Free moving inclined plane

  • #1

Homework Statement


Consider a small box mass m initially at the bottom of an inclined plane mass M, length L with angle of inclination of [tex]\theta[/tex]. The surface between the plane and the block and the plane and the horizontal are both frictionless. A force F is applied horizontally to the small box. Need to find the time when the small box reached the top of the inclined plane.

Homework Equations




The Attempt at a Solution


I have:
F - Nsin[tex]\theta[/tex] = mam,x
Ncos[tex]\theta[/tex] = mam,y
Nsin[tex]\theta[/tex] = MaM,x

for the relative motion of the small box to the inclined plane:
tan[tex]\theta[/tex] =[tex]\frac{am,y}{am,x - aM,x}[/tex]

then i try to use the distance travelled in y direction, so
1/2 * am,y * t^2 = L sin [tex]\theta[/tex]

I am not sure they are the correct equations.

the answer given is t = [tex]\sqrt{\frac{2L(1+(m/M)(sin\theta)^2)}{(F/m)cos\theta - g(1+m/M)sin\theta}}[/tex]


Thanks for any help given :-)
 
Last edited:

Answers and Replies

  • #2
well i have solved it. thanks for anyone who tried or trying to do this question.

cheers,
weesiang_loke
 

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