Work and Energy
Beginner
work-energy
Source: High school physics (Chinese)
Problem Sets:
work-energy 1019
Problem
A car of mass $m$ is traveling on a level road at an initial speed $v_i$. The driver applies the brakes, causing a constant braking force $F_b$. The car's speed reduces to $v_f$ over a distance $d$.
Determine the magnitude of the braking force $F_b$.
$$F_b = \frac{m(v_i^2 - v_f^2)}{2d}$$
According to the work-energy theorem, the net work done on an object equals the change in its kinetic energy. The work done by the braking force, which opposes the motion, is $W_{net} = -F_b d$. The change in kinetic energy is $\Delta K = K_f - K_i$.
$$W_{net} = \Delta K$$ $$-F_b d = \frac{1}{2}mv_f^2 - \frac{1}{2}mv_i^2$$Solving for the magnitude of the braking force $F_b$:
$$F_b = \frac{\frac{1}{2}m(v_i^2 - v_f^2)}{d} = \frac{m(v_i^2 - v_f^2)}{2d}$$