Question

A 5.0 kg chair sits on a ramp which is at an angle of 10^0 with respect to the horizontal. A boy wants to push the chair up the ramp. The coefficient friction between the chair and the floor is (0.3, 0.2) Draw a free-body diagram. Does the boy need to push on the chair to keep it from sliding down the incline? (Be sure to show your work.) If the chair is at rest, then what is the maximum force that the boy can push the chair with before it begins to move up the incline?

Answer 1

First of all we have to divide the mass of chair into rectangular components, then

1st component in a direction perpendicular to plane in downward direction is, $W_1=mgcos10^{\circ}= (5)(9.8)(0.98)= 48.255 N$

2nd component in a direction parallel to plane in a downward direction is, $W_2=mgsin10^{\circ}= (5)(9.8)(0.173)= 8.508 N$

b). Now since the chair will slide down the slope due to force W₂. Thus child need to push it in order to stop it from sliding down.

c). Maximum Static Friction Force on chair is, $F_{s}=\mu_sW_1=(0.3)(48.255)= 14.47 N$

Thus if the boy wants to push it upwards, Minimum force required is, ( as both the forces will act downward along the ramp if the box tend's to move up)

d). When is starts moving up with constant velocity ( zero acceleration), Kinetic friction force will come into play.

Then total force acting on chair will be friction force and 2nd component of chair's weight as acceleration of motio is zero.

then Force needed by boy is, $F_n= W_2+F_{k}=8.50+ \mu_k W_1 = 8.50+(0.2)(48.255)=18.151 N$