course Phy 121
I had quite a bit of trouble with this problem. I did not know what to do when I was only given `ds, vo, and a. So I used the formulas from the lecture on uniform acceleration. Do we get graded on accuracy for these assignments?
A ball starting from rest rolls 13 cm down an incline on which its acceleration is 25 cm/s2, then onto a second incline 30 cm long on which its acceleration is 7 cm/s2. How much time does it spend on each incline?For the first ramp:
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vo = 0, a = 25cm/s^2, and `ds = 13cm
The only equation we can use if we have no more information than this is vf^2 = vo^2 + 2a`ds. We could also combine two equations (vf = vo + a`dt and `ds = ((vf + vo)/2)`dt), but this is the shorter method.
vf^2 = 0 + 2(25cm/s^2)(13cm)
vf^2 = 650cm^2/s^2
TAKE SQUARE ROOT
vf = 25.495 cm/s
Now we use acceleration and change in velocity to find the time interval.
`dt = `dv / a = (vf - vo)/a
`dt = (25.495cm/s - 0) / 25cm/s^2
`dt = 1.019 seconds
For the second ramp, we can say that the final velocity for the first ramp is the initial velocity for the second ramp and use the same equation. a = 7cm/s^2, `ds = 30cm
vf^2 = vo^2 + 2a`ds
vf^2 = (25.495cm/s)^2 + 2(7cm/s^2)(30cm)
vf^2 = 1070
vf = 32.711 cm/s
Now we use acceleration and change in velocity to find the time interval.
`dt = `dv / a = (vf - vo)/a
`dt = (32.711cm/s - 25.495cm/s) / 7cm/s^2
`dt = 1.031 seconds "
Excellent. Let me know if you have questions.
You are graded to an extent on accuracy, so it's best to be correct. However you get a lot of credit for effort also.
On either criterion you are doing very well so far.