Question

a girl coasts down a hill on a sled, reaching the bottom with a velocity of 18m/s. the coeffecient of friction between the sled's runners and the snow is 0.045, and the girl and the sled weight 500lbs. How far does the sled travel on the surface before coming to rest?

Answer 1

Question 27040

According to frictional force, the motion will be with negative acceleration. For vertical axis $N = P = mg$ . The force of friction is $F_{f} = \mu N = \mu P = \mu mg$ . The law of accelerated motion is $v = v_{0} - at$ , where $v_{0} = 18\frac{m}{s}$ is the velocity at the bottom of the hill. According to $2^{\text{nd}}$ Newton's Law, $a = \frac{F_f}{m} = \mu \frac{P}{m} = \mu g$ . At the moment of stop, $v = 0 \Rightarrow t = \frac{v_0}{a} = \frac{v_0}{\mu g} \approx 40.8s$ . Thus, time needed to stop is $t = 40.8s$ .