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: init vel=20cm/s. ds=120cm. acc=980cm/s/s.
What therefore are its final velocity, displacement, change in velocity and average velocity in the vertical direction?
Answer: vf^2=v0^2 + 2ads = 400cm^2/s^2 + 2(980cm/s/s)(120cm) = 400cm^2/s^2 + 235200 = 235600cm^2/s^2. vf = 485cm/s. ds = 120cm. dv=485cm/s-20cm/s=465cm/s. ave vel= (v0+vf)/2 = (20cm/s+485cm/s)/2=253cm/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: a=980cm/s. v0=80cm/s. (Using vertical data to find dt): a=dv/dt, dt=dv/a=465cm/s/980cm/s = .5s.
What therefore are its displacement, final velocity, average velocity and change in velocity in the horizontal direction during this interval?
Answer: vf=v0+adt = 80cm/s+(980cm/s/s)(.5s)=570cm/s. ave vel=(v0+vf)/2=325cm/s. ave vel=ds/dt, ds=ave vel*dt=325cm/s*.5s=163cm. dv=vf-v0=570cm/s-80cm/s = 490cm/s.
The acceleration in the horizontal direction is 0, assuming the ball to be an ideal projectile. Your work here is based on the assumption that horizontal acceleration is 980 cm/s^2.
After the instant of impact with the floor, can we expect that the ball will be uniformly accelerated?
Yes because the ds is small enough that gravity will accelerate the object uniformly. If the ds was very large in the vertical direction, gravity would stop accelerating the object. The ball is falling freely fro the table.
Why does this analysis stop at the instant of impact with the floor?
Answer: It is very difficult to analyze the bounce and impact of the ball. We dont know what the floor is made of or have the tools so far in this physics 1 course to analyze the ball after hitting the floor.
This analysis assumes uniform acceleration, which condition ceases at the instant of impact.
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20 minutes
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