Physics Problem?
An incline plane makes an angle of 30 degrees with the horizontal. Find the constant force, applied parallel to the plane, required to cause a 15kg box to slide (a) up the plane with acceleration 1.2m/s^2 and (b) down the incline with acceleration 1.2m/s^2. Neglect friction forces.
I've been on this problem for about an hour now, and I haven't made any progress. I've looked through my notes and even found the answers in the book, but I haven't been able to find the way to finish the problem. Any help would be greatly appreciated.
Answer
solution
F̂ᵣₑ = mâ
acceleration of 1.2 m/s² up the plane:
F - 15gsin30° = 15a = 15(1.2)
=> F = 4.905(15) + 18 = 78.75 N
acceleration of 1.2 m/s² down the plane:
assuming F is directed parrallel to the plane downwards
F + 15gsin30° = 15a = 15(1.2)
=> F = 18 - 4.905(15) = - 42.75 N
this is a restraining (holding back) force in the direction up the plane so as to slow the acceleration of the box to 1.2 m/s² down the plane
hope this helps