How Do You Calculate Forces on an Inclined Plane with a Frictionless Pulley?

[physixnot4me]

This is the question I was given a homework assignment:

2) Two objects are connected by a light string that passes over a frictionless pulley. Draw a Free Body Diagram of both objects. If the inclide is frictionless and if m1= 2kg, m2=6kg and angle theta=55 degrees, find:
(a) the accelerations of the objects
(b) the tension in the string
(c) the speed of each object 2 sec after being released from rest.

**my question is: is the acceleration for both objects the same, just different directions?**

how do you incorporate the theta 55 degrees into this question?

 

[Diane_]

Yes, the acceleration will be the same. In these problems, unless stated otherwise, we typically assume the string doesn't stretch.
As for the 55 degree angle, well, think about it. When you draw the FBD, you're going to have some forces that act parallel to the plane, some that act normal to it, and some that are at some angle. You're going to need to resolve them so you have them all following some arbitrary set of axes - you'll need the angle then. Right?

Edit: About the accelerations - reconsider the "opposite directions" thing. It depends partly on how you're defining the directions, but if you pull on one object, which way will the other one move?

 

[quicknote]

I would respond by saying that yes, the acceleration for both objects will be the same, but in opposite directions. This is due to Newton's Second Law, which states that an object's acceleration is directly proportional to the net force acting on it and inversely proportional to its mass. Since both objects are connected by a light string, they will experience the same net force and therefore have the same acceleration.

To incorporate the angle theta of 55 degrees into this question, we need to consider the components of the forces acting on the objects. The weight of each object can be broken down into its x and y components, where the x component is equal to the weight multiplied by the cosine of the angle and the y component is equal to the weight multiplied by the sine of the angle. These components will affect the net force and thus the acceleration of the objects. Additionally, the angle theta will also affect the tension in the string, as it will determine the magnitude of the force pulling on the string. Overall, the angle theta is an important factor to consider when solving for the acceleration, tension, and speed of the objects in this system.