Consider a pure-rolling race where two objects A and B are simultaneously releas
ID: 1600187 • Letter: C
Question
Consider a pure-rolling race where two objects A and B are simultaneously released from the top of an inclined plane and roll down to a finish line. For each group below, answer which object will win the race or it will be a tie (A or B or Tie). 1. A: 100g solid cylinder with R = 10cm vs B: 100g hollow cylinder with R = 10cm. 2. A: 100g solid cylinder with R = 10cm vs B: 100g solid sphere with R = 10cm. 3. A: 100g solid cylinder with R = 10cm vs B: 200g solid cylinder with R = 10cm. 4. A: 100g solid cylinder with R = 10cm vs B: 100g solid cylinder with R = 20cm.Explanation / Answer
in case of pure rolling,
a = (m g sin(theta) - f) / a
and f r = I alpha
f = I a / r^2
ma = m g sin(theta) - I (a / r^2)
a = m g sin(theta) / (m + I/r^2)
g sin(theta will be same so we have to compare term X = m / (m + I/r^2))
1. A: X = 100 / (100 + (100 / 2)) = 0.667
B: X = 100 / (100 + 100) = 0.5
A will win.
2. A: X = 0.667
B: X = 100 / (100 + (2 x 100 / 5)) = 0.714
B will win.
3. A: X = 0.667
B: X = 200 / (200 + (200 / 2)) = 0.667
Tie
4. A : X = 0.667
B: X = 100 / (100 + (100/2)) = 0.667
Tie