Chapter 04, Problem 086 Refer to Concept Simulation 4.4 for background relating

Question

Chapter 04, Problem 086 Refer to Concept Simulation 4.4 for background relating to this problem. The drawing shows a large cube (mass - 28.0 kg) being accelerated across a horizontal frictionless surface by a horizontal force P. A small cube (mass = 3.5 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? s 0.71 Frictionless Number Units the tolerance is +/-290

Explanation / Answer

If the small cube does not slide down, the friction force between the cubes must be mg= 3.5*9.8 = 34.3 N,
so the normal force by the large cube to small cube (in forward direction) must be f/u=48.3 N. This will provide the small cube an acceleration of F/m= 48.3/ 3.5 = 13.8 m/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= 435 N

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