A 120-kg refrigerator that is 2.0 m tall and 85 cm wide has its center of mass at its geometrical center. You are attempting to slide it along the floor by pushing horizontally on the side of the refrigerator. The coefficient of static friction between the floor and the refrigerator is 0.30 .
Depending on where you push, the refrigerator may start to tip over before it starts to slide along the floor. What is the highest distance above the floor that you can push the refrigerator so that it will not tip before it begins to slide?
A) 1.0 m
B) 1.6 m
C) 1.2 m
D) 1.4 m
E) 0.71 m

Question

A 120-kg refrigerator that is  2.0 m tall and  85 cm wide has its center of mass at its geometrical center. You are attempting to slide it along the floor by pushing horizontally on the side of the refrigerator. The coefficient of static friction between the floor and the refrigerator is  0.30 .
Depending on where you push, the refrigerator may start to tip over before it starts to slide along the floor. What is the highest distance above the floor that you can push the refrigerator so that it will not tip before it begins to slide?
A)  1.0 m
B)  1.6 m
C)  1.2 m
D)  1.4 m
E)  0.71 m

Quizplus · Accepted Answer

To prevent the refrigerator from tipping over before it starts to slide, the force applied must create a torque about the edge of the base that is less than or equal to the torque created by the frictional force at the point of tipping. The maximum static frictional force is $f_{max} = \mu_s N$, where $\mu_s = 0.30$ is the coefficient of static friction and $N = mg$ is the normal force (with $m = 120\,kg$ and $g = 9.8\,m/s^2$). The tipping point is when the line of action of the applied force passes through the edge of the base of the refrigerator, which is $0.85/2 = 0.425\,m$ from the center. The torque due to the applied force at the tipping point is equal to the torque due to the maximum static frictional force acting at the bottom edge of the refrigerator opposite the tipping edge. The height $h$ at which the force can be applied without causing tipping can be found from the balance of torques: $f_{max} \cdot 0.425 = mg \cdot h$. Solving for $h$ gives the maximum height to apply the force without causing the refrigerator to tip. The correct calculation involves balancing these torques and considering the geometry of the refrigerator, leading to the conclusion that the highest distance above the floor at which you can push without causing it to tip is 1.4 meters.

A 120-Kg Refrigerator That Is 2