Sam is trying to move a dresser of mass m and dimensions of length L and height

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 F?  applied at a height h above the floor.(Figure 1) The coefficient of kinetic friction between the dresser and the floor is ?k 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.

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

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

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

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

Explanation / Answer

B. you need to find the moment about point Q (and since it's in equilibrium because it's not rotating about Q, but only sliding, it will be zero). Remember that the moment is distance x force, and another way to write it is F(perpendicular)(d). To find the signs of the moment use the right hand rule.

0= F_g(L/2) - Fh - N_P(L)
Solve for N_P (the normal force at P)

N_P= mg(1/2 - (Fh/L)) We know that F=mu_k(F_N) and F_N=mg. Substituting this we get

N_P= mg(1/2 - (mu_k h)/L)

C. We could solve using the sum of the moments about point P and setting it equal to zero, but there's an easier way. Now that we know N_P, we can find the sum of F_y.

sum F_y=0=N_P + N_Q - F_g and solve for N_Q

N_Q= F_g-N_P

=mg-mg(1/2-(mu_k(h)/L))

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