Question

W = F s

In this we know
Work done = Force × Displacement

But let me know why do we say this?
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Answer 1

Explanation:

because that is the definition of Work. It is the thing that says what we mean by the label “work” when we use it in physics. The label is arbitrary, and we have this particular one for historical reasons related to the development of Newtonian mechanics.

It’s the kind of reasoning that gives the label “force” to the rate of change of momentum.

It’s a definition.

You know how definitions um work.

It is confusing to me when I think about energy intuitively.

Is your intuition a good guide to truth?

Let me demonstrate why I'm confused.

OK. IT may be that you have misunderstood the concept of energy as it is used in physics. Certainly the words work and energy are used differently in everyday language.

Scenario 1: I have a 1kg object at rest, and apply a 1N force for 1 second. By the time the force has finished acting, velocity is 1 meter per second. Displacement during that time the force acted was 0.5m. Therefore work done is 0.5J.

The work done by whatever agent applied the force was 0.5J… that is, whatever supplied the force lost 0.5J of energy.

Scenario 2: I have a 1kg object which has a velocity of 3 meters per second, with no forces acting on it. If I now apply a 1N force for 1 second in the direction of the motion, velocity is now 4 metres per second, and displacement is 3.5m. Therefore work done is 3.5J. Despite the fact that in both scenarios I have applied the same impulse [Force*Time], the "energy transferred" to the object is different.

Yep.

If you rework it as: Force is the rate of change of momentum, and work is the change in (kinetic, in this context) energy, and impulse is the change in momentum … you get internal consistency between the concepts.

Answer 2

Answer:

When a force acts on an object over a distance, it is said to have done work on the object. Physically, the work done on an object is the change in kinetic energy that that object experiences.

We can validate this statement by performing dimensional analysis, i.e., we can know whether the statement is correct or not by using the units of the physical quantities.

We have claimed that work is the change in kinetic energy of an object and that it is also equal to the force times the displacement. The units of these two should agree. Kinetic energy – and all forms of energy – have units of joules (J). Likewise, force has units of newtons (N) and distplacement has units of meters (m). If the two statements are equivalent they should be equivalent to one another. [Using the property that if a=b and b=c, then a=c]

Therefore, Work Done = Force x Displacement = Change in Kinetic Energy

This implies, $N.m = kg \frac{m}{s^{2} } .m = kg( \frac{m^{2}}{s^{2}} ) = Joules$

If you want to practice your understanding of work done by a constant force, here are some practice problems -

Q1)  Consider a constant force of two newtons (F = 2 N) acting on a box of mass three kilograms (M = 3 kg). Calculate the work done on the box if the box is displaced 5 meters.

Q2) Consider the same box (M = 3 kg) being pushed by a constant force of four newtons (F = 4 N). It begins at rest and is pushed for five meters (d = 5m). Assuming a frictionless surface, calculate the velocity of the box at 5 meters.

HOPE THIS ANSWER HELPS YOU AND NOW YOU UNDERSTAND THE CONCEPT OF WORK DONE BY A CONSTANT FORCE. OF COURSE, THIS TOPIC IS FAR MORE ADVANCED AND IF YOU WANT I WILL BE HAPPY TO EXPLAIN IT :) PLEASE MARK THIS ANSWER AS BRAINLIEST