Answer to Question #121515 in Mechanics | Relativity for Hanna

Question

A ball of 1.2kg with velocity 4ms-1 hit by a car which moving in same direction with the ball. the velocity of the ball increase to 10ms-1 in 0.5s. what is the impulse on the ball?

Answer 1

Explanations & Calculations

• Impulse is defined as the product of force & the time during which that force is applied.
• With the collision both the objects experience a mutual impulse which causes any increment or decrement in their velocities.
• As it's been stated, that impulse has increased it's velocity.

• In simplified form the relationship is written,

$\qquad\qquad \begin{aligned} \small I &=F t = \small \Delta mv=m\Delta v \end{aligned}$

• Therefore, applying that along the moving direction, impulse could be found as follows.

$\qquad\qquad \begin{aligned} \small \overrightarrow I &= \small 1.2kg\times(\overrightarrow {10}ms^{-1} -\overrightarrow {4}ms^{-1})\\ &= \small 1.2kg \times 6 ms^{-1}\\ &= \small \bold{7.2kgms^{-1}} \end{aligned}$

• Extra
• Impulsive force F could be found to be,

$\qquad\qquad \begin{aligned} \small \overrightarrow {Ft} &= \small 7.2kgms^{-1}\\ \small \overrightarrow F &= \small \frac{7.2}{0.5s}\\ &= \small 14.4N \end{aligned}$