course 201
8/4, 6:45pm
Class 090928The following conventions will allow your instructor to quickly locate your answers and separate
them from the rest of any submitted document, which will significantly increase the quality of the
instructor's feedback to you and to other students.
When answering these questions, give your answer to a question after the **** and before the &&&&.
When doing qa's, place your confidence ratings and self-assessment ratings on the same line as the prompt.
If you don't follow these guidelines you may well be asked to edit your document to make the changes before
I can respond to it.
Thanks.
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Fractional cycles of a pendulum
Regard the equilibrium position of a pendulum as the origin of the x axis. To the right of equilibrium x
values are positive, and to the left of equilibrium x values are negative.
Suppose you release a pendulum of length 16 cm from rest, at position x = 4 cm.
Estimate its position in cm, its direction of motion (positive or negative) and its speed as a percent of
its maximum speed (e.g., speed is 100 % at equilibrium, 0% at release, and somewhere between 0% and 100% at
every position between) after each of the following time intervals has elapsed:
1/2 cycle
****
-0%
&&&&
3/4 cycle
****
-100%
&&&&
2/3 cycle
****
-50%
&&&&
5/4 cycle
****
-30%
&&&&
7/8 cycle
****
-10%
&&&&
.6 cycle
****
-15%
&&&&
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Acceleration of Gravity
Drop a coin and release a pendulum at the same instant. Adjust the length of the pendulum so that it
travels from release to equilibrium, then to the opposite extreme point and back, reaching equilibrium the
second time at the same instant you hear the coin strike the floor. Measure the pendulum.
Give your raw data below:
****
-Pendulum = 16cm, `ds = 160cm, `dt = .6s, Vo = 0cm/s
&&&&
Show how to start with your raw data and reason out the acceleration of the falling coin, assuming constant
acceleration:
****
-We know from our definitions that first we need to find the average rate of change in velocity.
160cm/.6s = 270cm/s Now that we know Vo and Vave, we know that Vf is 540cm/s. (540cm/s)/.6s = 900cm/s^2.
&&&&
There are two delays between the events you are observing and your perceptions:
How long after the coin strikes the floor do you hear it?
How long after the light in the room reflects off the pendulum does it strike your eye?
Is either delay significant compared to other sources of uncertainty in this experiment?
****
-Possibly 1/100th of a second after the event. Almost immediately. These delays are very miniscule
to the results of the test.
&&&&
Introduction to Projectile motion
Time a ball down a ramp, and measure how far it travels in the horizontal direction.
Give your raw data below:
****
-Pendulum = 15.24cm, `dt_ramp = 2.1s, `ds_ramp = 30.48cm, Vf_ramp = 14.5cm/s, `ds_x_projectile =
12.5cm, `ds_y_projectile = 90cm, `dt_projectile = .9s
These aren't raw data. Some of these quantities have been calculated from what you actually
observed.
&&&&
To keep things straight, let's use the following notation in the rest of this analysis:
`dt_ramp is the time required to travel the length of the ramp starting from rest
`ds_ramp is the displacement of the ball along the ramp
vf_ramp is the ball's final velocity on the ramp
`ds_x_projectile is the horizontal displacement of the ball between leaving the ramp and striking
the floor
`ds_y_projectile is the vertical displacement of the ball between leaving the ramp and striking the
floor (for the tables in the lab we may assume that `ds_y_projectile is about 90 cm).
`dt_projectile is the time interval between leaving the ramp and striking the floor
Answer the following questions:
According to the time `dt_ramp required to travel down the ramp and its length `ds_ramp, what are the
average and final velocities on the ramp, assuming uniform acceleration?
****
-Vave = 14.5cm/s, Vf = 29cm/s
&&&&
Moving at vf_ramp, how long would it take the ball to travel through displacement `ds_x_projectile?
****
-.4s
&&&&
Accelerating at 1000 cm/s^2, how long would it take the ball to fall from rest through displacement
`ds_y_projectile?
****
-.4s.
&&&&
In the time interval you just calculated, how far would the ball travel if moving at velocity v_f_ramp?
****
-11.6cm
&&&&
Accelerating at the rate you calculated in the preceding exercise, how long would it take the ball to fall
from rest through displacement equal to `ds_y_projectile?
****
- .4s
&&&&
Ball up and down ramp
'Poke' a ball (perhaps using your pencil as a 'cue stick') so that it travels partway up a ramp then
back. Observe the clock time and position at three events: the end of the 'poke', when the ball comes
to rest for an instant before rolling back down, and its return to its original position.
Choose your positive direction.
**-Positive direction is up the ramp.
Determine the initial velocity and acceleration of the ball for the interval between the first and second
event.
****
-A = -37.5cm/s^2, Vo = 45cm/s
&&&&
Determine the final velocity and acceleration of the ball for the interval between the second and third
event.
****
-A = -37.5cm/s^2, Vf = -45cm/s
&&&&
Do you think the acceleration of the ball is greater between the first and second event, or between between
the second and third event? Or do you think it is the same for both? Give reasons for your answer.
****
-Theyre the same. There is only one, constant force acting on the ball, and thats gravity. Since
theres no other major source of movement, we would assume that its effect on the ball would be the same in
both directions.
&&&&
Are your data accurate enough to determine on which interval the acceleration is greater? If so, on which
interval do you determine it is greater? If not, how accurate do you think your data would need to be to
decide this question?
****
-Yes, I determined that they are almost identical, giving room for error due to friction and human
responses.
&&&&
"
You didn't get the first set of questions about the pendulum.
Your work on the acceleration of gravity experiment is good.
You don't show much of your work on the ramp-and-projectile experiment but your results are close to what's
expected.
You may have assumed the same force going up and down that last ramp. That's not a valid assumption, and
your results should have been based on your timings of the three events.
See the notes below.
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