A baton twirler in a marching band competition grabs one end of her 1.2 kg, 1.0 meter long baton. She throws her baton into the air such that it rises to a height of 5.0 meters while spinning end over end at a rate of 3.5 revolutions per second. How much work did she do on the baton?
Question
Answer:
349 J
Explanation:
Length L of baton = 1.0 m
Mass m of baton = 1.2 kg
Weight W of baton = 1.2 kg x 9.81 m/[tex]s^{2}[/tex] = 11.772 N
Height h reached = 5.0 m
Angular speed ω = 3.5 rev/s = 2π x 3.5 (rad/s) = 21.99 rad/s
Total work done on baton will be the work done in taking it to a height of 5.0 m and the kinetic energy with which the baton rolls.
Work done to bringing it to the height of 5.0 m = weight x height above ground
W x h = 11.772 x 5 = 58.86 J
Velocity v of spinning baton = ω x L = 21.99 x 1 = 21.99 m/s
Kinetic energy = [tex]\frac{1}{2}[/tex]m[tex]v^{2}[/tex] =
Total work done on baton = 58.86 + 290.14 = 349 J