# Finding how high up object travels

## Homework Statement

A block of inertia m is launched up a rough incline by a spring,
as shown in the ﬁgure. The coeﬃecient of kinetic friction is µk.
The angle of incline is θ, and the spring is parallel to the surface
of the incline. The spring constant is k, and the spring has been
compressed a distance d from its relaxed position. How far up the
incline, from the point of release, does the block travel before it
stops?

## Homework Equations

Im thinking of using the potential energy equation

## The Attempt at a Solution

Since its asking how far up, i would assume that we need to separate h in the potential energy equation, but this question really threw me off. How am I supposed to start with no numbers really?

PeterO
Homework Helper

## Homework Statement

A block of inertia m is launched up a rough incline by a spring,
as shown in the ﬁgure. The coeﬃecient of kinetic friction is µk.
The angle of incline is θ, and the spring is parallel to the surface
of the incline. The spring constant is k, and the spring has been
compressed a distance d from its relaxed position. How far up the
incline, from the point of release, does the block travel before it
stops?

## Homework Equations

Im thinking of using the potential energy equation

## The Attempt at a Solution

Since its asking how far up, i would assume that we need to separate h in the potential energy equation, but this question really threw me off. How am I supposed to start with no numbers really?

One way to solve the problem is to set up your own, similar, problem with numbers and solve that, then have a careful look at how you used each value, and replace then with the algebra here.

As an overview: in the beginning there is energy stored in the spring.
Upon release, that will convert to kinetic energy as well as a small amount of gravitational Potential Energy [as the spring expands the mass moves slightly higher up the slope] as well as a little bit of mechanical energy being lost [converted mainly to heat] as the mass moves against friction as the spring expands.
Once the mass leaves the spring, the kinetic energy will be converted to even more Potential energy, with some more mechanical energy lost in overcoming friction as it moves.
This second "conversion phase" means you never actually have to calculate the kinetic energy value.

It kind of makes sense. When you talk about kinetic energy, I had someone of a similar problem in which it asked to find how high this object jumped, and I think to calculate the answer I used h=-Δk/mg. Is this what I should sort of end up getting as well?

PeterO
Homework Helper
It kind of makes sense. When you talk about kinetic energy, I had someone of a similar problem in which it asked to find how high this object jumped, and I think to calculate the answer I used h=-Δk/mg. Is this what I should sort of end up getting as well?

You do use that but have to allow for the energy lost through friction as the mass moves up the slope. The distance it moves along the slope is far greater than the height gained since this is a slope, not a vertical displacement.

Alright! ill just keep looking into it, thanks :)