Force Formula and Numericals on it

Force Formula

Force is basically an interaction between the objects of and force is responsible to change the motion of an object. The unit of force is Newtons (N). For a constant mass, Force is the product of mass and acceleration.

According to Newton’s 2nd law of motion

F ∝ mv-mu/t

F ∝ ma (∵ v-u/t = a)

F = Kma

Where, k is constant

m is mass

a is acceleration

if k = 1 then,

F = ma —— (1)

This is required equation of force.

Or

‘The rate of change in momentum is proportional to the applied force and momentum is in the direction of force’.

Consider an object of mass m and initial velocity ‘u’. When force is applied on an object for time ‘t’ then  velocity becomes ‘v’.

Initial momentum of object = mu

Final momentum after time ‘t’ = mv

∴ Rate of change at momentum = Change in momentum/time

Rate of change at momentum mv-mu/t

= m (v-u)/t = ma

a = (v-u)/t

From the above statement we can write in mathematical form.

∴ F ∝ ma

∴ F = k ma (K is constant of proportionality and its value is 1.)

So, F = m × a ——- (2)

This is required equation of force.

Numericals on Force Formula

(1) Calculate the force needed to speed up a bike with acceleration at 3m/s2, it the mass of bike is 500 kg.

Solution:

a = 3m/s2

m = 500 kg

We know the formula.

F = m × a

F = 500 × 3

F = 1500 kg m/s2

The required force is 1500 m/s2 or 1500 N

(2) The object accelerate at the rate of 8m/s2 after applying a force of 30000 N. Find the mass of an object.

Solution:

a = 8 m/s2

F = 30000N

mass (m) = ?

F = m×a

= 30000 = m × 8

m = 30000/8

m = 3,750 kg

Thus mass of object is 3,750 kg.

Updated: August 19, 2021 — 2:03 pm

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