# How Is Energy Conservation Used to Calculate Sliding Distance on an Incline?

• minimax
In summary, a block with a mass of 8.7kg slides down a hill with an initial velocity of 1.66m/s at an angle of 27.4 degrees. The friction coefficient between the block and hill is 0.62. By using components and kinetics, the distance the block slides down the hill is calculated to be 1.56m. However, the equation could also be solved using energy conservation, where the initial kinetic energy is equal to the work done by gravity and friction. This method also yields a distance of 1.56m. It is important to understand and use the correct methods in solving such problems.
minimax

## Homework Statement

A block with a mass of 8.7kg slides down a hill with an angle of 27.4 degrees at an initial velocity of 1.66m/s. The friction uk between the block and hill is 0.62. What is the distance the block slides down the hill?

I solved the equation using components and kinetics, but I'm not quite sure how to solve it using energy conservation.

## Homework Equations

For energy:
I know
initial energy=final energy
KE+PE= ? +ukNx ?

## The Attempt at a Solution

Here is my work solving it with components
N(0,1)+mg(sin27.4, -cos27.4)+ukN (-1,0)=ma (1,0)
N=mgcos27.4

a=gsin27.4-ukmgcos27.4
=-.89m/s^2

Vf^2=Vi^2+2ad
d=-vo^2/2a
d=1.56m

hopefully doing it this way is also right. Thank you for any help!

> a=gsin27.4-ukmgcos27.4

m shouldn't be there.

Oops, looks like i made a typo. but regardless of that the acceleration is still -0.89m/s^2

however, I'm still pondering on how to do this que with energy conservation.

KE-Wf=0?

Initial KE + difference of PE_grav between initial and final positions = work done against friction = frictional force*distance.

KE_f - KE_i = Work by gravity + Work by friction
0 - KE_i = Work by gravity + Work by friction
- 0.5 m * (1.66)^2 = (m * 9.81 * sin 27.4 - m * 9.81 * 0.62 * cos 27.4)*ans
ans = 1.56 m

Sorry, I wouldn't be able to explain any concepts behind what I did: use geometry and FBDs.
But, this is the way you should be doing this; if you keep doing these questions
your way, you will be in a big mess one day (maybe on your exam day)

## What is the concept of energy?

The concept of energy is the ability of a system to do work. It is a scalar quantity that can exist in different forms such as kinetic, potential, thermal, chemical, and electrical energy.

## What is the relationship between energy and motion?

Energy and motion are closely related. When an object is in motion, it possesses kinetic energy. The amount of kinetic energy depends on the mass and velocity of the object. On the other hand, energy can also cause motion, as seen in the case of potential energy being converted into kinetic energy.

## What is an inclined plane?

An inclined plane is a flat surface that is tilted at an angle. It is commonly used to reduce the effort needed to lift an object by increasing the distance over which the force is applied.

## How does energy affect an object on an inclined plane?

When an object is placed on an inclined plane, the force of gravity acting on it is not directed straight down but is now split into two components – one parallel to the plane and one perpendicular to the plane. The component parallel to the plane causes the object to move down the slope, while the component perpendicular to the plane is balanced by the normal force of the plane. The potential energy of the object will decrease as it moves down the slope, and its kinetic energy will increase.

## What is the formula for calculating the potential energy of an object on an inclined plane?

The formula for calculating the potential energy of an object on an inclined plane is PE = mgh sinθ, where m is the mass of the object, g is the acceleration due to gravity, h is the height of the object above the ground, and θ is the angle of inclination.

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