Slide Cube

Slide Cube A large cube (mass = 41 kg) being accelerated across a horizontal frictionless surface by a horizontal force P? A small cube (mass = 3.7 kg) is in contact with the front surface of the...

Slide Cube

A large cube (mass = 41 kg) being accelerated across a horizontal frictionless surface by a horizontal force P?

A small cube (mass = 3.7 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 0.71. What is the smallest magnitude that P can have in order to keep the small cube from sliding downward?

The small cube is pulled down by gravity with a force of 37 newtons.

This has to be matched by friction. The force of friction will be acting upwards with 0,71 times the force exerted by the big cube on the small. Therefore the big cube must exert at least 37/0.71 = 52.11 N of force on the small cube.

This force is given by F=ma, where m=410N. Thus a = 52.11/410 =0.127.

in order to accelerate the two cubes at this rate a force of 0.127*447=56.8N is required, (where 447 is the mass of both cubes.

Thus P is greater than or equal to 56.8 N

NB: It was a while since I studied mechanics, but it should be right, I hope.

Also note that this, as see it, assumes that the weight of the small cube acts along the side that's against the big cube, which it doesn't. But since there is no info on the size of the cube, I can't see how you would take this into account, so maybe it's irrelevant somehow.