# Work done by force applied for an instant

We know $${\rm work} = \int F \cdot dl$$ , where $$dl$$ is the displacement of point of application of force.

Suppose I apply an instant force of $$100~\rm N$$ on a body and then remove the force; after that the body moves a distance $$d$$. When the body is moving there is no external force (other than friction, $$mg$$, normal reaction force). So what is the work done by $$100~\rm N$$ force?

Is is zero? Because when the body moved distance $$d$$, the $$100~\rm N$$ force was not there.

• If we draw a free body diagram while the body is moving, there will be only forces like mg, normal,air drag and no external force, so where is the work done by that force??I am just confused a lot Jun 9, 2018 at 6:38
• In the formula $W=\vec{F} . \vec{l}$ , $l$ is zero , cause it is the distance traversed as long as $F$ acts ... Jun 9, 2018 at 8:28
• Thanks , thats a perfect reply.dl should be calculated as long as F acts. Jun 9, 2018 at 8:49

$d=0$ in your example, because the work is zero and so the kinetic energy of the body is zero. A finite force applied for an instant doesn't do any work.

• I explain my question further.Suppose a 100 N force is applied on a body and due to this 100 N force, body moves 10 m. After moving 10 m, the 100 N force is removed, and body moves 5 m further before coming to rest. what is the work done by the 100 N force :;; W=100*10=1000 J or W= 100 *(10+5)=1500 J. please guide Mr Chris Jun 9, 2018 at 8:57
• It's $1000 J$ work ... Jun 9, 2018 at 9:37

The work done by the force would be F*d, where d is the distance it travels WHILE the force is still being applied. The work done by the force provides the block some kinetic energy, i.e its velocity. Since the block is coming to a halt, friction or other drag forces must be acting on the body. The work done by these drag forces dissipates the kinetic energy of the block in form oh heat/sound and bring it to a halt.

Work done = Force being applied on the body * displacement is travels while is the force is still present on the body.

Therefore , Force applied when removed after certain moment becomes 0 on the body. We won’t consider the displacement it travels because that is not the distance it travelled while the force was present on the body.

Therefore , W = 0 but we can also say that work done would be wrong to calculate for such a moment which can be said as not defined.