Impulse integration for a Tennis Racket hitting a Tennis Ball

In summary, the conversation discusses the integration of impulse over time and the use of the endpoints or the function itself as the bounds. It is noted that if the impulse is a function of time, then integrating from ##t_i## to ##t_f## is reasonable. However, omitting the "t=" from the bounds can be misleading.
  • #1
ChiralSuperfields
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Homework Statement
Please see below
Relevant Equations
Please see below
For this,
1684125887202.png

Can someone please tell me why they integrate the impulse over from ##t_i## to ##t_f##? Why not from ##j_i## to ##j_f##? It seems strange integrating impulse with respect to time.

Many thanks!
 
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  • #2
ChiralSuperfields said:
Homework Statement: Please see below
Relevant Equations: Please see below

For this,
View attachment 326569
Can someone please tell me why they integrate the impulse over from ##t_i## to ##t_f##? Why not from ##j_i## to ##j_f##? It seems strange integrating impulse with respect to time.

Many thanks!
If you are using
##\displaystyle \int d \textbf{J}##
and you have the ##\textbf{J}##'s at the endpoints, the use the ##\textbf{J}##'s.

If you don't have the ##\textbf{J}##'s then you need to use
##\displaystyle \int \textbf{F}(t) \, dt##

-Dan
 
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  • #3
ChiralSuperfields said:
Can someone please tell me why they integrate the impulse over from ##t_i## to ##t_f##? Why not from ##j_i## to ##j_f##? It seems strange integrating impulse with respect to time.
If you think of ##\vec J## as the cumulative impulse given over some period of time then ##\vec J=\vec J(t)## and it is reasonable to write ##\int_{t=t_i}^{t_f}d\vec J(t)##. But omitting the "t=" from the bounds is a bit naughty.
 
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  • #4
haruspex said:
If you think of ##\vec J## as the cumulative impulse given over some period of time then ##\vec J=\vec J(t)## and it is reasonable to write ##\int_{t=t_i}^{t_f}d\vec J(t)##. But omitting the "t=" from the bounds is a bit naughty.
Thank you for your reply @topsquark and @haruspex!

@haruspex, now that you say J is a function of t I think that helps.

Many thanks!
 

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