Fridge on truckutter frustration

1. Dec 3, 2003

Rockdog

I've included a pic.

A refrigerator is approximately a uniform parallelepiped h = 8 ft tall, w = 3 ft wide, and d = 2 ft deep. It sits upright on a truck with its 3 ft dimension in the direction of travel. Assume that the refrigerator cannot slide on the truck and that its mass is 110 kg. For the first three parts of this problem, the rope shown in the picture is not there.

a) When the truck is not accelerating, what is the normal force exerted on the refrigerator by the truck bed?
b) If the truck now accelerates at 2 m/s2, what is the horizontal force exerted on the refrigerator by the truck bed?
c) What is the maximum acceleration the truck can have such that the refrigerator does not tip over?
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d) Suppose now that a rope connects the top of the refrigerator with the cab of the truck, which now accelerates at twice the acceleration calculated in (c). The refrigerator lifts off slightly at the front but is held in place by the horizontal rope. Find the tension in the rope.

Ok. Part a and b were trivial.

I'm stuck badly on part c and d. I know I got to do a net torque equation here, but not sure how to write it up.

The hints for part c weren't that much help.
It says "Since the fridge is not rotating, the sum of all the torques about an axis through the CM must be zero.
and For the maximum acceleration, assume that the fridge is just starting to tip, so that the point of contact with the floor of the truck is at the back corner.

So yea, still stuck.

part d)
Similiar to part c. Not sure how to go about writing the equations. :(

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2. Dec 3, 2003

NateTG

So in the reference frame of the refrigerator you've got the following forces:
the normal force
the force of gravity
friction between the truck and the refrigerator
the 'inertial force' which represents the fact that the refrigerator is in an accelerated reference frame.

the acceleation force and gravity exert zero net torque about the CM.

The FBD redily gives that the normal force is equal to mg and the force of friction is equal to ma.

As the refrigerator tips over the back edge, the normal force exerts torque about the CM since it's only applying at the back edge of the refrigerator. Similarly, friction is only applying at the back edge of the refrigerator. You know that the net torque zero, what more do you need?