Worked Examples-Calculation Part 1 - Newtons Law and Linear Momentum

Considered Formula;

$$\text {i)}\quad P = mv$$ $$\qquad \text {Where}~~P \to Momentum,\quad m \to Mass, \quad v \to Velocity$$ $$\text {ii)}\quad F =ma$$ $$\qquad \text {Where}~~F \to Force,\quad m \to Mass, \quad a \to Acceleration$$

Example 1

Find the linear momentum of a body of mass 5000 g moving with the velocity of 2m/s

Solution

Data given

$$\text {Mass (m)}= 5000 g = \Bigl( \frac {5000}{1000}\Bigr)~Kg = 5 Kg$$

Velocity (v) = 2 m/s

Momentum (P) =?

$$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~P = mv$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~= 5 \times 2$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~= 10 Kgm/s$$

The linear momentum of the body = 10 Kgm/s

Example 2

A man of mass 1000 kg is moving with a velocity of 60 km/h. find its momentum

Solution

Data given

Mass (m) = 1000 Kg

$$\text {Velocity (v)}= 60 km/h = \Bigl( \frac {60 \times 1000}{3600}\Bigr)~m/s = 16.67 m/s$$

Momentum (P) =?

$$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~P = mv$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~= 1000 \times 16.67$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~= 16670~Kgm/s$$

linear momentum of the man = 16670 Kgm/s

Example 3

What force is required to give a mass of 200 g an acceleration of 0.5m/s²?

Solution

Data given

$$\text {Mass (m)}= 200 g = \Bigl( \frac {200}{1000}\Bigr)~Kg = 0.2 Kg$$

Accelaration (a) = 0.5 m/s²

Force (F) =?

$$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~F = ma$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~= 0.2 \times 0.5$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~= 0.1~N$$

The required force = 0.1 N

Example 4

What acceleration will be given to a body of mass 6kg by a force of 15N?

Solution

Data given

Mass (m) = 6 Kg

Force (F) = 15 N

Accelaration (a) = ?

$$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~F = ma$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~15 = 6a$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\frac {15}{6} = \frac {6a}{6}$$ $$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a = 2.5 m/s^2$$

The acceleration = 2.5 m/s²