Law of Conservation of Energy

In summary, the problem involves a 2.0 kg load with an initial velocity of 0.65m/s sliding down an inclined plane with a coefficient of friction of 0.30. Using the given data and equations, the force of friction and work against friction are calculated. To find the final velocity, the constant acceleration equation is used, resulting in the correct value.
  • #1
andorei
37
0

Homework Statement



A 2.0 kg load has an initial velocity of 0.65m/s. If a frictional force acts to slow it down, how fast is it sliding down the inclined plane just before it reaches the ground? The coefficient of friction between the load and the inclined is 0.30.

Given/Known Data:
M: 2.0 kg
Velocity (Initial): 0.65m/s
Coefficient: 0.30

Homework Equations



f=[itex]\mu[/itex]Fn
f=[itex]\mu[/itex]Wy
f=[itex]\mu[/itex]mg(cos[itex]\Theta[/itex])

The Attempt at a Solution


=(0.30)(2.0kg)(9.8m/s2)(cos 30)
= 0.30 (19.6N) 0.866
= 5.88N(.866)
= 5.09208N

Workagainstfriction
= 5.09208(2m)
= 10.18416Nm
= 10.18416J

ΔKE = 1/2mv^2 - 1/2mv^2 <--- This is the part where I screw up.

Any help will do. Thanks
 
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  • #2
Erm, in your workings:
5.09208(2m) which I assume is force x distance, correct? Where did you get the value of distance from? Then I might be able to help.
 
  • #3
This is the hypotenuse I got from the triangle formed by the height given which is 1m and the angle 0.30 degrees. So the 2m is where the load slides down.
 
  • #4
From that, I'd assume constant acceleration. Find the decceleration due to the frictional force, and apply one of the constant acceleration equations, you should get the correct value, don't really know why you're using Work and Kinetic Energy.
 
  • #5


The Law of Conservation of Energy states that energy cannot be created or destroyed, only transferred from one form to another. In this problem, the initial kinetic energy of the load is being converted into work against friction, which is then being converted into potential energy as the load slides down the inclined plane. Therefore, we can use the equation for conservation of energy to solve for the final velocity of the load just before it reaches the ground.

Initial kinetic energy = Final potential energy
1/2mv^2 = mgh
Where m is the mass of the load, v is the final velocity, g is the acceleration due to gravity (9.8m/s^2), and h is the height of the inclined plane.

Substituting the given values, we get:
1/2(2.0kg)v^2 = (2.0kg)(9.8m/s^2)(2m)
Simplifying, we get:
v^2 = 19.6m^2/s^2
Taking the square root of both sides, we get:
v = 4.43m/s

Therefore, the load will be sliding down the inclined plane with a final velocity of 4.43m/s just before it reaches the ground.
 

1. What is the Law of Conservation of Energy?

The Law of Conservation of Energy states that 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 over time.

2. Why is the Law of Conservation of Energy important?

This law is important because it helps us understand and predict how energy behaves in various systems. It also allows us to make calculations and solve problems related to energy.

3. How is the Law of Conservation of Energy related to the First Law of Thermodynamics?

The First Law of Thermodynamics is a specific application of the Law of Conservation of Energy in thermodynamic systems. It states that energy cannot be created or destroyed in a thermodynamic process, but can only be transferred from one form to another.

4. Can the Law of Conservation of Energy be violated?

No, the Law of Conservation of Energy is a fundamental law of nature and has been tested and proven to hold true in all observed cases. If it appears to be violated, it is due to a lack of understanding or accounting for all the energy involved in a system.

5. How does the Law of Conservation of Energy apply to everyday life?

The Law of Conservation of Energy applies to everyday life in many ways. For example, when we turn on a light switch, the electrical energy is converted into light and heat energy. When we ride a bike, our body's chemical energy is converted into kinetic energy. Understanding this law can help us make more sustainable choices and conserve energy in our daily activities.

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