Week 5 quiz

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course Phy 231

3/27 5

A ball starting from rest rolls 13 cm down an incline on which its acceleration is 27 cm/s2, then onto a second incline 39 cm long on which its acceleration is 13 cm/s2. How much time does it spend on each incline?

'dt incline 1 = 0.98 s

'ds a v0

vf = (v0^2 +2*a*'ds)^(1/2) = (2 * 27 cm/s^2 * 13 cm) = 26.495 cm/s

vAve = 'dv /2 = 26.495 cm/s \ 2 = 13.248 cm/s

'dt 1 = 'ds / Vave = 13 cm / 13.248 cm/s = .98 s

'dt incline 2 = 1.15 s

V0 = 13.248 cm/s a = 13 cm/s^2 'ds = 39 cm

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The initial velocity on the second ramp is equal to the final velocity on the first, not to the average velocity on the first.

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vf = (v0^2 + 2*a*'ds)^(1/2) = 41.4244 cm/s

vave = (vf + v0) /2 = (41.4244 cm/s + 26.495 cm/s) / 2 = 33.9597 cm/s

'dt 2 = 'ds / vave = 39 cm / 33.9597248 cm/s = 1.15 s

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Good approach. You might have used the wrong quantity for the initial velocity on the second ramp. Check my note.

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