A refrigerator 2.0 m tall and 0.8 m wide has its centre of mass at its geometric centre. 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 0.4. 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)0.4 m
B)1.0 m
C)1.2 m
D)2.0 m

Question

Quizplus · Accepted Answer

The refrigerator will start to slide rather than tip over if the force applied does not exceed the torque that would cause it to tip. The maximum height at which you can push without causing it to tip can be found by equating the torque due to the force of friction (which causes sliding) to the torque due to the force applied at a height (which causes tipping). The force of friction is $F_{friction} = \mu N$, where $\mu$ is the coefficient of static friction and $N$ is the normal force (equal to the weight of the refrigerator if on level ground). The torque due to friction, which causes sliding, is maximized when it is applied at the edge of the base, i.e., at a distance of half the width of the refrigerator from the pivot point (the edge of the refrigerator). The maximum force before sliding occurs is $F_{max} = \mu mg$, where $m$ is the mass of the refrigerator and $g$ is the acceleration due to gravity. The torque that causes tipping is $T = Fh$, where $F$ is the force applied and $h$ is the height above the ground at which the force is applied. For tipping to be on the verge of occurring, this torque must be equal to the torque due to the friction force acting at the maximum distance from the pivot point, which is half the width of the refrigerator (0.4 m). Thus, the height at which you can push without causing tipping is equivalent to the height at which the torque due to the applied force equals the torque due to the maximum static friction force, which can be simplified to a problem of balancing torques. Given the coefficient of static friction and the dimensions of the refrigerator, the calculation involves finding the height at which the applied force's torque equals the resisting torque of static friction. The correct answer, based on the principles of static equilibrium and the given conditions, is 1.0 m, which ensures that the refrigerator will slide rather than tip when pushed at this height.

A Refrigerator 2