Phy 231
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A ball rolls off the end of an incline with a vertical velocity of 20 cm/s downward, and a horizontal velocity of 80 cm/s. The ball falls freely to the floor 120 cm below.
For the interval between the end of the ramp and the floor, hat are the ball's initial velocity, displacement and acceleration in the vertical direction?
ANSWER:
v0 = 20 cm/s
'ds = 120 cm
a = 980 cm/s^2
What therefore are its final velocity, displacement, change in velocity and average velocity in the vertical direction?
ANSWER:
vf = sqrt( v0^2 + 2 a 'ds )
vf = sqrt( (20 cm/s)^2 + 2 * 980 cm/s^2 * 120 cm)
vf = sqrt( 400 cm^2/s^2 + 235200 cm^2/s^2)
vf = sqrt( 235600 cm^2/s^2 ) = 485.39 cm/s
'ds = 120 cm
'dv = 485.39 cm/s - 20 cm/s = 465.39 cm/s
vAVe = 485.39 cm/s + 20 cm/s = 505.39 cm/s / 2 = 252.7 cm/s
from these, we can determine 'dt, which should be the same both vertically and horizontally:
'dt = 'ds / vAve = 120 cm / 252.7 cm/s
'dt = 0.47 s
What are the ball's acceleration and initial velocity in the horizontal direction, and what is the change in clock time, during this interval?
ANSWER:
v0 = 80 cm/s
a = 980 cm/s^2
'dt = 0.47 s
What therefore are its displacement, final velocity, average velocity and change in velocity in the horizontal direction during this interval?
ANSWER:
'ds = v0 * 'dt + 0.5 a * 'dt^2
'ds = 80 cm/s * 0.47 s + 0.5 * 980 cm/s^2 * (0.47 s) ^2
'ds = 37.6 cm + 108.24 cm = 145.84 cm
vf = sqrt( (80 cm/s)^2 + 2 * 980 cm/s^2 * 145.84 cm )
vf = sqrt( 6400 cm^2/s^2 + 285846.4 cm^2/s^2 )
vf = sqrt( 292246.4 ) = 540.6 cm/s
vAve = ( 540.6 cm/s + 80 cm/s ) / 2 = 310.3 cm/s
'dv = 540.6 cm/s - 80 cm/s = 460.6 cm/s
horizontal acceleration is zero, not 980 cm/s^2
After the instant of impact with the floor, can we expect that the ball will be uniformly accelerated?
ANSWER: no, once the ball impacts the floor, it will no longer be uniformily accelerating.
Why does this analysis stop at the instant of impact with the floor?
Once the ball hits the floor, it is no longer uniformily accelerating as it was before. The ball is no longer free falling.
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30 mins
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No revision is necessary if you understand everything, but do see the link below.
&#At least part of your solution does not agree with the solution and comments given at the link below. You should view the solution at that link and self-critique as indicated there.
Solution
This link also expands on these topics and alerts you to many of the common errors made by students in the first part of this course. &#