A light but rigid stick is attached to a small weight. The other end of the stic

Question

1. A light but rigid stick is attached to a small weight. The other end of the stick is attached to a pivot. The pivot allows the stick and weight to spin in a vertical circle. The weight is pulled to the side making the stick horizontal and is thrown down. If the length of the stick is 0.40 m, how fast should the weight be thrown downward so that it will just make it all the way around the circle?
2. A toy car begins rolling down a track from a height of H = 2.0m above the floor. The end of the track is h' = 0.20 m above the floor and makes an angle of theta =37 degrees as shown. When the car reaches the end of the track it flies through the air reaching a maximum vertical height h above the floor. Determine h.

Explanation / Answer

1)
at the top point it shold have minimum velocity, v = sqrt(g*R) = 1.98 m/s


workdone by gravity = change in kinetic energy of the ball

-m*g*R = (1/2)*m*v^2 - (1/2)*m*vo^2

-2*g*R = v^2 - vo^2

vo^2 = v^2 + 2*g*R

vo = sqrt(v^2 +2*g*R)

vo = 3.43 m/s
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2)let vos is the speed at the bottom

m*g*H = (1/2)*m*vo^2

2*g*h = vo^2

vo = sqrt(2*g*H) = 6.26 m/s

h = vo^2*sin^2(37)/2*g = 0.724 m

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