Block on inclinded plane, and falls

[thomsm10]

Homework Statement

A box of mass M, is falling down a ramp with velocity v1,the ramp is inclined at 60 degrees, the momentum is mv. The force on the box is gcos 30. The time it takes to reach the bottom is t1. Then the box falls off the ramp with a velocity v2, it falls some distance h. The time it falls is t2.

find t1 and t2.

Homework Equations

h = 1/2 at2^2 + v2 sin60t.
Equation of motion Mg-F=ma

The Attempt at a Solution

Now I know by conservation of energy 1/2 Mv1^2 + mgd = 1/2 mv2^2.
and conservation of momentum mv1=mv2
But how am I supposed to get the time out of this?

 

[Simon Bridge]

Welcome to PF;
The problem statement is garbled, and you have not said what you are supposed to find.

Lets see if I've put the clues together:

A box mass m accelerates from rest (at t=0) down a ramp inclined at 60deg to the horizontal, reaching the end of the ramp at t=t1 where it leaves the ramp with speed v(t1)=v1 and falls freely until it strikes a surface at time t=t1+t2 (i.e. from ramp to floor take time interval t2)

Is that about it?

I still cannot tell what you are supposed to find from all that, so I cannot work out what your method is supposed to achieve. I'll just deal with what you wrote.

Now I know by conservation of energy 1/2 Mv1^2 + mgd = 1/2 mv2^2.

You should show your reasoning as well. What is v2 and d here? This is the first time you've mentioned them.

Guessing: if v2=v(t2) then d=h in the description.
Is there a special reason you changed the variable name for the height fallen from h to d?

Presumably you don't have t2, or v1 or v2 ?

But you should have a conservation of energy for the journey down the ramp.

and conservation of momentum mv1=mv2

However - you should notice that total momentum is allowed to change because the box is being acted on by an unbalanced force.

But how am I supposed to get the time out of this?

You need as many equations as you have unknowns.
From what you've written, you only now the angle of the slope (and maybe the acceleration of gravity)? So variables in the problem statement you don't know are: t1, t2, v1, h ...

You can, however, use kinematic equations to help you, since the acceleration is constant in each leg of the journey (a different constant in each leg). For the second, free falling, leg, it may help to divide the motion into horizontal and vertical components.

Hint: ballistics