A 120-kg refrigerator,2.00 m tall and 85.0 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 0.300.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 won't tip before it begins to slide?
A) 0.710 m
B) 1.00 m
C) 1.21 m
D) 1.42 m
E) 1.63 m

Question

Quizplus · Accepted Answer

To prevent the refrigerator from tipping over before it slides, the force applied must not exceed the force of static friction. The maximum force of static friction is $F_{\text{max}} = \mu_s N$, where $\mu_s$ is the coefficient of static friction and $N$ is the normal force, which equals the weight of the refrigerator ($mg$). The torque about the tipping point (the edge of the base of the refrigerator) due to the force of static friction must be equal to or greater than the torque due to the applied force at the point of application to prevent tipping. The maximum height ($h$) at which the force can be applied without causing the refrigerator to tip can be found by equating the torques: $\mu_s mg \cdot \frac{w}{2} = F_{\text{max}} \cdot h$, where $w$ is the width of the refrigerator. Solving for $h$ gives the maximum height at which the force can be applied without tipping the refrigerator. Given the width ($w = 0.85$ m) and the coefficient of static friction ($\mu_s = 0.300$), the calculation leads to the conclusion that the highest distance above the floor at which you can push without the refrigerator tipping over is approximately 1.42 m.

A 120-Kg Refrigerator,2