Refer to Concept Simulation 4.4 for background relating to this problem. The dra

Question

Refer to Concept Simulation 4.4 for background relating to this problem. The drawing shows a large cube (mass = 23.0 kg) being accelerated across a horizontal frictionless surface by a horizontal force P. A small cube (mass = 3.1 kg) is in contact with the front surface of the large cube and will slide downward unless P is sufficiently large. The coefficient of static friction between the cubes is 0.710. What is the smallest magnitude that P can have in order to keep the small cube from sliding downward?

Explanation / Answer

If the small cube does not slide down, the friction force between the cubes must be mg=3.1*9.8=30.38N, so the normal force by the large cube to small cube (in forward direction) must be f/u=30.38/0.71=42.78N. This will provide the small cube an acceleration of F/m=42.78/3.1 =13.8m/s^2. The large cube must have the same acceleration forward with the small cube, so the force P that provide both cubes with the acceleration is P=(M+m)a=(23+3.1)(13.8) =360.18N

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