Kinetic Energy and the Work-Energy Theorem
KE = ½mv², the work formula, and the work-energy theorem with two worked examples.
The rules
- KE = ½mv²
- W = F · d · cos θ
- W_net = ΔKE
Net work done on an object equals its change in kinetic energy.
Example 1
A 2 kg cart moves at 3 m/s. What is its kinetic energy?
- KE = ½(2)(3)²
- KE = ½(2)(9)
9 J
Example 2
A 10 N force pushes a box 4 m along the floor, in the same direction. How much work is done?
- θ = 0°, so cos θ = 1
- W = 10 × 4 × 1
40 J
Common mistake
Doubling the speed doubles the KE
KE depends on v², so doubling speed quadruples KE.
A force perpendicular to the motion (θ = 90°) does zero work.
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