Answer to Question #121515 in Mechanics | Relativity for Hanna

Question #121515
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?
1
Expert's answer
2020-06-11T10:35:09-0400

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,

I=Ft=Δmv=mΔv\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.

I=1.2kg×(10ms14ms1)=1.2kg×6ms1=7.2kgms1\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,

Ft=7.2kgms1F=7.20.5s=14.4N\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}


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