How long was the mallet in contact with the ball?

[tony873004]

11. [Walker2 9.P.010.] A 0.50 kg croquet ball is initially at rest on the grass. When the ball is struck by a mallet, the average force exerted on it is 235 N. If the ball's speed after being struck is 2.6 m/s, how long was the mallet in contact with the ball? (in miliseconds)

F = ma
235 = 0.50 * a
a = 235 / 0.5
a = 470
v = at
2.6 = 470 t
t = 2.6 / 470
t = 0.00553191489361702 s
t = 5.53 ms

I got this correct according to the online grading system, but if they were picky about significant figures wouldn't I have done?:

t = 0.00553191489361702 s
2.6 is the value with the least amount of significant digits with 2, therefore
t = 0.0 s
t = 0 ms

 

[jamesrc]

No, those placeholder zeros in front of the 5 are not significant.

Also, I think using the impulse-momentum theorem is a better (albeit mathematically equivalent) way to think of the problem:

F_{\rm avg}t = \Delta mv
t = m\frac{v-v_o}{F_{\rm avg}}

 

[tony873004]

No, those placeholder zeros in front of the 5 are not significant.

Also, I think using the impulse-momentum theorem is a better (albeit mathematically equivalent) way to think of the problem:

F_{\rm avg}t = \Delta mv
t = m\frac{v-v_o}{F_{\rm avg}}

Thanks, that makes sense. We spent the first week of class on significant figures, and now he doesn't enforce it so we all got lazy.

Thanks for the impulse formulas. I did this problem before I read the impulse chapter by using the force formulas, but your way looks more elegant.