(See attached file for full problem description with diagram and equations)
The acceleration of a block of mass that is pulled up a frictionless plane inclined at angle with respect to the horizontal by a perfect string that passes over a perfect pulley to a block of mass that is hanging vertically.
Visualize the problem and identify special cases
First examine the problem by drawing a picture and visualizing the motion. Apply Newton's 2nd law, , to each body in your mind. Don't worry about which quantities are given. Think about the forces on each body: How are these consistent with the direction of the acceleration for that body? Can you think of any special cases that you can solve quickly now and use to test your understanding later?
One special case in this problem is if , in which case block 1 would simply fall freely under the acceleration of gravity: .
A) Consider another special case in which the inclined plane is vertical ( ). In this case, for what value of would the acceleration of the two blocks be equal to zero?
Express your answer in terms of some or all of the variables and .
This solution addresses the questions with concepts of inclined planes, sum of forces on a force body diagram and also the direction of forces on a vertical and horizontal plane. All identified answers are justified with explanations.