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A 57g tennis ball is served at 45m/s .
If the ball started from rest, what impulse was applied to the ball by the racket?
Express your answer using two significant figures.
Before we can talk about the concept of impulse, it is necessary to examine the notion of momentum. Momentum is a measurement of strength and also a measure of the difficulty stopping an object. If an object isn’t moving has no momentum.♦ Relevant knowledgeIn physics, the term “impulse” refers to an idea that is based on the momentum of an object changing as force is applied to it for a certain period of time.
This problem can be solved using two concepts: the momentum expression principle and the change in momentum principle.
First, calculate the momentum using the momentum formula. Next, use the momentum formula to calculate the ball’s momentum.
Momentum is:
[katex]P = mv[/katex]
Here, [katex]m[/katex]
The change in momentum is equal to the impulse.
[katex]\begin{array}{c}\\I = \Delta P\\\\ = {P_{\rm{f}}} – {P_{\rm{i}}}\\\end{array}[/katex]
Here, [katex]{P_{\rm{f}}}[/katex]
Calculate the ball’s final momentum.
Momentum is:
[katex]P = mv[/katex]
Here, [katex]m[/katex]
Substitute [katex]57{\rm{ g}}[/katex]
[katex]\begin{array}{c}\\{P_{\rm{f}}} = \left( {57{\rm{ g}}} \right)\left( {45{\rm{ m/s}}} \right)\\\\ = \left( {57{\rm{ g}}} \right)\left( {\frac{{{{10}^{ – 3}}{\rm{ kg}}}}{{1{\rm{ g}}}}} \right)\left( {45{\rm{ m/s}}} \right)\\\\ = \left( {57 \times {{10}^{ – 3}}{\rm{ kg}}} \right)\left( {45{\rm{ m/s}}} \right)\\\\ = 2.6{\rm{ kg}} \cdot {\rm{m/s}}\\\end{array}[/katex]
Calculate the intial momentum.
The ball is initially at rest, so its initial momentum is zero.
[katex]{P_{\rm{i}}} = 0[/katex]
Calculate the rocket’s impulse to the ball.
The change in momentum is equal to the impulse.
[katex]\begin{array}{c}\\I = \Delta P\\\\ = {P_{\rm{f}}} – {P_{\rm{i}}}\\\end{array}[/katex]
Here, [katex]{P_{\rm{f}}}[/katex]
Substitute [katex]m[/katex]1
[katex]m[/katex]2Ans:
The impulse to the ball by [katex]m[/katex]1