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August 30, 2014

August 30, 2014

Posted by **Erin** on Sunday, April 6, 2008 at 10:56pm.

Find the speed of each of these objects when it reaches the bottom of the hill.

V_ice=

V_marble=

- physics -
**drwls**, Monday, April 7, 2008 at 12:50amFor ice, you can use conservation of energy. If h is the height that the block descends,

(1/2)MV^2 = M g h

V = sqrt (2gH)

For the marble block, since it rolls, I assume it is a cylinder. Static friction is what helps it roll instead of slip, but it does not result in a of of energy, since there is no relative motion at the line of contact. Equate the potential energy change to the increase in both translational and rotational kinetic energy. V = r w, where w is the angular velocity of the rolling cyliner. The moment of inertia is I = (1/2)M r^2

M g H = (1/2) M V^2 + (1/2)I w^2

= (1/2) M V^2 + (1/2)(1/2)Mr^2(V/r)^2

= (3/4) M V^2

V = sqrt[(4/3)gH]

- physics -
**Anonymous**, Monday, November 22, 2010 at 10:55pmsd

- physics -
**Marc**, Wednesday, April 6, 2011 at 3:11pmactually for the second part, it wouldn't be a cylinder but a sphere. thus beta = 2/5. the velocity equation in this case would be V = sqrt[(2gH)/(1+beta)]

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