# Potential and Kinetic Energy: Down an incline with spring

• jti3066
In summary, a 4.1 kg block slides down a 26.0 deg incline, encountering a spring with a spring constant of 428 N/m. Using relevant equations, the value of d is found to be 0.213 m. To solve for the distance between the point of first contact and the point where the block's speed is greatest, the equation mgsin()=kx' is used, yielding a distance of 0.162 m.
jti3066

## Homework Statement

A 4.1 kg block starts at rest and slides a distance d down a frictionless 26.0 deg incline, where it runs into a spring. The block slides an additional 18.0 cm before it is brought to rest momentarily by compressing the spring, whose spring constant is 428 N/m .

What is the value of d?..(answered)

What is the distance between the point of first contact and the point where the block's speed is greatest?...(need help)

U = mgh

U = .5k(x^2)

## The Attempt at a Solution

I found the answer to the first question by using the above relevant equations:

U = mgh = .5k(x^2)

4.1 * 9.81 * h = .5 * 428 * (.18^2)

h = 0.172 m

then some trig..

sin(26)=.172/(.18 + d)

d = .213 m

As far as how to solve the second question I am completely lost. At the point of contact with the spring the acceleration should be zero correct. From there would I need to find the intial velocity? We know that V_f = 0, but how to use these "known" quantities in relationship to the block being slowed by the spring is confusing me. I think I'm making this problem more complicated than it really is. TIA for your help.

Last edited by a moderator:
I tried using:

mgh = F_net * delta(x)

0.172 = (mgsin() - .5k(x^2))(.18 - x)

x = .162 m

This approach did not work...

Ok, I found with some help that mgsin()=kx' will get me the correct answer...however I am still confused where this came from...

## 1. What is potential energy?

Potential energy is the stored energy an object has due to its position or state. It is also known as energy of position.

## 2. What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion. It is directly proportional to the mass and velocity of the object.

## 3. How does potential energy change along an incline with a spring?

Potential energy changes along an incline with a spring due to the change in height and compression of the spring. As the object moves down the incline, its potential energy decreases and the spring becomes more compressed, storing potential energy in the spring.

## 4. How does kinetic energy change along an incline with a spring?

Kinetic energy changes along an incline with a spring due to the change in velocity of the object. As the object moves down the incline, its potential energy is converted into kinetic energy, resulting in an increase in its velocity.

## 5. What is the relationship between potential and kinetic energy in this scenario?

In this scenario, potential and kinetic energy are interchanged. As potential energy decreases, kinetic energy increases and vice versa. This is known as the law of conservation of energy, where energy cannot be created or destroyed, only transferred from one form to another.

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