Angie and Bob are discussing the class demo in which we raced various wheels of
ID: 1555450 • Letter: A
Question
Angie and Bob are discussing the class demo in which we raced various wheels of different shapes and sizes down a ramp. (In class, the loser was the hoop, with I = MR2.) Angie claims that she has designed a wheel which will accelerate even slower than the hoop. It is a large solid disk (radius R) which rolls on a small axle (radius r), as in this picture. You need a ramp with a slot in it to actually perform this experiment. But Angie claims that if you were to do this, it would roll slower than any hoop. Bob disagrees, saying that Angies wheel will be faster than the hoop. Who is right? Or does it depend on the sizes of the wheel and hoop? Explain using physics.Explanation / Answer
using law of conservation of energy
For solid disk
energy at the top = energy at the bottom
m*g*h = (0.5*m*v^2)+(0.5*I*w^2)
m*g*h = (0.5*m*v^2) + (0.5*0.5*m*R^2*(v/R)^2)
m cancels
g*h = (0.5*v^2)+(0.5*0.5*v^2)
g*h = 0.75*v^2
v = sqrt(g*h/0.75) = 0.866*sqrt(g*h)......(1)
For hoop
energy at the top = energy at the bottom
m*g*h = (0.5*m*v^2)+(0.5*I*w^2)
m*g*h = (0.5*m*v^2) + (0.5*m*R^2*(v/R)^2)
m cancels
g*h = (0.5*v^2)+(0.5*v^2)= v^2
v= sqrt(g*h).............(2)
From (1) and (2)
we can say speed of the hoop is greater than speed of the solid disk
Angie is correct,Angies wheel moves slower than the any hoop