# Mass sliding down incline with spring

• fireearthair8
In summary: This should give you an equation for d.In summary, the problem involves a 3kg mass sliding down a smooth incline and coming into contact with an unstressed spring with a spring constant of 400N/m. The mass slides an additional 0.2 m after being momentarily stopped by the spring. Using the equations F=ma, Vf = Vi + at, Us = 1/2kx^2, Ug = mgh, and K = 1/2mv^2, the initial separation d between the mass and the spring can be found by equating the work done by the spring to the work done by gravity along the entire distance traveled.
fireearthair8

## Homework Statement

A 3kg mass starts at rest and slides a distance d down a smooth 30deg incline, where it contacts an unstressed spring. It slides an additional 0.2 m as it is brought momentarily to rest by compressing the spring (k=400N/m)

What is the initial separation d between the mass and the spring?

F=ma
Vf = Vi + at
Us = 1/2kx^2
Ug = mgh
K = 1/2mv^2

## The Attempt at a Solution

I'm not sure how to approach this problem yet. I know that you need to find the Vf, using mgsin30 as the acceleration and Vi=0.

Hi fireearthair8,

They give you Vf in the problem statement (the final velocity of that part of the motion they are referring to). What is it? Now that you also know the final speed, does that help you know what approach to use?

Welcome to PF!

fireearthair8 said:
F=ma
Vf = Vi + at
Us = 1/2kx^2
Ug = mgh
K = 1/2mv^2

Hi fireearthair8! Welcome to PF!

Hint: forget F = ma and Vf = Vi + at.

You can do this just using energy (and d = h cos theta).

another hint:

find the work done by the spring, then compare that to the work done by gravity, which acts along the distance traveled without before touching the spring as well as the .2 m after it comes in contact with the spring.

## 1. What is the concept of mass sliding down an incline with a spring?

The concept of mass sliding down an incline with a spring is a classic example of energy conversion and conservation. It involves the gravitational potential energy of a mass sliding down an inclined plane being converted into kinetic energy, and then being stored as elastic potential energy in a spring attached to the mass. This process is governed by the principles of work, energy, and power.

## 2. What factors affect the speed of the mass on the incline?

The speed of the mass on the incline is influenced by several factors, including the angle of the incline, the mass of the sliding object, the coefficient of friction between the object and the incline surface, and the stiffness of the attached spring. A steeper incline and a lighter mass will result in a higher speed, while a higher coefficient of friction and a stiffer spring will slow down the object's movement.

## 3. How does the angle of the incline affect the motion of the mass?

The angle of the incline plays a crucial role in determining the motion of the mass. As the angle increases, the potential energy of the mass increases, resulting in a higher speed. However, if the angle becomes too steep, the frictional force acting on the mass will become significant, slowing down its movement. Therefore, there is an optimal angle at which the mass will slide down the incline with the maximum speed.

## 4. How does the stiffness of the spring affect the motion of the mass?

The stiffness of the spring also affects the motion of the mass. A stiffer spring will store more elastic potential energy, resulting in a higher speed of the mass. On the other hand, a less stiff spring will store less energy, leading to a slower movement of the mass. Therefore, the stiffness of the spring should be carefully chosen to achieve the desired speed of the mass.

## 5. What happens to the energy of the system as the mass slides down the incline?

The energy of the system remains constant as the mass slides down the incline. The potential energy of the mass is converted into kinetic energy as it accelerates down the incline, and then into elastic potential energy as the spring is compressed. When the mass reaches the bottom of the incline, all its potential energy has been converted into kinetic and elastic potential energy, and the total energy of the system remains the same.

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