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A small box of mass m is placed on a top of a larger box of mass 2m as shown in the diagram. When a force F is applied to the large box, both boxes accelerate to the right with the same acceleration. If the coefficient of friction between all surfaces is μ what would be the force accelerating the smaller mass?

Question

A small box of mass m is placed on a top of a larger box of mass 2m as shown in the diagram. When a force F is applied to the large box, both boxes accelerate to the right with the same acceleration. If the coefficient of friction between all surfaces is μ what would be the force accelerating the smaller mass?

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Solution

The force accelerating the smaller mass (m) is the frictional force between the small box and the large box.

Step 1: Identify the forces acting on the small box. These are the gravitational force (mg), the normal force (N), and the frictional force (f).

Step 2: Calculate the normal force. The normal force is equal to the gravitational force, so N = mg.

Step 3: Calculate the frictional force. The frictional force is given by the equation f = μN. Substituting N = mg, we get f = μmg.

Step 4: Identify the net force acting on the small box. Since the small box is moving with the large box, the net force acting on it is the frictional force, which is also the force accelerating the small box.

So, the force accelerating the smaller mass is μmg.

This problem has been solved

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