Work-Energy Theorem Physics Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
A 4ย kg4 \text{ kg} box initially at rest is pushed with a net force of 20ย N20 \text{ N} over 5ย m5 \text{ m}. What is the final speed of the box?

Solution

  1. 1
    The work-energy theorem states: Wnet=ฮ”KE=12mvf2โˆ’12mvi2W_{\text{net}} = \Delta KE = \frac{1}{2}mv_f^2 - \frac{1}{2}mv_i^2.
  2. 2
    Net work done: W=Fd=20ร—5=100ย JW = Fd = 20 \times 5 = 100 \text{ J}.
  3. 3
    Since vi=0v_i = 0: 100=12(4)vf2โ€…โ€ŠโŸนโ€…โ€Švf=2004=50โ‰ˆ7.07ย m/s100 = \frac{1}{2}(4)v_f^2 \implies v_f = \sqrt{\frac{200}{4}} = \sqrt{50} \approx 7.07 \text{ m/s}

Answer

vfโ‰ˆ7.07ย m/sv_f \approx 7.07 \text{ m/s}
The work-energy theorem directly connects the net work done on an object to its change in kinetic energy. It provides an alternative to using kinematics equations for finding final speeds.

About Work-Energy Theorem

The net work done on an object by all forces acting on it equals the change in its kinetic energy.

Learn more about Work-Energy Theorem โ†’

More Work-Energy Theorem Examples