Answer to Question #257297 in Classical Mechanics for Anonymous005

Question

A loaded dogsled has mass of 400 kg and is being pulled across a horizonal, packed snow surface at a velocity of 4.0 m/s (N). Suddenly the harness separates from the sled. If the coefficient of kinetic friction for the sled on the snow is 0.0500, how far will the sled coast before stopping?

Answer 1

We can find the distance that the sled will coast before stopping from the work-kinetic energy theorem:

$$\Delta KE=W_{fr},$$ $$\dfrac{1}{2}mv^2-\dfrac{1}{2}mv_0^2=-F_{fr}d,$$ $$-\dfrac{1}{2}mv_0^2=-\mu_kmgd,$$ $$d=\dfrac{v_0^2}{2\mu_kg}=\dfrac{(4.0\ \dfrac{m}{s})^2}{2\times0.05\times9.8\ \dfrac{m}{s^2}}=16\ m.$$