Conservation of Energy

Physics
Tutor: None Selected Time limit: 1 Day

Mr. Maloney's pendulum is swing back and forth. He has a 1 kg mass on the end, the string length is 2 meters, and he started it by pulling it back 35 degrees, determine:

a. The initial potential energy

b. Speed at the bottom

c. Speed half way to the bottom

d. How high would it go if a student have it a 3 m/s push

Jun 3rd, 2015

Thank you for the opportunity to help you with your question!

a-Ep(0)=m*g*l(1-cos(theta0))

Ep(0)=1*9.81*2*(1-cos(35°)=3.55 J

b-Ec=1/2*m*v^2=Ep(0)

v=sqrt(2*Ep(0)/m)

v=2.7 m/s

c-   m*g*l(1-cos(theta))+1/2*m*v^2=Ep(0) with theta=35/2=17.5

v=sqrt(2(Ep(0)-m*g*l(1-cos(theta)))/m)

v=2.3 m/s

d-1/2mv^2+m*g*l(1-cos(theta0))=m*g*l(1-cos(theta))

1-cos(theta)=1/2mv^2+m*g*l(1-cos(theta0))=(1/2*1*3^2+3.55 )/(mgl)

cos(theta)=0.59

so theta=53,8° 

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jun 3rd, 2015

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