Question

Sam is trying to move a dresser of mass m and dimensions of length L and height H by pushing it with a horizontal force F⃗ applied at a height h above the floor. (Figure 1) The coefficient of kinetic friction between the dresser and the floor is μk and g is the magnitude of the acceleration due to gravity. The ground exerts upward normal forces of magnitudes NP and NQ at the two ends of the dresser. Note that this problem is two dimensional.

1)If the dresser is sliding with constant velocity, find F, the magnitude of the force that Sam applies.

Express the force in terms of m, g, and μk.

I found this one : F= uk(mg)

2)Find the magnitude of the normal force NP. Assume that the legs are separated by a distance L, as shown in the figure.

Express this normal force in terms of m, g, L, h, and μk.

3)Find the magnitude of the normal force NQ. Assume that the legs are separated by a distance L, as shown in the figure.

Answer in terms of m, g, μk, h, and L.

4) Find hmax, the maximum height at which Sam can push the dresser without causing it to topple over.

Express your answer for the maximum height in terms L and μk.

Answer 1