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## 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**-

**N**sin[tex]\theta[/tex] =

**m**

**a**

_{m,x}

**N**cos[tex]\theta[/tex] =

**m**

**a**

_{m,y}

**N**sin[tex]\theta[/tex] =

**M**

**a**

_{M,x}

for the relative motion of the small box to the inclined plane:

tan[tex]\theta[/tex] =[tex]\frac{

**a**

_{m,y}}{

**a**

_{m,x}-

**a**

_{M,x}}[/tex]

then i try to use the distance travelled in y direction, so

1/2 *

**a**

_{m,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{2

**L**(1+(

**m**/

**M**)(sin\theta)^2)}{(

**F**/

**m**)cos\theta - g(1+

**m**/

**M**)sin\theta}}[/tex]

Thanks for any help given :-)

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