Work
Work – the product of the component of a force along the direction of displacement and the magnitude of the displacement.
Work is done on an object when a force causes a displacement of the object.
Work is done only when components of a force are parallel to a displacement.
Example 1
A 20.0 kg suitcase is raised 3.0 m above a platform by a conveyor belt. How much work is done on the suitcase?
Work at an angle
Example 2
A flight attendant pulls her 70.0 N flight bag a distance of 253 m along a level airport floor at a constant velocity. The force she exerts is 40.0 N at an angle of 52.0˚ above the horizontal. Find the following:
(a) the work she does on the flight bag
(b) the work done by the force of friction on the flight bag
(c) the coefficient of kinetic friction between the flight bag and the floor
Net Work Done by a Constant Net Force
Sign Conventions for Work
| Positive Work | Negative Work |
|---|---|
 |
 |
 |
 |
Example 3
A sailor pulls a boat a distance of 30.0 m along a dock using a rope that makes a 25.0˚ angle with the horizontal. How much work does the sailor do on the boat if he exerts a force of 255 N on the rope?
Example 4
A bicycle rider pushes a bicycle that has a mass of 13 kg up a steep hill. The incline is 25˚ and the road is 275 m long. The rider pushes the bike parallel to the road with a force of 25 N.
(a) How much work does the rider do on the bike?
(b) How much work is done by the force of gravity on the bike?
Energy
Kinetic Energy – the energy of an object that is due to the object's motion
Example 5
A 6.0 kg cat runs after a mouse at 10.0 m/s. What is the cat's kinetic energy?
Work-Kinetic Energy Theorem
Example 6
A 105 g hockey puck is sliding across the ice. A player exerts a constant 4.50 N force over a distance of 0.150 m.
(a) How much work does the player do on the puck?
(b) What is the change in the puck's energy?
Example 7
John pushes a crate across the floor of a factory with a horizontal force. The roughness of the floor changes, and John must exert a force of 20 N for 5 m, then 35 N for 12 m, and then 10 N for 8 m.
(a) Draw a graph of force as a function of distance.
(b) Find the work John does pushing the crate.
Potential Energy
Potential Energy – the energy associated with an object because of the position, shape, or condition of the object.
Gravitational Potential Energy – the potential energy stored in the gravitational fields of interacting bodies.
Gravitational potential energy depends on the height from a zero level.
Gravitational Potential Energy
Example 8
You lift a 7.30 kg bowling ball from the storage rack and hold it up to your shoulder. The storage rack is 0.610 m above the floor and your shoulder is 1.12 m above the floor.
(a) When the bowling ball is at your shoulder, what is the bowling ball's gravitational potential energy relative to the floor?
(b) When the bowling ball is at your shoulder, what is its gravitational potential energy relative to the storage rack?
(c) How much work was done by gravity as you lifted the ball from the rack to shoulder level?
Elastic Potential Energy – the energy available for use wehn a deformed elastic object returns to its original configuration.
Spring Constant – a parameter that is a measure of a spring's resistance to being compressed or stretched.
Example 9
When a 2.00 kg mass is attached to a vertical spring, the spring is stretched 10.0 cm such that the mass is 50.0 cm above the table.
(a) What is the gravitational potential energy associated with this mass relative to the table?
(b) What is the spring's elastic potential energy if the spring constant is 400.0 N/m?
(c) What is the total potential energy of this system?
Example 10
You get a spring-loaded toy pistol ready to fire by compressing the spring. The elastic potential energy of the spring pushes the rubber dart out of the pistol. You use the toy pistol to shoot the dart straight up. Draw bar graphs that describe the forms of energy present in the following instances.
(a) The dart is pushed into the gun barrel, thereby compressing the spring.
(b) The spring expands and the dart leaves the gun barrel after the trigger is pulled.
(c) The dart reaches the top of its flight.
Conservation of Energy
When something is conserved it means that the amount does not change. The form might change but the amount does not change.
Mechanical Energy – the sum of kinetic energy and all forms of potential energy.
Conservation of Mechanical Energy
Example 11
A small 10.0 g ball is held to a slingshot that is stretched 6.0 cm. The spring constant is 200 N/m.
(a) What is the elastic potential energy of the slingshot before it is released?
(b) What is the kinetic energy of the ball just after the slingshot is released?
(c) What is the ball's speed at that instant?
(d) How high does the ball rise if it is shot directly upward?
Example 12
A skier starts from rest at the top of a 45.0 m high hill, skis down a 30˚ incline into a valley, and continues up a 40.0 m high hill. The heights of both hills are measured from the valley floor. Assume that you can neglect friction and the effect of the ski poles.
(a) How fast is the skier moving at the bottom of the valley?
(b) What is the skier's speed at the top of the next hill?
Power
Power – a quantity that measures the rate at which work is done or energy is tranformed.
or
Example 13
Two horses pull a cart. Each exerts a force of 250.0 N at a speed of 2.0 m/s for 10.0 minutes.
(a) Calculate the power delivered by the horses.
(b) How much work is done by the two horses?
Example 14
An electric motor lifts an elevator 9.00 m in 15.0 s by exerting an upward force of 12000 N. What power does the motor produce in kW?
Example 15
You push a wheelbarrow a distance of 60.0 m at a constant speed for 25.0 s, by exerting a 145 N force horizontally.
(a) What power do you develop?
(b) If you move the wheelbarrow twice as fast, how much power is developed?