To perform a work some force should be applied. Without the application of force, no work will be done. The primary requirement for work to be done is the application of force. On the application of force if some displacement of the point of application of force takes place towards the direction of force then some work is done by the force. And work is measured by the product of force and displacement.
Work(W)=Force(F) \(\times\) displacement(d)
Even if a force is applied, no work is considered to be done unless there is a displacement at the point where the force is applied. For instance, applying a strong force to a heavy object without causing any movement results in zero work. Then word will be F \(\times\) 0= 0
W=F \(\times\) d \(\times\) \(\cos \theta\)
[\(\theta\)=Angle between force and displacement]
Displacement should be towards the direction of the force. When displacement is done towards the direction of the force
W= F \(\times\) d \(\times\) \(\cos 0^{o}\)
= F \(\times\) d \(\times\) 1
=F \(\times\) d
If you are walking with a suitcase in your hand on a horizontal path. The angle between force and displacement is \(90^{o}\). In this case, the work done will be
W= F \(\times\) S \(\times\) \(\cos 90^{o}\)
= F \(\times\) S \(\times\) 0
=0
If the force acts perpendicularly with the direction of displacement then no work is done despite occurring some displacement. This force is called no workforce.
Work Done in Favor of Force: Work done in favor of force refers to the work done when the force applied on an object and the displacement of the object occur in the same direction. This means that the force and displacement vectors are aligned, resulting in positive work being done.
Examples of Work Done in Favor of Force:
a) Pushing a box along a flat surface:
When you push a box horizontally, the force you apply and the displacement of the box occur in the same direction. Thus, the work done is positive.
b) Gravity pulling an object downward: When an object falls freely under the influence of gravity, the force of gravity and the displacement of the object are both downward.
Significance of Work Done in Favor of Force: Work done in favor of force represents the transfer of energy to an object. Positive work means energy is added to the object, which leads to a rise in its kinetic energy. This concept is fundamental in understanding the principles of energy conservation and the relationship between force and motion.
Work Done Against Force:
Work done against force refers to the work done when the force applied on an object and the displacement of the object occur in opposite directions. This indicates that the force and displacement act in opposite directions, causing the work done to be negative.
Examples of Work Done Against Force:
a) Slowing down a moving object:
When a force is applied in the opposite direction of an object's motion, the force and displacement vectors are anti-parallel. For instance, when applying brakes to a moving car, the force exerted by the brakes opposes the car's motion, resulting in negative work done against the force of motion.
b) Lifting an object against gravity:
When lifting an object against the force of gravity, the force applied and the displacement of the object are in opposite directions. Here, the work is performed in opposition to gravitational force, which leads to negative work.
Significance of Work Done Against Force:
Work done against force represents the transfer of energy from an object. Negative work occurs when energy is extracted from an object, leading to a reduction in its kinetic energy. This concept is important for understanding situations where forces act in opposition to motion—such as during braking, when encountering resistance, or when working against gravity.
Unit of work:
1. CGS unit is dyne \(\times\) cm= erg
2. SI unit is newton \(\times\) m=N.m= joule(J)
1 J=1N \(\times\) m=\(10^{5}\) dyne \(\times\) \(10^{2}\) cm= \(10^{7}\) erg
Gravitational Unit:
1. 1 gram cm=980.6 erg
2. 1 kg m=9.8 J
Facebook
Twitter
Linkedin