According to the work-energy theorem, the net work done on an object equals its change in kinetic energy. In the case of a horizontal force and displacement, the work done by the force is equal to the change in the kinetic energy of the object.
Mathematically, the work done by a constant horizontal force F over a displacement d is given by:
W = Fd cos(theta)
where theta is the angle between the force vector and the displacement vector. If the force is horizontal, then theta is 0 degrees, and the cosine of 0 is 1, so the equation simplifies to:
W = Fd
The change in kinetic energy of an object of mass m moving with a velocity v is given by:
ΔK = 1/2 mv^2 - 1/2 mv0^2
where v0 is the initial velocity of the object. If the object starts from rest, then v0 is 0, and the equation simplifies to:
ΔK = 1/2 mv^2
Thus, we can equate the work done by the force to the change in kinetic energy of the object:
W = ΔK
Fd = 1/2 mv^2
This relationship shows that the work done by a horizontal force over a displacement is equal to the change in kinetic energy of the object. If the force and displacement are not perpendicular to the force of gravity, then the gravitational potential energy of the object will also change. In this case, the work done by the force will equal the change in both the kinetic energy and the gravitational potential energy of the object:
W = ΔK + ΔU
where ΔU is the change in gravitational potential energy. The total work done by the force will be the sum of the work done on the object to change its kinetic energy and the work done to change its gravitational potential energy.
*IG:whis.sama_ent