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

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a. The initial potential energy can be determined by the expression mgh. Assuming the pendulum touches the ground at an angle of 0, the height is 0.264. This gives the potential energy of 2.64J.

b. The speed at the bottom can be solved by using the equation 2.64 = (1/2)mv^2. This gives a speed of 2.30m/s

c. The speed halfway to the bottom can be solved by using the equation (1/2)2.64 = (1/2)mv^2. This gives a speed of 1.62m/s

d. This increases the initial total energy by 4.5J so 2.64 + 4.5 = mgh. Solving for h gives a height of 0.714m

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