# Easy Conservation of Energy Problem

• BioBabe91
In summary: F⋅D=|F||D|cosφ=0so no work would be done.In summary, the skier of mass 55.0 kg slides down a slope 11.7 m long, inclined at an angle θ to the horizontal. The magnitude of kinetic friction is 41.5 N. The skier's initial speed is 65.7 cm/s (0.657 m/s) and the speed at the bottom of the slope is 7.19 m/s. By using the law of conservation of energy and substituting in the given values, the angle θ cannot be solved for because the work done by kinetic friction is taken over the length of the incl
BioBabe91

## Homework Statement

A skier of mass 55.0 kg slides down a slope 11.7 m long, inclined at an angle θ to the horizontal. The magnitude of kinetic friction is 41.5 N. The skier's initial speed is 65.7 cm/s (0.657 m/s) and the speed at the bottom of the slope is 7.19 m/s. Determine the angle θ from the law of conservation of energy. Air resistance does not matter.

## Homework Equations

Ek = 1/2*m*v^2
Eg = mgh
Ethermal = W = Fk*cosθ*Δd

## The Attempt at a Solution

Eth= Fk*cosθ*Δd
Substituted in the values, then used conserv. of energy:
mgh + 1/2*mv^2 = 1/2*mv^2 + Eth
where h = 11.7/sinθ.
But I got stuck solving for the angle. Where did I go wrong?

Welcome to PF.

I think the work from the kinetic friction is taken over the length of the incline because the cosφ relative to the motion of the skier is 0, along the plane of the slope, not the angle θ of the incline.

Otherwise, I think you have the right idea.

That's true. But in what cases would cosφ not be equal to 0, for future questions like this?

Thanks.

BioBabe91 said:
That's true. But in what cases would cosφ not be equal to 0, for future questions like this?

Thanks.

For friction I'd guess that the angle φ is usually always 0, if it acts against the direction of motion. Now on circular motion problems, friction that would be say keeping a car from sliding down an incline would contribute no energy loss because there the friction would be at 90°

Work = F ⋅ D

(which is the dot product if you are familiar with vectors)

## 1. What is the concept of conservation of energy?

Conservation of energy is the principle that states energy cannot be created or destroyed, but can only be transformed from one form to another. This means that the total amount of energy in a closed system remains constant.

## 2. How is energy conserved in an easy conservation of energy problem?

In an easy conservation of energy problem, the total amount of energy before and after the transformation remains the same. This means that the initial and final energy states of the system must be equal.

## 3. What are some common examples of conservation of energy in everyday life?

Some common examples of conservation of energy in everyday life include turning on a light bulb (electrical energy to light energy), using a battery-powered device (chemical energy to electrical energy), and using a spring to launch a toy car (potential energy to kinetic energy).

## 4. How does conservation of energy relate to the first law of thermodynamics?

The first law of thermodynamics states that energy cannot be created or destroyed, but can only be transferred or converted. This is directly related to the concept of conservation of energy, as it also states that the total amount of energy in a closed system remains constant.

## 5. What are the implications of violating the principle of conservation of energy?

If the principle of conservation of energy is violated, it would imply that energy is being created or destroyed, which goes against the fundamental laws of physics. This would also lead to inconsistencies in calculations and predictions, making it important to always consider the conservation of energy in scientific problems.

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