Impulse
Impulse is defined as the product of average A push or a pull. The unit of force is the newton (N). and time of contact for a collision:
\(\text{impulse} = F\times t\)
There is no symbol for impulse but the units are Unit of force named after British scientist Isaac Newton (1642-1727), eg the frictional force on the boat is 20,000 N. seconds (Ns)
The equations of motion can be used to show that impulse is equal to the change in momentum.
Use the equation for change in velocity \( \Delta v = v - u\)
Change in momentum equals:
\(mv - mu = m(v - u)= m\Delta v\)
Newton's Second Law:
\(F=ma=m\frac{{\Delta v}}{t}\)
Rearranging:
\(F\times t = m\Delta v\)
ie, \(\text{impulse} = \text{change}\,\text{in}\,\text{momentum}\)
This means that the units of impulse (Ns) and the units of momentum (kg ms-1) must be equivalent.
Example
A squash ball of mass 25 g is moving from left to right at 3.2 ms-1. It is hit by a squash racquet which applies a force for 4 milliseconds, so that the ball leaves the racquet at 8.4 ms-1 moving from right to left. Impulse-momentum can be used to calculate the average force on the ball.
Initial momentum of ball:
\(=m\times u\)
\(= 0.025 \times 3.2\)
\(= 0.08kg\,m{s^{ - 1}} \,\) (to the right)
Final momentum of ball:
\(=m\times v\)
\(= 0.025\times -8.4\)
\(= -0.21kg\,m{s^{- 1}} \,\) (moving to the left)
Change in momentum = final momentum 鈥 initial momentum
\(= -0.21 - 0.08\)
\(= -0.29kg\,m{s^{ - 1}} \,\) (moving to the left)
This change in momentum is equal to the impulse so:
\(F \times t = -0.29\)
\(F = \frac{{-0.29}}{{0.004}}\)
\(F = -72.5N \,\) (value is negative as moving to the left)
The negative sign in front of the \(-72.5N\) indicates that the movement is to the left, but you can also write this down in order to make it clear.
Newton's Third Law in collisions
Newton's Third Law of motion states that every action force has an equal and opposite reaction force.
In collisions this means that the force of one object on the other is equal in magnitude but opposite in direction.
In this example, the ball exerts a force to the right on the racquet. By Newton's Third Law, the racquet exerts a force to the left on the ball, causing its change in direction.