Question

In each of the following cases state whether the work done by the specified force is positive, negative or zero. Also state whether the kinetic energy of the object in question increases, decreases or remains the same.

(a) A ball is moving upward, acted on by a downward gravitational force.

(b) A ball is falling downward, acted on by a downward gravitational force.

(c) A car is moving rapidly to the left and Superman exerts a force on it to the right to slow it down, backing up to the left as he pushes to the right.

(d) You throw a ball downward. Consider the force exerted by your hand on the ball while they are in contact.

(e) In a 6 month period the Earth travels halfway around its nearly circular orbit of the Sun. Consider the gravitational force exerted on the Earth by the Sun during this period.

Short answer

(a). Work done by the specified force is Negativeand the Kineticenergy of the object decreases.

(b). Work done by the specified force is Positiveand the Kinetic energy of the object Increases.

(c). Work done by the specified force is Negativeand the Kineticenergy of the object decreases.

(d). Work done by the specified force is Positiveand the Kinetic energy of the object Increases.

(e). Work done by the specified force is Zero and Kinetic energy of the object is Zero.

Step-by-step solution

Definition of Work and Kinetic energy

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.

Relation between kinetic energy and work

(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${180}^{\circ }$and$\cos {180}^{\circ }=-1$

$W=F.△r\cos {180}^0=-F.△r$

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

Relation between kinetic energy and work

(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 $0^{\circ }$and $\cos 0^0=+1$

$W=F.△r\cos 0^0=F.△r$

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

Relation between kinetic energy and work

(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 $0^{\circ }$ and role="math" localid="1668514521583" $\cos {180}^{\circ }=-1$.

$W=F.△r\cos {180}^{\circ }=-F.△r$

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

Relation between kinetic energy and work

(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 $0^{\circ }$ and $\cos 0^{\circ }=+1$.

$W=F.△r\cos 0^0=F.△r$

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

Relation between kinetic energy and work

(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.