In physics, the work done by a force is a fundamental concept that relates to how forces affect the motion of objects. When a force (
f) acts on an object and causes it to move a certain distance (
s), the relationship can be expressed as:
w = f × s
Here, w represents the work done, f is the applied force, and s is the displacement in the direction of the force.
Now, to show that the work done (w) results in a change in kinetic energy (k), we can reference the work-energy theorem. This theorem states that the work done by the net force acting on an object is equal to the change in its kinetic energy:
w = Δk
Where Δk is the change in kinetic energy, defined as:
Δk = k_final – k_initial
To understand this deeper, consider an object that starts from rest and is subjected to a constant force causing it to accelerate. According to Newton’s second law:
f = m × a
Here, m is the mass of the object and a is the acceleration. The displacement under constant acceleration can be expressed using the kinematic equations. For an object starting from rest:
s = (1/2) × a × t²
After some time, its final velocity (v) can be found using:
v = a × t
The kinetic energy (
k) of the object is given by:
k = (1/2) × m × v²
Substituting the expression for v gives:
k = (1/2) × m × (a × t)² = (1/2) × m × a² × t²
Combining this with our earlier equations and the relationship between s and a, we can express the work done as:
w = f × s = (m × a) ×
s = m × a ×
s = m × a × (1/2) × a × t²
This shows that the work done on the object is converted into kinetic energy. Hence, we can conclude that:
In summary, work done by a force results in a change in the kinetic energy of an object, confirming:
w = Δk