A garage door is mounted on an overhead rail (the figure( Figure 1 ) ). The whee

Question

A garage door is mounted on an overhead rail (the figure(Figure 1) ). The wheels at A and B have rusted so that they do not roll, but rather slide along the track. The coefficient of kinetic friction is 0.50. The distance between the wheels is 2.00 m, and each is 0.50 m from the vertical sides of the door. The door is uniform and weighs 984N . It is pushed to the left at constant speed by a horizontal force F? .

(a) If the distance h is 1.43m , what is the vertical component of the force exerted on the wheel A by the track?

(b)

If the distance h is 1.43m , what is the vertical component of the force exerted on the wheel B by the track?

(c) Find the maximum value h can have without causing one wheel to leave the track.

Explanation / Answer

Frictional force = (normal force)*(coefficient of friction) = F
Normal force = the weight of the door = 984 N
Coefficient of friction = 0.5
F = 0.5*984 = 492 N

a)

Fa*2 + F*1.43 = w*1
Fa = (1/2)[w - F*1.43] = (1/2)[984 - 492*1.43] = 140.22 N

b)

Fb*2 = w*1 + F*1.43
Fb = (1/2)[984 + 492*1.43] = 843.78 N

c)

Fa = (1/2)[w - F*h] = 0
w = F*h and h = w/F = 984/492 = 2 m

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