Solving Incline Plane Problems: A Step-by-Step Guide

[pinky2468]

The homework problem is confusing me a little bit especially b and c.
I have attached the picture of the incline plane and object.

Based on figure #1, assume the block is sliding down the inclined plane and that there is kinetic friction associated with the block and plane. Label all force vectors.

B.Write a mathematical expression for all force vectors ensure that you use the proper sign.

C.Using the mathematical expressions derived in step B derive an expression for the downward acceleration of the block.

 

[Sirus]

Identifying and labeling force vectors is a skill you will need to master in physics. Try to find all the forces acting on the mass on the inclined plane. Then simply label each vector (indicating the direction of the force). For B, try to define each vector in terms of what you are given: theta, m, and the coefficient of friction. This is an essential skill in inclined plane problems, so make sure you understand it. You should be able to get C after that.

 

[pinky2468]

That one I understand, but this ine involves 2 unknowns. I want to make sure I derived the right formulas:
Two blocks are connected by a cable via a pulley which are massless and frictionless.
Given the following: m1 = 300.0 kg, m2 = 100.0 kg, theta=40.0 ,uk=.350, determine:
a.The direction of acceleration (mathematically no guesses)
b.The value of the acceleration
c.The tension in the cable

So: a=m1g(-sintheta-ukcostheta)+m2g/m1+m2

-m1g(sintheta)+T-uk(costheata)=m1a

 

[Sirus]

You will have to show your work more clearly (start with basic equations then substitute stuff and the develop the work). The best way to do pulley questions is to spread the pulley horizontally as if it were on a table, then draw force vectors for all the forces present. Apply $F_{net}=ma$ after that.

 

[pinky2468]

To be honest I am not sure how I got to these equations. We worked on them in class and my teacher gave us these as the final equations(he does have a tendency to mess up though!) I am assuming it is going up the plane and I am pretty sure that the accelearation equation is right but not the tension equation

 

[maverick280857]

To be honest I am not sure how I got to these equations. We worked on them in class and my teacher gave us these as the final equations(he does have a tendency to mess up though!) I am assuming it is going up the plane and I am pretty sure that the accelearation equation is right but not the tension equation

The easiest way to avoid making mistakes is to follow the steps mentioned below:

1. Draw a freebody diagram.
2. Chose a mutually orthogonal pair of directions along which you will resolve the forces.
3. Resolve the forces by drawing their components along the chosen directions (for an incline, usually the best choice is to take directions parallel to the incline and perpendicular to it).
4. Show clearly how the normal reaction and friction (if any) forces act on the body. If there are ropes you might want to set up their constraint equations to help you with the acceleration of any mass in the system.
5. Write the equations of motion as mentioned by Sirus and solve them for the parameter(s) in question.

Cheers
Vivek