Answer to Question #255106 in Classical Mechanics for Sara

Question

Two packages at UPS start sliding down the 20 degree ramp shown in Figure. Package A

has a mass of 5.0 kg and a coefficient of friction of 0.20. Package B has a mass of 10 kg and a

coefficient of friction of 0.15. How long does it take package A to reach the bottom?

Answer 1

The acceleration of package A is

$$a=g(\sin\theta-\mu_A\cos\theta)=1.5\text{ m/s}^2,$$

the time it will take to reach the bottom of the ramp L meters long is

$$t=\sqrt{2L/a}=\sqrt{1.33L}\text{ s}.$$