Solving Accelerated Block Problem with Friction & Angle Alpha

[Kruger]

A block is accelerated with a, take a look at the picture. There is a friction between the red block and the other one with mass m1. The friction is given by the coefficient u1.

I have to determine a such that the blue block is not moving relative to the red one. a has to bi in depenence of angle alpha.

Homework Equations

The relevant equations are basically Newton's equations.

The Attempt at a Solution

What I have done so far is the following: One force acting on the block is coming from the gravitational field, so F_g=m1*g. I have splitted this one in components: F||=sin(alpha)*F_g and (already added friction) F_s=cos(alpha)*F_g*(1-u1).

I don't know how I can go on. The basic problem is I don't really know how a acts one the block. And how I've to balance the forces.

 

[OlderDan]

There will be a range of accelerations that will prevent the block from slipping because friction can act either up the plane or down the plane. Are you supposed to be finding the minimum accleration, maximum acceleration, or both?

You know the blue block must have the same acceleration as the red ramp. Draw all of the forces acting on the block. The sum of all the forces must be horizontal and have magnitude ma.

 

[m2003]

I would approach this problem by first identifying all the relevant forces acting on the system. In this case, we have the force of gravity acting on the mass m1, the normal force from the surface on which the block is resting, and the friction force between the two blocks. We can also consider the force of tension in the string connecting the two blocks, but it may not be relevant to the problem at hand.

Next, I would apply Newton's second law, which states that the net force on an object is equal to its mass times its acceleration. In this case, we can write the equation for the red block as:

ΣF = m1a = F_g - F_s

Where ΣF represents the sum of all the forces acting on the block, m1 is its mass, and a is its acceleration. The force of gravity, F_g, can be broken down into its components as you have already done. The friction force, F_s, can also be expressed as you have shown, but we must also consider the normal force, which is equal in magnitude but opposite in direction to the friction force.

Once we have this equation, we can solve for the acceleration, a, in terms of the angle alpha and the coefficient of friction, u1. This will give us the required acceleration to keep the blue block stationary relative to the red block.

In general, when solving problems in physics, it is important to clearly identify all the relevant forces and apply the appropriate equations to solve for the unknown quantities. It may also be helpful to draw a free-body diagram to visualize the forces acting on the system.