Dynamics - Normal and Tangential Check

[desibabu90]

Homework Statement

The question reads: Body A has a mass of 9kg and rests on a smooth plane. the force P applied to body A is increased from zero at a very slow rate. Determine the maximum force P that can be applied without causing the smooth 6-kg cylinder to leave body A at point C.

Homework Equations

Newton's Law: $$\Sigma$$F = ma{tangential}

The Attempt at a Solution

If you look at my solution in the picture you will see my work. I am just not sure if that is right. Are we supposed to use the information given to us about the force P being applied very slowly? Is the free body diagram right?

Please help

Thanks.

There is a error in the picture where I didn't carry over the terms from the left side to the right side but the final answer is right and I just forgot to show it on the picture.

 

[KataKoniK]

Hello,

Thank you for sharing your work and asking for feedback. Your solution looks correct to me. The free body diagram is also correct, as it shows all the forces acting on the system and their directions.

As for the question about the force P being applied very slowly, it does not affect the solution in this case. Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Since the mass of the system (9kg + 6kg) remains constant, the maximum force P that can be applied without causing the cylinder to leave body A at point C will also remain constant, regardless of the rate at which the force is applied.

I hope this helps. Keep up the good work!