How to Solve Dynamics of Rigid Bodies Problems Involving Friction?

[nella_ph]

Please Help! Mechanix problem assignment

Homework Statement

Please help me do my assignment in dynamics of rigid bodies. It's more on kinetics of particles and I have difficulty in figuring out how to draw the free body diagram of the blocks..

Question 1: The 20 lb block A and the 30 lb block B are initially at rest. If a force P = 30 lb is applied to B as shown, determine the acceleration of each block. The coefficient of kinetic friction between any two surface is 0.20.

Fig for this problem is prob1.jpg


Question 2: Body A has a mass of 50 kg while the mass of body B is 20 kg. A force F = 500 N is applied to body A parallel to the plane. Assuming that the plane is smooth, determine the least coefficient of friction between A and B so that slipping will not occur.

Fig for this problem is prob2.jpg.


Your solutions and answers will be appreciated. thanks.

Homework Equations

Friction Force = uN
Summation of Forces along the path of motion = ma

The Attempt at a Solution

Pre-Assumptions on Question 1:
Force P on A will be in opposite direction (?)
The weight of A will be added to B (?)

Pre-Assumptions on Question 2:
The weight of block B will be added on A (?)

 

[Beaker87]

Question 1: The 20 lb block A and the 30 lb block B are initially at rest. If a force P = 30 lb is applied to B as shown, determine the acceleration of each block. The coefficient of kinetic friction between any two surface is 0.20.

Pre-Assumptions on Question 1:
Force P on A will be in opposite direction (?)
The weight of A will be added to B (?)

For this problem, it may help you to first calculate all of the frictional forces between all of the surfaces.

When you solve for the friction between blocks A and B, note that the force will be acting forward on A, and backward on B, due to Newton's third law of motion.

When you solve for the friction between blocks B and the ground, you are correct in adding the weight of A to B.


Once you have done this, draw a force diagram for each block. The only forces acting on A will be the frictional force, and the forces acting on B will be both frictional forces, and the applied force.

Now you can simply use:

Summation of Forces along the path of motion = ma

to find the acceleration of each block.
*REMEMBER: you were given the weight of each block, for this formula you need to use the mass.

Question 2: Body A has a mass of 50 kg while the mass of body B is 20 kg. A force F = 500 N is applied to body A parallel to the plane. Assuming that the plane is smooth, determine the least coefficient of friction between A and B so that slipping will not occur.

For this problem, start by assuming that block B will not slip. This allows you to find the acceleration of the system by adding the masses of the two blocks, and dividing by the net force.

Now you can draw a force diagram for the system, remembering to break each force into its parallel and perpendicular components. Once you have all of the parallel forces (there should be two) you can find the acceleration of the system.

The acceleration of block B must be equal to the acceleration of the system.
What force needs to be applied to B by A in order to cause this acceleration?
What are the x and y components of the force applied to B by A?
How much Normal force is needed to cause the acceleration in the y direction?
How much frictional force is needed to cause the acceleration in the x direction?
Finally, what coefficient of friction will give the needed frictional force?

 

[nella_ph]

^ thanks beaker...that's a great help.