1) A boulder with a radius of 10 m and mass of 1000 kg starts from rest and roll
ID: 1387172 • Letter: 1
Question
1) A boulder with a radius of 10 m and mass of 1000 kg starts from rest and rolls down a hill of height h = 100m Use conservation of energy to determine the velocity of the boulder when it hits the bottom of the hill. I sphere = 2/5mr^2 2) A disk of gas and dust forming our solar system begins with a radius of 1 million km and a tangential velocity of v=100 m/& Over time it will shrink to a radius of 10000 km. Use conservation of angular momentum to determine the angular velocity of the disk after it shrink I desk = 1/2mr^2Explanation / Answer
1)
Apply conservation of enrgy
Initial potential energy = final kinetic enrgy
m*g*H = 0.5*m*v^2 + 0.5*I*w^2
m*g*H = 0.5*m*v^2 + 0.5*(2/5)*m*R^2*w^2
m*g*H = 0.5*m*v^2 +0.2*m*v^2
m*g*H = 0.7*m*v^2
==> v = sqrt(g*H/0.7)
= sqrt(9.8*100/0.7)
= 37.4 m/s <<<<<<<<<<<<-----------Answer
2)
Intial angular velosity of the disk, wi = v/r
= 100/(1*10^9)
= 1*10^-7 rad/s
Initail angular momentum = final angular momentum
Ii*wi = If*wf
wf = Ii*wi/If
= (0.5*m*ri^2)*wi/(0.5*m*rf^2)
= wi(ri/rf)^2
= 1*10^-7*(1*10^6/10000)^2
= 1*10^-3 rad/s <<<<<<<<<<<<-----------Answer
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