Work and Energy

Week 4 Content (LC 1)

What does work measure physically?

The amount of energy transferred by a force acting over a displacement.

In W=Fscos⁡θ, what does θ represent?

The angle between the force and displacement vectors.

When is work done by a force positive?

When the force has a component in the same direction as the displacement.

When is work done by a force negative?

When the force has a component opposite to the displacement.

What is the work done when force is perpendicular to displacement?

Zero.

A student pushes a box forward while friction acts backward. Does friction do positive or negative work?

Negative work.

What does the area under a Force-Displacement graph represent?

The work done by the force.

When should you use the area under a graph to find work?

When the force changes with position.

What does the negative sign in Hooke's Law tell you?

The spring force acts opposite to the displacement from equilibrium.

What does a larger spring constant mean?

The spring is stiffer.

A spring is stretched twice as far. What happens to the spring force?

It doubles.

A spring is stretched twice as far. What happens to its elastic potential energy?

It quadruples.

Why does work done by a spring often have a negative sign?

Because the spring force opposes the displacement.

What type of energy is kinetic energy?

Energy of motion.

If an object's speed doubles, by what factor does its kinetic energy change?

It becomes four times larger. [Work and Energy | PDF]

If an object's mass doubles while speed remains constant, what happens to its kinetic energy?

It doubles.

What does the Work-Kinetic Energy Theorem tell you?

Net work done on an object equals its change in kinetic energy.

What does positive net work do to kinetic energy?

It increases kinetic energy.

What does negative net work do to kinetic energy?

It decreases kinetic energy.

When is the Work-Kinetic Energy Theorem especially useful?

When forces and displacement are known but acceleration or time are not needed.

What does power measure?

How quickly work is done or energy is transferred.

Two machines do the same work. One takes half the time. Which has the greater power?

The machine that takes half the time.

What does a high power output tell you?

Energy is being transferred rapidly.

What causes an object to have gravitational potential energy?

Its position in a gravitational field.

What happens to gravitational potential energy when an object is raised?

It increases.

What happens to gravitational potential energy when an object falls?

It decreases.

Why does gravity do positive work on a falling object?

Gravity and displacement are in the same direction.

Why does gravity do negative work on a rising object?

Gravity and displacement are in opposite directions.

When is the formula Ug=mgh valid?

In a uniform gravitational field.

What is a conservative force?

A force whose work depends only on the initial and final positions.

What are the two key properties of a conservative force?

Work is path independent, and work around a closed path is zero.

Name two conservative forces from this topic.

Gravity and ideal spring forces.

What is a non-conservative force?

A force whose work depends on the path taken.

Why is friction a non-conservative force?

Different paths require different amounts of work against friction.

When can mechanical energy be conserved?

When only conservative forces act (or non-conservative forces like friction are negligible).

As an object falls without air resistance, what energy conversion occurs?

Gravitational potential energy is converted into kinetic energy.

As an object rises without air resistance, what energy conversion occurs?

Kinetic energy is converted into gravitational potential energy.

For a frictionless energy problem, what is usually the fastest solving method?

Conservation of mechanical energy