course phy 121
2/27 at 1:30 p.m.
A ball starting from rest rolls 11 cm down an incline on which its acceleration is 27 cm/s2, then onto a second incline 44 cm long on which its acceleration is 9 cm/s2. How much time does it spend on each incline?
v0 = 0cm/s a=27 cm/s^2 'ds=11 cm
v0= 24.372cm/s a=9cm/s^2 'ds= 44 cm
vf^2= v0^2 + 2a'ds
vf^2= 0 + 2(27cm/s^2)(11cm)
vf^2 = 594 cm^2/s^2
vf= 24.372 cm/s on the first ramp
'ds= (v0 +vf)/2 * 'dt
11cm=(0 + 24.372 cm/s)/2 * 'dt
11 cm= 12.186 cm/s*'dt
.903 s= 'dt (time on the first incline)
vf^2= v0^2 +2a'ds
vf^2 = (24.372cm/s)^2 + 2(9cm/s^2)(44cm)
vf^2 = 593.994 cm^2/s^2 + 792 cm^2/s^2
vf^2 = 1385.994cm^2/s^2
vf=37.229 cm/s
'ds= (v0 +vf)/2 * 'dt
44cm= (24.372cm/s + 37.229 cm/s)/2 * 'dt
44cm= 30.80 cm/s('dt)
1.429s= 'dt (time on second incline)
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