How is the work energy theorem represented as an equation?
The work-energy theorem relates the work done on an object to its change in kinetic energy. Mathematically, it can be represented by the following equation:
Work = Change in Kinetic Energy
In terms of equations, it can be expressed as:
W = ΔKE
where:
W represents the work done on the object,
ΔKE represents the change in kinetic energy.
The work-energy theorem is represented by the equation:
W = ΔKE
Here, W represents the work done on an object, ΔKE represents the change in kinetic energy of the object.
To understand how to derive this equation, it’s helpful to know that work done on an object can be represented by the formula:
W = F * d * cos(θ)
where W is the work done on an object, F is the applied force, d is the displacement of the object, and θ is the angle between the force vector and the displacement vector.
Now, for the work-energy theorem, we start with the concept of work done on an object as the transfer of energy. When work is done on an object, it results in a change in its kinetic energy.
The equation for kinetic energy is:
KE = 0.5 * m * v^2
where KE is the kinetic energy, m is the mass of the object, and v is the velocity of the object.
Considering a situation where an object starts from rest and accelerates to a final velocity v, we can use the equation for work done to solve for the change in kinetic energy:
W = F * d * cos(θ)
Since the object starts from rest, we can express the final velocity v in terms of the acceleration a:
v^2 = u^2 + 2ad
where u is the initial velocity of the object.
Rearranging the equation, we get:
2ad = v^2 - u^2
Now, substituting this value of 2ad in the equation for work done:
W = F * (v^2 - u^2) / (2a)
Since the object starts from rest (u = 0), the equation simplifies to:
W = F * v^2 / (2a)
We can rewrite the force F as mass times acceleration (F = ma):
W = m * a * v^2 / (2a)
Simplifying further, the acceleration cancels out:
W = 0.5 * m * v^2
Finally, we can substitute the change in kinetic energy as ΔKE in the equation:
W = ΔKE
Thus, the work-energy theorem is represented by the equation W = ΔKE.
The work energy theorem can be represented as an equation as follows:
W = ΔK + ΔU
where W is the work done on an object, ΔK is the change in kinetic energy, and ΔU is the change in potential energy.