Solved Examples on Conservation of Energy
Example 1: Find the work done when a force of F = x + 3 produces a displacement of 3 m.
Solution:
Work done by a variable force is given by,
W = ∫Fdx
F(x) = x + 3
Calculating the work done.
W = [Tex]\int^{x}_{0}Fdx \\ = \int^{x}_{0}(x + 3)dx \\ = [\frac{x^2}{2} + 3x]^{x}_{0} \\ = \frac{x^2}{2} + 3x [/Tex]
Here, the displacement is x = 3
W = x2/3 + 4x (at x = 3)
⇒ W = 32/3 + 4(3)
⇒ W = 15 J
Example 2: The work being done on a system is given by the following equation, W = 3t2
Calculate the instantaneous power at t = 4.
Solution:
Instantaneous power is given by,
P = dW/dt
Given: W = 3t2
Calculating power, P = dW/dt
[Tex]P = \frac{d(3t^2)}{dt} [/Tex]
⇒ P = 6t
At, t = 4
P = 6(4)
⇒ P = 24 J
Example 3: The work being done on a system is given by the following equation, W = t3 + 5t + 10
Calculate the instantaneous power at t = 2.
Solution:
Instantaneous power is given by,
P = dW/dt
Given:
W = t3 + 5t + 10
Calculating power,
P = dW/dt
⇒ [Tex]P = \frac{d(t^3 + 5t + 10)}{dt} [/Tex]
⇒ P = 3t2 + 5
At, t = 2
P = 3(t2) + 5
⇒ P = 3(22) + 5 J
⇒ P = 3(4) + 5
⇒ P = 17 J
Example 4: An object is kept at a height of 20m. It starts falling towards the ground. Find the velocity of the object just before it touches the ground.
Solution:
Potential energy at the start will be equal to the kinetic energy just before touching the ground.
P. E = K. E
mgh = 1/2mv2
Given:
g = 10
h = 20 m
Plugging the values inside the equation,
mgh = 1/2mv2
⇒ 2gh = v2
⇒ v = [Tex]\sqrt{2gh} [/Tex]
⇒ v = [Tex]\sqrt{2 \times 10 \times 20} [/Tex]
⇒ v = 20 m/s.
Law of Conservation of Energy
Law of Conservation of Energy is the most fundamental law of physics which states that “Energy can neither be created nor be destroyed it can only change from one form of the energy to another form of the energy.” It is the fundamental law of Physics that governs various processes in our environment.
Before learning deeply about the Law of Conservation of Energy we must know about Energy. Energy is the capacity of the object to do work, It is a physical quantity that allows an object to do different types of work.
Table of Content
- What is Energy?
- What is the Law of Conservation of Energy?
- Law of Conservation of Energy Derivation
- Law of Conservation of Energy Examples
- Application of Conservation of Energy
- Why Can Perpetual Motion Machines Never Work?
- Solved Examples on Conservation of Energy
Let’s learn more about the Law of Conservation of Energy, and others in detail in this article.
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