of work rank lower than positive works.
Least 1______2______3______4______5______6______Greatest
OR, all of the boxes have the same work done on them by the force, F. ______
OR, none of the boxes have work done on them by the force, F. ______
Explain the reasoning for your ranking. ______
How sure were you of your ranking?
Basically Guessed 1 2 3 4 5 6 7 8 9 10 Very Sure
12 Ranking Task 2: Work Done on Hand
In the figures below, identical boxes of mass 10 kg are moving at the same initial velocity to the right on a flat surface. The same magnitude force, F, is applied by a hand to each box for the distance, d, indicated in the figures.
Rank these situations in order of the work done by the box on the hand exerting the force F while the box moves the indicated distance to the right. Negative works rank lower than positive works.
Least 1______2______3______4______5______6______Greatest
OR, all of the boxes do the same (nonzero) work on the hand. ______
OR, none of the boxes do work on the hand. ______
OR, it is not possible to determine the work done on the hand. ______
Explain the reasoning for your ranking. ______
How sure were you of your ranking?
Basically Guessed 1 2 3 4 5 6 7 8 9 10 Very Sure
Exploration 2: Conservation of Energy: The Work-Energy Theorem
1. A fighter jet is launched from an aircraft carrier, with the aid of its jet engines and the steam- powered catapult. The thrust due to the exhaust gas of the engine has a force of 2.3 x 105 N. The catapult is in contact with the jet for 87 m. The jet has a kinetic energy of 4.5 x 107 J at lift-off. What is the force exerted by the catapult on the jet?
2. A 16 kg sled is pulled across a horizontal patch of snow, by a horizontal force of 24N. Starting from rest, the sled attains a speed of 2.0m/s in 8 m. What is the coefficient of kinetic friction between the sled runners and the snow?
3. A rescue helicopter lifts a 79 kg person straight up by means of a cable, with an upward acceleration of 0.70 m/s2. The person started lifted from rest through a distance of 11m. What is the final speed of the person after being lifted 11 m?
4. Susan’s 10 kg baby brother sits on a mat. Susan pulls the mat across the floor at an angle of 30 degrees with a tension of 30 N. The coefficient of kinetic friction is 0.20. What is the final speed if Susan pulls the baby from rest through a distance of 3.0m?
Exploration 3: Gravitational Potential Energy
1. Sliding masses on Incline – Change in PE
Rank, in order from greatest to least, the magnitude of change in gravitational potential energy of the sliding blocks, from top to bottom of frictionless inclined surface
Problem solving steps for Conservation of Energy
1. Draw a pictorial representation, showing initial and final v, s, h and θ, depending on problem statement. Draw a fbd if necessary to determine the net work done
2. Write the conservation of energy equation, using the terms for your particular problem.
3. Solve
Example: Christine runs forward with her sled at 2.0 m/s. She hops onto the sled at the top of a 5.0 m icy (i.e. frictionless) hill.
KnownFind: v1
y0 = 5.0m
v0 = 2.0 m/s
y1 = 0 m
s0 = 0 m
s1 = y0/(sin θ) – from trig
Since there is no work done by forces other than gravity, we do not need a fbd in this example, and the value of ∆s (the length of the slope) is not important:
For the following, draw a before and after pictorial representation, and write the conservation of energy equation for this particular situation. Leave out work or energy terms that you have determined are equal to zero.
2. A car runs out of gas and coasts up a hill until it finally comes to a stop.
3 A snowboarder with some initial speed, slides down a hill with friction
4. A skier gets towed up a hill with friction by the tow bar cable. He started at rest.
5. A woman pushes a box across a floor, with friction, at constant speed. Her push is at a downward angle of θ (use a fbd to determine net work).
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