Conceptual Dynamics - Independent Learning

Applying Newton's Second Law - Example Problem 5.6-7

 

A 200-lb crate is placed on a θ = 30 degree incline and a horizontal force F is applied in an attempt to push the crate up the incline. Determine the resulting acceleration of the crate if a) F = 0, b) F = 150 lb and c) F = 400 lb. The crate is made from wood and the inclined ramp is made from metal. Estimate the friction characteristics as μs = 0.5 and μk = 0.3.

 

 

Given:
  • W = 200 lb
  • θ = 30o
  • μs = 0.5
  • μk = 0.3

 

Find: a for the following cases
  1. F = 0
  2. F = 150 lb
  3. F = 400 lb

 

Video solution:

 

The following video walks you through the solution to this problem. It is suggested that you try solving the problem first and then, if you have difficulties with the solution, watch the video for help.

 

 

Interactive solution:

 

For each of the force conditions, we need to determine ...

  1. if the crate is moving.
  2. if the crate moves, is it moving up or down?

 

Draw 2 free-body diagrams of the crate. One for pushing up or intending to be pushed up the ramp, and one for sliding down or intending to slide down the ramp.

 

 

 

 

The normal force for both cases is the same. Applying Newton's first law (∑F = 0) in the y-direction, determine the normal force?

 




 

 

 

Applying Newton's second law (∑F = ma) in the x-direction, determine the equation of motion for the sliding down case.

 




 

 

 

Applying Newton's second law (∑F = ma) in the x-direction, determine the equation of motion for the pushing up case.