What speed vf does the ball have when the cable makes an angle of 19.1 ° with respect to the vertical?
A wrecking ball swings at the end of a 12.0-m cable on a vertical circular arc. The crane operator manages to give the ball a speed of 12.3 m/s as the ball passes through the lowest point of its swing and then gives the ball no further assistance. Friction and air resistance are negligible. What speed vf does the ball have when the cable makes an angle of 19.1 ° with respect to the vertical?
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Solution:
Energy conservation:
1/2 mu2 = 1/2 mv2 + mgh
simplify n remove mass m
u2 = v2 +2gh
where u = 12.3 m/s ; g = 10m/s2 ; h= 12 -12 cos 19.1 =0.66 m
final speed v2 = 12.3 *12.3 -2* 10* 0.66 = 151.29 - 13.2 = 138
v = 11.78 m/s
very simple