You slide a box of books at constant speed up a 30° ramp, applying a force of 200 n directed up the slope. the coefficient of sliding friction is 0.18. (a) how much work have you done when the box has risen 1 m vertically? (b) what's the mass of the box?

A. Work = integral of force across a path. Since the force is constant, just multiply them: force*distance = 200N * (1m*sin (30)) = 100 Nm = 100 J B. Use Newton: F=ma. For this, we need to use the sum of all the forces, not just the work we apply on the books, but gravity and friction too. Constant velocity means zero acceleration, which means the sum of forces is zero. Draw a free body diagram with the three forces and you'll see that the uphill force = the downhil force = > 200N = NormalForce*Coefficient + Gravity*mass*sin (30) 200N = Gravity*mass*cos (30) * coef. + Gravity*mass*sin (30) 200N = 9.81*mass * (cos (30) * 0.18 + sin (30)) mass = 200 / (9.81 * (cos (30) * 0.18 + sin (30))) m = 31.23 kg