# Significant figures question

1. Nov 24, 2004

### 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

2. Nov 24, 2004

### 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:

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

3. Nov 24, 2004

### tony873004

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. :tongue: