#$&*
course phy201
`q001. Report your data from the experiments conducted today.
Was not in class
So for the remainder of this assignment I will use Leanne’s data
#$&*
For the experiment where the domino slipped off the strap if it was going too fast, what was the maximum angular velocity of the system for which the domino did not slip off?
Max ang V was 179deg/s
#$&*
How far was the domino from the axis of rotation?
13cm
#$&*
How fast was the domino therefore moving?
Vave=179deg/s
Vf=179deg/sx2=358deg/s
358/360x13cm
12.9cm/s
@&
13 cm doesn't correspond to a 360 degree rotation.
What arc distance does correspond to a 360 degree rotation, and how does this change your result?
*@
#$&*
The centripetal acceleration of an object moving with speed v around a circle of radius r is
a_centripetal = v^2 / r.
The centripetal acceleration of the domino is the acceleration toward the center required to keep it moving in a circular path. What was the maximum centripetal acceleration, among your trials, for which the domino did not slip off?
Acent=12.9cm/s^2/13cm
Acent=12.8cm/s^2
@&
With the right velocity this calculation would give you the right acceleration.
*@
#$&*
What was the coefficient of friction between domino and strap, based on the slope required for the domino to begin sliding?
8cm/28.9cm
=.28cm
@&
8 cm / (28.9 cm) = .28, not .28 cm.
*@
#$&*
Assuming that the ball in the experiment required .42 seconds to fall to the floor, what speeds do you conclude for each trial?
24cm/.42=57.1cm/s
24.5cm/.42=58.3cm/s
26cm/.42=61.9cm/s
13.5cm/.42=32.1cm/s
14.5cm/.42=34.5cm/s
@&
Some of these are velocity components perpendicular to the direction of motion.
*@
#$&*
Do you conclude that the magnet sped the ball up, slowed it down, or that it had no significant effect?
May have sped the ball up but not enough to tell
#$&*
For each set of trials, how much speed did the magnet induce in the direction perpendicular to the original direction?
A small amount
@&
It isn't that small, and I believe you probably calculated it but didn't recognize that you did.
*@
#$&*
The magnet is 5 cm long. Assuming that the force exerted by the magnet has a significant effect for only this distance, for what time interval was the ball influenced by the magnet?
Around half of the time interval, the ball was affected by the magnet
@&
You know how fast the ball was moving at the end of the ramp, so you have a very good idea how fast it was going when it passed the magnet. You can therefore calculate the time it took to pass with pretty good accuracy.
*@
#$&*
By how much did the momentum of the ball change due to the effect of the magnet, based on the velocity it attained perpendicular to its original line of motion? Assume the ball's mass to be 20 grams.
??
#$&*
What do you conclude was the average force exerted on the ball by the magnet?
???
#$&*
@&
You need to find the velocity component perpendicular to the motion, and the time interval during which the ball was being affected by the magnet. From these quantities you can figure out the average force exerted by the magnet.
*@
`q002. The magnet and domino on the strap were located 10.5 cm and 17 cm from the axis of rotation. On one trial the system rotated through 210 degrees in 6 seconds, ending up at rest.
What were the average and initial angular velocities of the system, in degrees / second, if we assume uniform angular acceleration?
V=35d/s
#$&*
What is the circumference of each of the circles around which the magnet and domino traveled?
17cm=34pi/cm
10.5cm=21pi/cm
@&
Circumferences could be measure in cm, but not in / cm. Nothing is being divided here, so there's no way the cm will end up in the denominator.
*@
#$&*
How far did each actually travel during the 210 degree rotation?
210/360x2pi(17)
62.3cm
#$&*
What therefore was the average speed of each around the arc, in units of distance / time?
10^2/17=5.9cm/s^2
60cm/6s
10cm/s
#$&*
What was the initial speed of each?
Since vf=0
Vo=20cm/s
Vave=10cm/s
#$&*
`q003. A radian is the angle subtended by the arc of a circle whose arc length is equal to the radius of that circle.
What are the lengths of the arcs of a circle of radius 15 cm corresponding to angles of 2 radians, 1/2 radian and 6 radians?
2rad=30cm
1/2rad=7.5cm
6rad=90cm
#$&*
What are the angles subtended on the same circle by arcs of 45 cm, 5 cm and 25 cm?
45cm-3rad
5cm-1/3rad
25cm-5/3 rad
#$&*
What is the angle subtended by an arc consisting of the entire circumference of the circle?
C=30pixcm
@&
The angle would be measured in radians, not in cm.
The circumference would be 30 pi cm. Following the pattern of the preceding questions, to how many radians would that correspond on this circle?
*@
#$&*
The angle subtended by an arc consisting of the entire circumference of any circle is 360 degrees. That angle is also 2 pi radians.
How many degrees are therefore contained in a radian?
57.3 deg
#$&*
How many radians are there in a degree?
About .012 rad
#$&*
Returning to the preceding problem, where the strap rotated through 210 degrees in 6 seconds, through how many radians did the strap rotate?
210/360x2pi
.58x2pi
3.66 rad
#$&*
Based on your result for the number of radians, what were the average and initial angular velocities of the strap?
3.66/6sec
Intial=1.22 rad/s
Ave=.61rad/s
Final=0rad/s
#$&*
Your answers to the preceding question would be in radians / second. If the initial angular velocity was maintained, through how many radians would the system rotate in one second?
1.22 rad/s
#$&*
Recall that one radian of angle corresponds to an arc distance equal to the radius. What arc distance would therefore correspond to one second's worth of rotation for the domino, were the initial angular velocity to be maintained?
1.22 rad/sx15cm=18.3rad/sxcm
@&
Good. This could be written
18.3 rad * cm / sec.
A radian of angle multiplied by a cm of radius gives you a cm of arc. To rad * cm / sec is just cm / sec.
Your answer could therefore be expressed as
18.3 cm/sec.
*@
#$&*
What arc distance would correspond to one second's worth of rotation for the magnet, were the initial angular velocity to be maintained?
70ded/s
@&
Arc distance isn't measure in deg / sec.
*@
#$&*
How fast are the domino and the magnet therefore moving at the initial instant?
70/360x15cm
@&
15 cm is not an arc distance corresponding to a 360 deg rotation.
*@
#$&*
`q004. Assume that the center of the strap is halfway between the domino and the magnet. How far then is the center of the strap from the axis of rotation?
3cm
#$&*
If the strap has mass 70 grams then what is its torque about the axis of rotation? The torque is equal to the weight of the strap multiplied by the distance of its center from the axis of rotation.
Torque=70gx3
210Ncm
@&
70 g * 3 cm is not 210 N cm, it's 210 g cm.
The mass is 70 g. You need to multiply the weight by the 3 cm moment arm.
*@
#$&*
If the domino has mass 17 grams then what is its torque about the axis of rotation?
T=17gx3cm
51N/cm
@&
Nothing in your calculation involved division by cm.
Your units don't come out in Newton.
*@
#$&*
Are the domino and the center of strap both on the same side of the axis of rotation, or on opposite sides? Do their torques therefore reinforce or work counter to one another?
Yes,same side
#$&*
What therefore is the total torque exerted by strap and domino?
210+51=261Ncm
#$&*
The torque produced by the magnet is equal and opposite to the sum of the other torques. What therefore is the magnitude of that torque, and what do you conclude is the mass of the magnet?
M1xd1-m2xd2=0
17gx17-m2x10.3
27.5=m2
#$&*
University Physics students: Find the moment of inertia of the strap itself, assuming it to be a uniform rod of length 30 cm and mass 70 grams. Note that the strap doesn't rotate about its center, so you'll have to do an integral. Begin by partitioning the length of the strap.
****
#$&*
`q005. If you got a reasonable result for the mass of the magnet, use it. Otherwise assume that the mass of the magnet is 50 grams.
You previously determined how fast the magnet and the domino were moving at the initial instant. What therefore were their kinetic energies?
KE=1/2(17)10cmcm/s^2
KE=850J
KE=1/2(27.5)7cm/s^2)
KE=673.75J
#$&*
The magnet is about three times as massive as the domino, both are moving at the same angular velocity, but the kinetic energy of the magnet is much less than three times the kinetic energy of the domino. How can this be?
Our measurements were smaller but not 3 times smaller than that of the energy of the domino
#$&*
"
@&
You'll want to revise some of your calculations. Many others look good.
&#Please see my notes and submit a copy of this document with revisions, comments and/or questions, and mark your insertions with &&&& (please mark each insertion at the beginning and at the end).
Be sure to include the entire document, including my notes. &#
*@