Question

A 4.00-kg block rests on an inclined plane that has an inclination angle of 31.3o. A string attached to this block, goes uphill and over a frictionless pulley, and then is attached to a hanging block of mass M. The inclined plane has coefficients of friction μs = 0.22 and μk = 0.13.

Draw a real world picture of this scenario.

Draw the free body diagrams for each of the blocks.

Show how to determine the mass M that will cause the blocks to start moving.

Once the blocks are moving, show how to determine the acceleration of the blocks.

Show how to determine the speed and distance that the blocks have moved after 5.55 seconds

Answer 1

First, we define a few quantities being used in our calculations.

The tension in the rope, which is equal to the weight of the hanging block initially :

The static friction force:

The component of the four kilogram block into the incline:

The component of the four kilogram block along the incline:

The diagram of the system is as given below.

The free body diagram of the four kilogram block:

The free body diagram of the hanging mass is:

From this, we can see that the force acting down the incline is that particular component of the block's weight, and the forces acting up the incline are the static friction force and the tension in the string.

Since the four kilogram block is at rest, these forces are equal. From this, we can deduce the mass of the hanging block for which the system will just start moving.

Once the blocks start moving, the friction force is due to the kinetic coefficient of friction, .

This is equal to:

Finding the acceleration

Since the blocks are connected, the acceleration of either of the block is the acceleration of the system.

Let the acceleration of the system be .

Then, the tension in the rope will be

Rewriting the force equation.

The speed of the system after is

The distance travelled is