What is the acceleration of boxes as they move down the incline?

Question

A taut massless string connects two boxes. The boxes are placed on an incline plane at θ = 33.0⁰. What is the acceleration of boxes as they move down the incline, given m₂ = 1.0 kg, m₁ = 7.8 kg, μ₂ = 0.10 and μ₁ = 0.20. 

Answer 1

Kristyn;

You have posted quite a few problems that are closely related. Here is the general procedure to follow (whereever possible, draw a picture to see the relationships:

1. For each object with mass, draw the vector for the force of gravity. This is always straight down, and the magnitude is the mass times the acceleration of gravity (g = 9.8msec^-1)
2. For any object resting on an incline (AKA ramp), calculate (or write an expression) for the components of the force of gravity. One component is in-line with the incline, and the other is normal (perpendicular) to the incline. I call these the tangential and normal components. EXAMPLE: A 10kg block is on a 30^o incline. The force of gravity is 98 Newtons and the components are:
3. normal: 98cos(30)
4. tangential: 98sin(30)
5. Draw the force diagram for each relevant object. The components include:
6. The normal force (and the equal and opposite reaction force from the support)
7. The tangential forces, which include the tangential component of the force of gravity, and--as needed---the friction force, which is the normal force times the coefficient of friction.
8. Recognize that each object will accelerate in response to a net force (in the direction where motion is possible). The net force is typically the sum of a tangential force, a friction force, and perhaps a force from a rope or maybe someone pushing on the object. Once you have the net force, you get the acceleration of the object from F = ma.
9. The above steps either yield numbers---or just a set of equations that capture all the supplied information given. The final step is the arithmetic.

If you apply this general procedure to each of your problems, and post a picture labelled with your results, then someone will be able to spot any errors or omissions and give you further guidance.