Question

You are rearranging the furniture in your living room. In doing so, you push a 33 kg sofa to the left a total distance of 3 m and then you push it back to the right a distance of 1 m. The coefficient of kinetic friction between the sofa and the hardwood floor is 0.2. What is the work done by friction in moving the sofa? Express your answer in joules to one significant figure. Suppose that you had instead simply moved the sofa to its final position by moving it directly 2 m to the left. What is the work done by friction in this case? Express your answer in joules to one significant figure.

Answer 1

Case - i: - d = 3 m Left F_net = 0 therefore F - f_k = 0 F = f_k = mu_k N = mu_k(Mg) = 0.2(33 times 9.8) F = 64.68 N work done by force is w = Fd = 64.68 times 3 m w = -194.04 N work done by friction is positive dissection therefore w_friction = + 64.68 times 3 = + 194.04 N Now it is moved to 1 m right F_net = 0 F - F_k = 0 implies F = F_k = mu_k(Mg) = (0.2)(33 times 9.8) = 64.68 N w_Force = F times d = (64.68) times 1 m = 64.68 N w_friction = Fd = -64.68 times 1 m = -64.68 N therefore Net work done by friction w_final + w_instance = 194.04 - 64.68 = 129.36 N Rounding off is 1 significant figure w_friction = 100 N directly moved to 2 m F_net = 0\r\n