While visiting friends at Cal State Chico, you pay a visit to the Crazy Horse Sa

Question

While visiting friends at Cal State Chico, you pay a visit to the Crazy Horse Saloon. This fine establishment features a 200- kg mechanical bucking bull that has a mechanism that makes it move vertically in simple harmonic motion. Whether the “bull” has a rider or not, it moves with the same amplitude 2.95 m and frequency 0.468 Hz. Being from Texas you decide to ride it the “macho” way by NOT holding on. To no ones surprise you go flying out of the saddle. While waiting for your bruises and pride to heal, you decide to calculate how fast upward you were moving when you left the saddle.

Give your answer in m/s to the second decimal place.

The ansmwer is 8.01 m/s

Show the steps to solving this. At the end, simplify the final equation into variables and plug in the numbers to solve the equation.

Explanation / Answer

mass m =200 kg
amplitude A =2.95 m
frequency f =0.468 Hz

frequency f =(1/2)k/m

k =m(4^2f^2) =1727.6 N/m

force F =-kx   .....(1)

from Newton's second law of motion ,F =mg

so , mg =-kx

x =-mg/k =-1.13 m

speed v =[sq.rt(k/m)][sq.rt(A^2-x^2)]

speed v =8.008 m/s 8.01 m/s

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