The drawing shows a large cube (mass = 21.0 kg) being accelerated across a horiz

Question

The drawing shows a large cube (mass = 21.0 kg) being accelerated across a horizontal frictionless surface by a horizontal force P. A small cube (mass = 3.6 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?

The drawing shows a large cube (mass = 21.0 kg) being accelerated across a horizontal frictionless surface by a horizontal force P. A small cube (mass = 3.6 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

force = ma = normal reaction

so finding acceleration of the two objects:

a = F/(M+m)

normal reaction = ma = F*m/(M+m)

friction force = normal reaction * u = F*m*u/(M+m)

this force should hold up the weight

F*m*u/(M+m) = mg

=> Fu/(M+m) = g

=> F = g*(M+m)/u = 9.8*(3.6+21)/0.71 = 339.5492957746478873 N

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