#$&*
course phy 241
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?v0=0cm/s
vf=?
'dt=?
`ds=13cm
a=25cm/s^2
`ds = v0 `dt + .5 a `dt^2
13cm= 0 `dt + .5 25cm/s^2 `dt^2
13cm=12.5cm/s^2 `dt^2
`dt^2=1.04s^2
`dt=1.02s
vf = 0 + 25cm/s^2 * 1.02s
vf=25.5 cm/s
v0=25.5 cm/s
vf=?
'dt=?
`ds=30cm
a=? It will initially enter the ramp with 25cm/s^2 and then decrease to 7cm/s^2. I think averaging this should give us the proper acceleration.
@&
Your solution for the first ramp is correct.
I supect, though, that you're now confusing the roles of velocity and acceleration.
Among other things, the acceleration on the first ramp has nothing to do with the acceleration on the second.
The ball enters the second ramp moving at 25.5 cm/s and accelerates 30 cm at 7 cm/s^2.
*@
aAve=25+7/2= 16cm/s^2
`ds = v0 `dt + .5 a `dt^2
30cm = 25.5cm/s `dt + .5 16cm/s^2 `dt^2
30cm = 25.5cm/s `dt + 8cm/s^2 `dt^2
Dt=0.9s
@&
Good for the first ramp. I don't believe you are correctly conceptualizing the situation on the second.
&#Please see my notes and submit a copy of this document with revisions, comments and/or questions, and mark your insertions with &&&& (please mark each insertion at the beginning and at the end).
Be sure to include the entire document, including my notes. &#
*@