# Cinservatuon of energy icline and spring problem

• theyo
In summary, the problem involves a 3.20 kg block sliding down a frictionless 30.0° incline and colliding with a spring with a spring constant of 430 N/m. The block slides an additional 19.5 cm before coming to a stop due to the compressed spring. The question asks for the value of d and the distance between the point of first contact and where the block's speed is greatest. Using conservation of energy, the solution can be found by setting mgh equal to .5kx^2. The final answer for d is 8.175 m, and the distance between the points is unknown.
theyo
1. Homework Statement

A 3.20 kg block starts at rest and slides a distance d down a frictionless 30.0° incline, where it runs into a spring (Fig. 8-6). The block slides an additional 19.5 cm before it is brought to rest momentarily by compressing the spring, whose spring constant k is 430 N/m.

(a) What is the value of d?

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

## The Attempt at a Solution

You must attempt at a solution.

Since you know energy is conserved. Can you list what energy type of energy is started with and end with?

i did mgh=.5kxsquared

and the found 31.36h=8.175 but that is wrong and i know m should be less than 1 b/c that would make sense

It didn't ask you to find height. It asked you to find distance that it travels.

I don't know what you mean by m < 1. m as in mass?

## What is the conservation of energy principle?

The conservation of energy principle states that energy cannot be created or destroyed, but it can be transferred or transformed from one form to another.

## What is the relationship between energy and a spring?

A spring has potential energy when it is compressed or stretched, and this potential energy can be converted into kinetic energy when the spring is released or stretched. This is known as the spring potential energy problem.

## How do you calculate the potential energy of a spring?

The potential energy of a spring can be calculated using the equation PE = 1/2kx^2, where k is the spring constant and x is the displacement from the equilibrium position.

## What is the role of gravity in the conservation of energy principle?

Gravity is a force that can do work on an object, which can then be converted into different forms of energy. In the case of a spring, gravity can do work on the object to compress or stretch the spring, resulting in potential energy.

## How is the conservation of energy principle applied to a spring problem?

In a spring problem, the conservation of energy principle is applied by equating the initial potential energy of the compressed or stretched spring with the final kinetic energy of the released or stretched spring. This can be represented by the equation PEinitial = KEfinal.

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