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Work, Energy, and Power
W = Fd, Kinetic and Potential Energy, and P = W/t
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Work, energy, and power describe how forces cause motion and how energy is transferred or transformed. These ideas connect pushes, lifts, friction, and speed into one framework that explains many everyday and engineering situations. In mechanics, they help predict how fast an object moves, how high it rises, and how much effort a machine must deliver. Understanding these quantities is essential for solving problems involving ramps, vehicles, machines, and human motion.
When a force acts through a displacement, it can do work and change an object's energy. The work-energy theorem states that the net work on an object equals its change in kinetic energy, while gravity and elastic forces can store energy as potential energy. On an inclined plane, applied force, friction, and the component of weight along the slope all affect the energy balance. Power adds the time dimension by measuring how quickly work is done or energy is transferred.
Key Facts
- Work done by a constant force: W = Fd cos(theta)
- Net work changes kinetic energy: W_net = Delta K = 1/2 mv_f^2 - 1/2 mv_i^2
- Gravitational potential energy near Earth: U = mgh
- Kinetic energy: K = 1/2 mv^2
- Mechanical energy with nonconservative work: W_nc = Delta K + Delta U
- Average power: P = W/t, and instantaneous power for constant velocity direction: P = Fv cos(theta)
Vocabulary
- Work
- Work is the energy transferred when a force acts on an object through a displacement.
- Kinetic energy
- Kinetic energy is the energy an object has because of its motion.
- Potential energy
- Potential energy is stored energy associated with position or configuration, such as height in a gravitational field.
- Power
- Power is the rate at which work is done or energy is transferred.
- Friction
- Friction is a force that opposes relative motion between surfaces and often converts mechanical energy into thermal energy.
Common Mistakes to Avoid
- Using W = Fd for every problem, which is wrong when the force is not parallel to the displacement because the correct expression is W = Fd cos(theta).
- Confusing force with work, which is wrong because force is measured in newtons while work is measured in joules and requires both force and displacement.
- Ignoring friction on an incline, which is wrong because friction can do negative work and reduce the mechanical energy available for motion.
- Treating power and work as the same quantity, which is wrong because work is an amount of energy transferred while power tells how fast that transfer happens.
Practice Questions
- 1 A 12 kg box is pushed 5.0 m up a ramp by a constant force of 40 N directed parallel to the ramp. How much work does the applied force do on the box?
- 2 A 3.0 kg cart starts from rest and gains 24 J of net work. What is its final speed?
- 3 A block moves up a rough incline at constant speed while being pushed upward. Explain how the applied work is distributed among kinetic energy, gravitational potential energy, and thermal energy.