Friction with moving block question

[ethrust2]

The drawing shows a large cube (mass = 49 kg) being accelerated across a horizontal frictionless surface by a horizontal force P. A small cube (mass = 4.6 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 0.71. What is the smallest magnitude that P can have in order to keep the small cube from sliding downward?

http://www.flickr.com/photos/42276194@N04/3981264713/

Anyone have any idea?

I tried both normal forces multiplied by the static friction coefficient.

 

[tiny-tim]

Welcome to PF!

Hi ethrust2! Welcome to PF!

Hint: for a particular P, what is the acceleration of the small block?

and so what is the reaction force on the small block? ​

 

[tomcue]

I also tried using the acceleration of the large cube and setting it equal to the force of P.

I would approach this problem by first identifying the relevant equations and variables involved. In this case, we have the force P, the masses of the two cubes, and the coefficient of static friction between them. The goal is to determine the minimum value of P needed to prevent the smaller cube from sliding downward.

To start, we can use Newton's second law of motion, which states that the net force on an object is equal to its mass multiplied by its acceleration. In this case, we can apply this equation to the larger cube, since it is the one being accelerated by the force P. This gives us:

net force = mass x acceleration

Since the surface is frictionless, the only force acting on the larger cube is the force P. Therefore, we can rewrite the equation as:

P = mass x acceleration

Next, we need to determine the acceleration of the larger cube. We can use the formula for acceleration, which is the change in velocity divided by the change in time. In this case, the larger cube starts from rest and reaches a final velocity in a given time. Therefore, we can use the equation:

acceleration = (final velocity - initial velocity) / time

Since the larger cube is moving horizontally, we can assume that its final velocity is the same as its initial velocity (since it doesn't change direction). Therefore, we can simplify the equation to:

acceleration = velocity / time

Now, we can use the information given in the problem to solve for the acceleration of the larger cube. The problem states that the larger cube has a mass of 49 kg and is being accelerated by the force P. Therefore, we can use the equation:

P = mass x acceleration

to rewrite the acceleration as:

acceleration = P / mass

Now, we can substitute this into our previous equation for acceleration to get:

P = velocity / time x P / mass

Next, we need to determine the velocity and time values. The problem does not give us any specific values, so we can use general variables v for velocity and t for time. This gives us:

P = v / t x P / mass

Now, we can use the formula for the coefficient of static friction to determine the maximum force that can be applied before the smaller cube starts to slide downward. The formula is:

maximum force = coefficient of static friction