A truck is carrying a refrigerator. The height of the refrigerator is 182.0 cm, the width is 62.0 cm. The center of gravity of the refrigerator is 75.0 cm above the midpoint of the base.
What is the maximum acceleration the truck can have so that the refrigerator doesn't tip over? (The static friction between the truck and the refrigerator is very large.)
What is the maximum acceleration the truck can have so that the refrigerator doesn't tip over? (The static friction between the truck and the refrigerator is very large.)
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from the frame of accelerating truck which is a non inertial frame we can solve the problem using the concept of pseudo force...if the required acceleration is a ....then ma will be the force on the refrigerator acting in the backward direction through the centre of mass...m=mass of refrigerator
now consider the figure of the freezer toppling it will stand on one side while the other side will just be lifted off the ground a little bit...just enough that the normal force stops acting there,it will act on the pivoting side!!....now just balance the torque produced by the pseudo force and weight (the friction is large enough to prevent sliding,just toppling occurs as if it is pinned at one end)
so equation net torque to 0 we get ....mgX62/2=maX75
so we get a(max)=31g/75=4.055m/s2
now consider the figure of the freezer toppling it will stand on one side while the other side will just be lifted off the ground a little bit...just enough that the normal force stops acting there,it will act on the pivoting side!!....now just balance the torque produced by the pseudo force and weight (the friction is large enough to prevent sliding,just toppling occurs as if it is pinned at one end)
so equation net torque to 0 we get ....mgX62/2=maX75
so we get a(max)=31g/75=4.055m/s2
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sorry,I don't have idea