# Force and energy

It is not uncommon during the service of a professional tennis player for the racket to exert an average force of 156.0 N on the ball. If the ball has a mass of 0.070 kg and is in contact with the strings of the racket for 0.030 s, what is the kinetic energy of the ball as it leaves the racket? Assume that the ball starts from rest. Assume that air resistance is negligible.

__ J

An archer puts a 0.25 kg arrow to the bowstring. An average force of 187 N is exerted to draw the string back 1.3 m. Assume that air resistance is negligible.

(a) Assuming that all the energy goes into the arrow, with what speed does the arrow leave the bow?

m/s

(b) If the arrow is shot straight up, how high does it rise?

m

https://brainmass.com/physics/newtons-second-law/force-energy-285131

## SOLUTION This solution is **FREE** courtesy of BrainMass!

1. The problem is based on the second law of Newton.

We have .

- Force acting =156 N

Mass of the ball=0.07 kg

is the acceleration of the ball =

The velocity of the ball after hitting the racket can be calculated from the formula . Final velocity of the ball, is the initial velocity of the ball=0

And t is the time=0.03 s

Substituting the values

Kinetic energy =

2. , Here , m =0.25 kg

Her displacement of the arrow ,

The equation of motion for displacement , since =0, the equation becomes or

................................ (answer1)

The maximum displacement which the arrow can be calculated from the equation of motion , here acceleration is acceleration due to gravity in the opposite direction or a=-9.8 m/s2

Or ........ (answer2)

https://brainmass.com/physics/newtons-second-law/force-energy-285131