Coefficient of the static friction homework

[touma]

A large cube with a mass of 25 kg is being accelerated across a horizontal frictionless surface by a horizontal force P. A small cube with a mass of 4.0 kg is in contact with the front surface of the large cube and will slide downwards unless P is sufficiently large. The coefficient of the static friction between the cubes is 0.71. What is the smallest magnitude that P can have in order to keep the small cubbe from cliding downward?


I got an answer of 4.0 x 10^2 N. But I am unsure if that is correct. Can someone try this? And show work please?

 

[OlderDan]

Can someone try this? And show work please?

It really does not work that way here. You show your work and then people will help you.

 

[m2003]

I would first like to clarify the problem and make sure all necessary information is included. The problem states that the large cube is being accelerated across a frictionless surface, but it does not specify the acceleration or the direction of the force P. It also does not specify the angle at which the small cube is in contact with the large cube. Additionally, the problem mentions a possible downward motion of the small cube, but it does not mention any other forces acting on it.

Assuming that the force P is acting horizontally in the same direction as the acceleration of the large cube, and that the small cube is in contact with the front surface of the large cube at a 90 degree angle, the problem can be solved as follows:

First, we need to determine the maximum frictional force that can act between the two cubes. We can do this by multiplying the coefficient of static friction (0.71) by the normal force between the cubes, which is equal to the weight of the small cube (4.0 kg x 9.8 m/s^2 = 39.2 N). Therefore, the maximum frictional force is 0.71 x 39.2 N = 27.8 N.

Next, we need to determine the minimum force P that is necessary to counteract the downward motion of the small cube. This force must be equal to the maximum frictional force, so P = 27.8 N.

Finally, we need to convert this force into magnitude. Since the problem does not specify the direction of P, we can assume that it is acting in the same direction as the acceleration of the large cube. The magnitude of this force can be calculated using Newton's Second Law, F = ma, where F is the force, m is the mass, and a is the acceleration. In this case, the mass of the large cube is 25 kg and the acceleration is unknown. Therefore, we can rearrange the equation to solve for acceleration, a = F/m. Plugging in the values, we get a = 27.8 N / 25 kg = 1.112 m/s^2.

In conclusion, the smallest magnitude that P can have in order to keep the small cube from sliding downward is 27.8 N. However, if the acceleration of the large cube is known, the magnitude of P can be calculated using the equation P = ma.