p08_014.pdf

14. We use Eq. 8-18, representing the conservation of mechanical energy. The reference position for com-

puting U is the lowest point of the swing; it is also regarded as the “ﬁnal” position in our calculations.

cos θ )atthe

position shown in Fig. 8-29 (which we consider to be the initial position). Thus, we have

−

K i + U i = K f + U f

0+ mgL (1

−

cos θ )= 1

2 mv 2 +0

which leads to

v = 2 mgL (1

−

cos θ )

= 2 gL (1

−

cos θ ) .

Plugging in L =2 . 00 m and θ =30 . 0 ◦ we ﬁnd v =2 . 29 m/s.

(b) It is evident that the result for v does not depend on mass. Thus, a diﬀerent mass for the ball must

not change the result.

(a) In the solution to problem 8 (to which this problem refers), we found U = mgL (1