Example 2.2.2.
A 300 kg horse running with 40 m/s has a momentum of \(p=300\times 40 = 12000 \,kgm/s.\)
Subsection 2.2.3 Momentum
It is the quantity of motion contained in a body. If a body of mass \(m\) is moving with a velocity \(v\) then its momentum \(p =mv\text{.}\) Momentum (also called linear Momentum) is a product of mass and velocity of the object. Momentum is represented by \(p\text{,}\) its SI unit is \(kgm/s\text{.}\) Momentum is a vector quantity and its direction is along the velocity of the object. From Newton’s II law:
\begin{align*}
F \amp =ma = m\left(\frac{v_f-v_i}{t}\right)\\
F \amp =\frac{m\Delta v}{t}
\end{align*}
\begin{equation}
\therefore Ft = \Delta mv\tag{2.2.5}
\end{equation}
Here \(Ft=I\) is called impulse and \(\Delta mv\) is called change in momentum. They are two different physical quantities but their magnitude remains the same. A force acting on an object for a certain time changes the momentum of that object, such change in momentum is called the Impulse. Impulse is a vector quantity and has the same direction as the average force. SI unit of impulse is \(Ns\text{.}\)
Example 2.2.3.
When a 430 g soccer ball is kicked, the impact lasts for 0.04 s. Find the magnitude of force that is needed to fly off the ball at 8 m/s.
Solution.
\begin{align*}
Ft \amp= \Delta mv\\
or, Ft \amp= m (v_f-v_i)\\
or, F\times 0.04\, s \amp= 0.43 kg (8 \,m/s-0)\\
\therefore F\amp= 86 \,N
\end{align*}
