Statement

difficulty

A 50 g rubber ball is hit by a racket. Ball´s velocity before the hit is ,after the hit, the velocity is .

Determine the impulse exerted by the racket on the ball and the value of the force, assumed constant, if the are in contact for 0.05 s.

Solution

Data

• Mass of the ball: m = 50g = 0.05 kg
• Velocity before and after the crash:
• Force´s time of performance t = 0.05s

Resolution

Impulse-momentum theorem  says the impulse coincides with the variation of the linear momentum, so:

$\stackrel{\to }{J}=∆\stackrel{\to }{p}={\stackrel{\to }{p}}_{f}-{\stackrel{\to }{p}}_{i}=m·{\stackrel{\to }{v}}_{f}-m·{\stackrel{\to }{v}}_{i}=m·\left({\stackrel{\to }{v}}_{f}-{\stackrel{\to }{v}}_{i}\right)=\phantom{\rule{0ex}{0ex}}=0.05·\left(15·\stackrel{\to }{i}+20\stackrel{\to }{j}-\left(-20·\stackrel{\to }{i}-20\stackrel{\to }{j}\right)\right)=35·\stackrel{\to }{i}+40·\stackrel{\to }{j}N·s$

On the other hand, from definition of impulse, we can calculate the force exerted by the racquet:

Formulas worksheet

These are the main formulas that you must know to solve this exercise. If you are not clear about their meaning, we recommend you to check the theory in the corresponding sections. Furthermore, you will find in them, under the Formulas tab, the codes that will allow you to integrate these equations in external programs like Word or Mathematica.

Formulas
Related sections
$\stackrel{\to }{p}=m·\stackrel{\to }{v}$