Show all work. A solid sphere, mass 1.0kg, radius 0.12m, begins at rest at the t
ID: 1467825 • Letter: S
Question
Show all work. A solid sphere, mass 1.0kg, radius 0.12m, begins at rest at the top of a hill. It rolls without slipping down that hill and at the bottom has a speed v of 3.0 m/s. What's the height of the hill( the initial height of the sphere)? Show all work. A solid sphere, mass 1.0kg, radius 0.12m, begins at rest at the top of a hill. It rolls without slipping down that hill and at the bottom has a speed v of 3.0 m/s. What's the height of the hill( the initial height of the sphere)? A solid sphere, mass 1.0kg, radius 0.12m, begins at rest at the top of a hill. It rolls without slipping down that hill and at the bottom has a speed v of 3.0 m/s. What's the height of the hill( the initial height of the sphere)?Explanation / Answer
Vup = 3.0 m/sec
Applying energy conservation , h being equal to 2R :
Vdown = Vup^2+2*g*h = 3^2+4*0.12*9.806 = 7.71 m/sec (minimum speed down the hill)
Total kinetic energy Ek inside a rolling solid sphere :
Ek = Ekt+Ekr = 1/2mV^2+1/5 mV^2 = 0.7mV^2 (translating plus rotating energies respectively)
Applying energy conservation
0.7*m*Vdown^2 = m*g*h
m cancels out,
h = 0.7*7.71^2/9.806 = 4.24 m