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course Phy 201
9-27 9
A ball starting from rest rolls 11 cm down an incline on which its acceleration is 24 cm/s2, then onto a second incline 44 cm long on which its acceleration is 12 cm/s2. How much time does it spend on each incline?Vf^2 = Vo^2 + 2a * ds
Vf^2 = (0cm/s)^2 + 2(24 cm/s^2) (11cm)
Sqrt Vf^2 = sqrt 528 cm/s
Vf = 22.98
a = dV/dt
dt = dV/a
22.98 cm/s / 24 cm/s^2 = 0.95s = dt on the first ramp
Vf^2 = Vo^2 + 2a * ds
Vf^2 = (0cm/s)^2 + 2(12 cm/s^2) (44cm)
Sqrt Vf^2 = sqrt 1056 cm/s
Vf = 32.50 cm/s
a = dV/dt
dt = dV/a
32.50 cm/s / 12 cm/s^2 = 2.708 s = dt on the second ramp
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Good solution for the first ramp.
The ball doesn't have initial velocity 0 on the second ramp. It rolls from the first incline onto the second, so its initial velocity on the second with be its final velocity on the first.
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