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course PHY 201
9/05 5:30pm
Questions:1. What was your count for the pendulum bouncing off the bracket, and how many seconds did this take? What therefore is the time in seconds between collisions with the bracket? What was the length of your pendulum?
My count was about 4 seconds of clock time for the pendulum to hit 8 times.
The clock time was about one half second between collisions with the bracket
Length of pendulum was 11cm
2. What was the period of your pendulum when it was swinging freely? Give your data and briefly explain how you used it to find the period. How does your result compare with the time between 'hits' in the first question?
I don’t think I got the right data on this exercise. I will retake the data on Wednesday and then resubmit this part of the questions.
3. Give your data for the ball rolling down the ramp, using the bracket pendulum as your timer. Assuming the ball traveled 30 cm each time, what are the resulting average velocities of the ball for each number of dominoes?
With 1 domino, it took the ball 6 beats of the pendulum to go down the ramp resulting in 3 seconds clock time. Because the ramp is 30 cm long, the average velocity for 1 domino is 10 cm/sec.
With 2 dominos, it took the ball 4 beats to go down the ramp resulting in 2 seconds of clock time. Because the ramp is 30cm long, the average velocity for 2 dominos is 15cm/sec.
With 3 dominos, it took the ball 3 beats to go down the ramp resulting in 1.5 seconds of clock time. Because the ramp is 30 cm long, the average velocity for 3 dominos is 20cm/sec.
4. How did your results change when you allowed the ball to fall to the floor? What do you conclude about the time required for the ball to fall to the floor?
The results changed from falling to the floor because the ball had a greater distance to travel before hitting something that would stop it’s fall.
With 1 domino, it took 7 beats of the pendulum for the ball to hit the floor (3.5 seconds of clock time)
With 2 dominos, it took 5 beats of the pendulum for the ball to hit the floor (2.5 seconds of clock time)
With 3 dominos, it took 4 beats of the pendulum for the ball to hit the floor (1.5 seconds of clock time)
Good. Specifically it looks like falling to the floor required an extra beat, or about an extra half second.
5. Look at the marks made on the paper during the last class, when the ball rolled off the ramp and onto the paper. Assuming that the ball required the same time to reach the floor in each case (which is nearly but not quite the case), did the ball's end-of-ramp speed increase by more as a result of the second added domino, or as a result of the third? Explain.
Yes, the ball’s end of ramp speed increased because it had a higher horizontal velocity. With 1 domino, the ball traveled a total of 35.4cm. With 2 dominos, the ball traveled a total of 40.5cm. With 3 dominos, the ball traveled a total of 44.5cm.
As was stated in class, the ball had a higher horizontal velocity, therefore allowing it to travel further out until it hit the paper.
Assuming a .4 second fall, what then were the average velocities? Did the velocity change by more from the 1 domino ramp to the 2 domino ramp, or from the 2 domino ramp to the 3 domino ramp?
6. A ball rolls from rest down a ramp. Place the following in order: v0, vf, vAve, `dv, v_mid_t and v_mid_x, where the quantities describe various aspects of the velocity of the ball. Specifically:
* v0 is the initial velocity,
* vf the final velocity,
* vAve the average velocity,
* `dv the change in velocity,
* v_mid_t the velocity at the halfway time (the clock time halfway between release and the end of the interval) and
* v_mid_x the velocity when the ball is midway between one end of the ramp and the other.
Explain your reasoning.
The order from smallest to greatest is
vO (this is the start of the experiment when the ball starts from zero velocity)
v_mid_t (the velocity of the ball at the beginning of the 1st half of the ramp is zero where at the middle of the ramp, the ball’s velocity is not zero)
v_mid_x (as the ball travels down the ramp, it is going faster at the midpoint of the ramp than it was at the beginning because it’s velocity was greater than vO)
dV (because the ball is going faster after the midpoint, we can now see the change in velocity)
vF (this is the velocity of the ball when it stops)
vAve (this has to be last because you can’t find the average until you have total distance traveled and total time traveled)
Good thinking. I'm not going to say if you're right. We'll talk Wednesday about designing an experiment to test the various velocities.
7. A ball rolls from one ramp to another, then down the second ramp, as demonstrated in class. Place the following in order, assuming that v0 is relatively small: v0, vf, vAve, `dv, v_mid_t and v_mid_x .
Place the same quantities in order assuming that v0 is relatively large.
vO
v_mid_t
v_mid_x
dV
vF
vAVE
Regardless of vO being small or large, there will still be the same order of the given velocities.
Which of these quantities will get larger when v0 gets larger? Which will get smaller when v0 gets larger? Which will be unchanged if v0 gets larger?
If vO gets larger, then all of the listed velocity’s will get larger because vO is starting out larger. Similar to comparing vO at zero and vO at 30cm/sec
Again, good thinking. As noted above, we'll talk more about these situations and think about how to test this.
8. If a ball requires 1.2 seconds to travel 30 cm down the ramp from rest:
* What is its average velocity? 25cm/sec (divide length traveled by clock time)
* What is its final velocity? 45cm/sec (Multiply length traveled by clock time)
multiplying displacement by change in clock time doesn't give us a velocity.
* What is the average rate of change of its velocity? 20 cm/sec because that is the difference between the average velocity and the final velocity.
You're on the right track, but the change in velocity is from initial to final, not average to final. Also, the rate of change of the velocity with respect to clock time involves both the change in velocity and the change in clock time.
Be sure to explain your reasoning.
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&#This looks good. See my notes. Let me know if you have any questions. &#
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