How High Does the Block Reach on a Moving Ramp?

[datdo]

Difficult: Block sliding up moving ramp

Homework Statement

A block of mass m with initial velocity of v₀ slides up up a ramp of angle $$\theta$$ and mass M that is not pinned to the ground. It doesn't reach the top before sliding back down. What is the highest point that the block reaches in terms on $$\theta$$, v₀, and m. There is no friction between any surfaces.

Homework Equations

$$p = mv$$
$$J=Ft$$
$$E_i=E_f$$

The Attempt at a Solution

$$E_i=E_f$$
$$.5mv_0^2=.5Mv_r^2+mgh$$

$$p_i=p_f+J$$
$$mv_0= Mv_r+Ft$$<-at top height

$$F=mg+mgcos\theta$$<-from standard block on ramp problems

Is this correct?

 

[LowlyPion]

Welcome to PF.

What is I = Ft ? Impulse?

And what do you do with getting rid of F and t?

Maybe consider the conservation of energy as you were starting to do?

1/2mVo² = (horizontal kinetic energy) + m*g*h

Focus on what the horizontal kinetic energy is at the top. And as well express h in terms of the distance up the ramp and θ.

 

[datdo]

I guess I should explain a bit:

First things I thought were energy is conserved but momentum is not due to a external net force but I can still work with momentum if I just figure out the impulse.

$$E_i = E_f$$

$$p_i =p_f +J$$

The problem I'm having is I don't know how to solve for time. Nor do I am I sure what the net force is. I know its due to gravity but I'm not sure how the weight and the normal force cancel.

Basically the question I'm really wondering is what is the impulse of this "collision"

 

[LowlyPion]

I guess I should explain a bit:

First things I thought were energy is conserved but momentum is not due to a external net force but I can still work with momentum if I just figure out the impulse.

$$E_i = E_f$$

$$p_i =p_f +J$$

The problem I'm having is I don't know how to solve for time. Nor do I am I sure what the net force is. I know its due to gravity but I'm not sure how the weight and the normal force cancel.

Basically the question I'm really wondering is what is the impulse of this "collision"

Is there a drawing that shows the block initially traveling horizontally only? Or is the Vo initially directed up the incline?

 

[datdo]

v₀ is completely horizontal

 

[Doc Al]

I guess I should explain a bit:

First things I thought were energy is conserved but momentum is not due to a external net force but I can still work with momentum if I just figure out the impulse.

There's no external horizontal force on the system, so momentum is conserved in that direction. Find the speed of system when the block reaches the highest point, then use LowlyPion's hint in post #2.

 

[datdo]

but the normal force due to the ramp has a horizontal component which is not canceled by any other force.

Also if there were no horizontal force the block would continue moving to the right. Newton's first law.

Also in response to LowlyPion:

Energy is a scalar so you can't take components of it.

 

[Doc Al]

but the normal force due to the ramp has a horizontal component which is not canceled by any other force.

Also if there were no horizontal force the block would continue moving to the right. Newton's first law.

Of course if you look at the block alone, then there's an unbalanced force on it. Instead of doing that, look at the block + ramp as a single system. There are no external horizontal forces on the system, thus the momentum of the system is conserved in that direction.