Check Net Work against Kinetic Energy

Supplied materials

• Use the supplied fictional observations or model. Paper and pencil are optional; spoken answers are welcome. No equipment or real experiment is needed.

Learn the idea

For a constant net force parallel to displacement, net work Wnet = Fnet × displacement. Kinetic energy K = 1/2 mv² depends on speed squared. In this model, net work equals the change in kinetic energy. Right-positive force and right-positive displacement give positive work, increasing kinetic energy; opposite signs give negative work.

A fictional 2 kg cart starts at rest and experiences a constant net force of 4 N right over a 4 m rightward displacement. The listed net includes all horizontal forces; vertical forces do no work along this horizontal path. Net work is 16 J. Its final kinetic energy is 16 J, so 1/2 × 2 × v² = 16 gives a final speed of 4 m/s. This paper calculation assumes the stated constant-force interval.

1. Multiply 4 N by 4 m to find net work.
2. Write initial kinetic energy as zero because the cart starts at rest.
3. Use final kinetic energy = 16 J and solve v² = 16.
4. Explain how positive net work changes energy rather than creating it.

Check your reasoning

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Take it further

Change mass to 8 kg with the same 9 J from rest. Then 4v² = 9, so final speed is 1.5 m/s; the same net work need not give the same speed for different masses.

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