91Ó°ÊÓ

Work, in physics, measures the energy transfer that occurs when an object is moved over a distance by an external force.

Kinetic energy, a form of energy that an object or a particle has by reason of its motion.

(a)

The work here is negative, where the displacement direction is upward while the force direction is downward. Hence, as the displacement and the force are in the opposite direction, therefore the work is negative where the angle between both elements is${180}^{∘}$and$\cos {180}^{∘}=-1$

$W=F.â–³r\cos {180}^0=-F.â–³r$

Also, the kinetic energy of the object decreases as the work is negative.

(b)

The work here is positive, where the displacement and the force directions are downward. Hence, as the displacement and the force are in the same direction, therefore, the work is positive where the angle between both elements is $0^{∘}$and $\cos 0^0=+1$

$W=F.â–³r\cos 0^0=F.â–³r$

Also, the kinetic energy of the object increases as the work is positive.

(c)

The work here is negative, where the displacement direction of the car is to left while the force direction is to right. Hence, as the displacement and the force are in the opposite direction, therefore, the work is negative where the angle between both elements is $0^{∘}$ and role="math" localid="1668514521583" $\cos {180}^{∘}=-1$.

$W=F.△r\cos {180}^{∘}=-F.△r$

Also, the kinetic energy of the object decreases as the work is negative.

(d)

The work here is positive, where the displacement and the force directions are downward. Hence, as the displacement and the force are in the same direction, therefore, the work is positive where the angle between both elements is $0^{∘}$ and $\cos 0^{∘}=+1$.

$W=F.â–³r\cos 0^0=F.â–³r$

Also, the kinetic energy of the object increases as the work is positive.

(e)

The work here is zero, the force here is perpendicular to the orbit of the earth and has no effect on the displacement of the earth. Where circular orbit under the influence of the earth's gravitational force, which always acts perpendicular to the motion if the orbit is a circle.