Text for problems 1-5: A cube bxbxb F B b with mass m lies on the flat, horizont

Question

Text for problems 1-5: A cube bxbxb F B b with mass m lies on the flat, horizontal ground. One side is shown in the figure. The thickness normal to the plane of the figure is b. The cube is subject to earth's gravity and friction coefficient between the cube and the ground is u. Impulsive horizontal loading Lis applied on the edge B, such that force F() is applied during the very short time At: Fond During the interval At, the force varies from 0 to the maximum value F and back to 0. max. 1. (10 points) we first consider the question of whether cube slides or rotates about the edge O. The criterion for sliding will depend on: (Check only one box.) angular impulse: Lb nd on: 2. (10 points) he criterion f neither

Explanation / Answer

1) Criterion for sliding will depend on Fmax . Because when force applied is more than opposing frictional force the cube will slide.

2) Criterion for sliding will depend neither in Ig or Io. As moment of inertia is related to rotation and not sliding.

3) To determine the Lcrit that leads to tipping let us consider the cube to be in equilibrium such that sum of torques actiong on it is 0.

The cube rotates about O. so Lcrit has a lever arm of length b. Weight of the cube acting downwads also produce a torque with lever arm of length b/2 , as the center of mass of cube is at midpoint of cube(Assuming the cube to be of unuform density)

So from sum of torques equal to 0. W is weight of cube.

W =mg

Lcrit x b = W x b/2

So  Lcrit =W/2

NOw when mass of cube is doubled, W will also be doubled. And hence  Lcrit will change by a factor of 2.

4) Now if mass remains same and cube side is doubled.

Lcrit will remain same as W will not change.

5) Lcrit = W/2 = mg/2

So if gravitational acceleration is doubled,  Lcrit will change by a factor of 2.

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