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We define force as an external effort in the form of push or pull; it can do things like:

Produce motion in a body at rest.

Stops or tries to stop a moving body.

Change the direction of motion.

Change the shape of a body.

According to Newton’s first law of motion, a body continues to be in a state of rest or motion unless an external force is applied to it.

For example, when we push a ball lying on the road, it starts rolling. The force applied produces motion in the ball.

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According to Newton’s second law of motion, the change in linear momentum per unit time is directly proportional to the external force applied to the body. This change always occurs in the direction of motion.

⇾ ⇾ ⇾ ⇾

dp/dt α F or F α dp/dt

⇾ ⇾

F = k.dp/dt

=> k is a proportionality constant.

⇾ ⇾

F = k.m a….(1)

Here a = dv/dt represents the acceleration of the body.

Substituting the value of k = 1 in eq(1):

⇾ ⇾

F = ma….(2)

If an acceleration produced in three dimensions, having components ax, ay, az along X, Y, and Z-axis respectively, then

a = iax + jay + kaz

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∵ F = ma

F = m(iax + jay + kaz)

If Fx, Fy , Fz are the components along X, Y and Z-axis, respectively.

Then, F = iFx + jFy + kFz

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We obtain:

F = max, F = may ,and F = maz

As acceleration is a vector quantity, mass, a scalar quantity.

∴ F is the product of m and a is a vector quantity.

The direction of F is in the direction of a.

The scalar form of eq(2) is,

F = ma

The magnitude of the force can be calculated by multiplying the mass of a body and the acceleration produced in it.

Hence Newton’s second law of motion gives us a measure of force.

The SI unit of force is Newton, symbolized by N.

The dimensional formula:

By the formula,

F = ma

Where m is in kg = [M], a in m/s^{2} = [LT^{-2}]

So, Formula = [MLT^{-2}]

Units of Force:

In MKS system, the unit of force is = 1 N = 1 kg ms

^{-2}CGS system = Dyne =1 g cms

^{-2 }

Where 1 N = 10^{5} dyne

In Foot-pound-second-system = Foot-pound (ft .lbf)

We define friction as a force that generates between two surfaces in contact, and the static surface impedes or opposes the motion of the body over it.

Let us consider a block of weight mg that is kept on the table.

As the block presses over its surface, the surface deforms even though it appears to be rigid.

The deformed force pushes on the body with a normal force N that is perpendicular to the surface, which is balanced by mg acting downward.

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So, N = mg

If a small force, F is applied on the block. The force of friction, Ff opposes its motion.

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F = Ff

The block doesn’t move as F and Ff balance each other.

For example, when the elevator is at rest.

Acceleration of the person inside the elevator = 0

The net force on the person f = 0

I.e., N - mg = 0

=> N = mg

We define the power of the body as the rate at which it can do the work.

Mathematically,

Power = Work/time = W/t…(1)

So, power measures how fast a body can do the work, which means if it takes less time to do work, its power is greater and vice versa.

As ⇾ ⇾ ⇾ ⇾

P = W/t = F . s/t = F . v (∵ v = s/t)

⇾ ⇾

If Ө is the angle between F and v, then

⇾ ⇾

P = F . v = F . v CosӨ

When F is along with v, then putting Ө = 0°, we get:

P = Fv Cos 0° = F . v

Since power is the ratio of two scalar quantities, i.e., W and t, therefore, its product is scalar. ⇾ ⇾

That’s why it’s expressed as a dot product of F and v.

The unit of power is Watt.

∵ 1 Watt = 1 Joule/1 sec

∴ 1 Watt = 1 J/s

Thus, power of a body is said to be 1 watt if it can do 1 J of work in 1 s.

FAQ (Frequently Asked Questions)

Q1: How do You Calculate Power from Force?

Ans: The formula P = Fv is often used for calculating the average power.

We know that P_{avg} = W/t = FsCosӨ/t

So, v_{avg} = s/t

P_{avg} = FCosӨv_{avg}

It turns out that this is a general form, so instantaneous power can be calculated from the above expression:

P_{Instantaneous} = FCosӨv..(a)

It is in vector form.

Generally, in many cases, the direction of velocity is not in the direction of force, then we use the scalar form of eq(a): P = Fv.

Q2: Does Speed Affect Power?

Ans: Yes, speed affects power. The more the speed of a body, quickly a task will be done in less time, so more will be the power of an agent.

Q3: Does Speed increase Force?

Ans: Yes, the force increases with increasing speed.

Let’s consider a body exhibiting a circular motion.

To maintain its uniform circular motion, a centripetal force is applied to it, which is,

F ∝ v^{2}/r

∴ Centripetal force is directly proportional to the square of velocity.

Q4: Is Gravity a Force?

Ans: Gravity is the force of attraction between any two bodies in the universe.