p10_082.pdf

82. We use J = Fdt = m ∆ v = mv f . The integral Fdt is estimated from the area under the curve in

Fig. 10-61 as approximately4N

0 . 35) (with t in milliseconds) will ﬁt it once the

parameter ξ is adjusted so that F = 2200 N when t is midwaybetween 0 . 35ms and 3 . 25ms. Then the

integral can be done explicitly.) Thus, the ﬁnal speed of the ball is

−

3 . 25)( t

−

v f = J

m = 4N

0 . 5kg =8m / s .

s. (If one doesn’t want to “count squares” one can assume the curve

to be a parabola, in which case F = ξ ( t