Calculating Net Force from Acceleration and Distance: A Problem Solving Approach

[pookisantoki]

When a 53.4g tennis ball is served, it accelerates from rest to a speed of 40.5m/s. The impact with the racket gives the ball a constant acceleration over a distancce of 46.6cm. What is the mgnitude of the net force acting on the ball?

I converted the 53.5g into kg=.0535kg
I converted 46.6cm into m=.466
So we have the distance, mass, force but not the net force.
I figured out the time by
40.5=.466/x
x=.01150secs
and figured out the acceleration byt 40.5/.0111506=3519.8
and then net force=acceleration * mass
f=.0534kg*3519.8=187.9599
But it's wrong, what am I doing wrong?

 

[Delphi51]

Good idea to do those conversions right away.

I figured out the time by 40.5=.466/x

Looks like you used v = d/t to do this. But this is the d = vt that applies only to motion at constant speed. For this accelerated motion you could use d = Vi*t + .5*a*t^2.

The rest looks okay, but I recommend you clearly show what formula you are using to make your work easily readable by yourself and the rest of us (including the overworked and underpaid grad student who marks your tests).

 

[pookisantoki]

Sorry!
So i did what you suggested and from where I found the time I plugged all the numbers into the formula you gave me: x=vt+.5at^2

.466=40.5*(.011506)+1/2a(.011506)^2
.466=.46599+1/2a(.000132388)
.932=.46599+a(.000132388)
7031.911=46599+a
a=7039.445

Then I plugged the "a" into the sum of forces=a*mass

7039.445*.0534= 375.906N but its coming up wrong...I'm not sure what I am doing wrong. Thank you

 

[Delphi51]

x=vt+.5at^2
.466=40.5*(.011506)+1/2a(.011506)^2

Your time is still wrong because you still used d = vt to find it.
Your initial velocity should be zero, not 40.5.

You know d, Vi and Vf. Do you have a formula for finding anything when you know only these quantities? An accelerated motion formula with no t in it would be perfect. Once you get the acceleration, you'll be able to find the force easily.

If you don't have such a formula (it is a more advanced one), you could use the very basic idea that the area under a velocity vs time graph is the distance. Sketch the V vs t graph for this situation and write in that its area is 0.466 m. The area is just a triangle, and you know the formula for area of a triangle, so you can make up a little formula with the width (time) being the only unknown and use it to find the time to accelerate the tennis ball.