The apparatus shown above consists of two identical springs of negligible mass, each with spring constant k = 20.4 N/m and each attached at one end to a vertical rotating pole. Identical small spheres of mass m are attached to the other ends of the springs. The spheres are constrained by horizontal guides of negligible friction, each of which has a ruler below it for measuring the radial position r of the sphere. The system can be manually rotated about the pole’s axis. In a lab experiment, a student adjusts the rotational speed so that the spheres move to a desired radius r. For each such value of r, the student measures the rotational period T. The student’s partially completed data table is shown below. The length of each unstretched spring is L = 0.15 m. horizontal motion

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Chapter1: Units, Trigonometry. And Vectors
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(a) Calculate the missing values from the table above. Show
your
work in the space below
(b) On the axes below, plot the data points for the spring force F
Label the axes, including the scale. Draw a straight line that best represents the data
as a function of the acceleration a..
spring
(c)
i. Calculate the slope of your line.
ii. Indicate what the slope calculated in part (c)-i represents.
(d) One sphere and one spring are removed from the rotation apparatus. They are hung vertically so that
the sphere is now suspended from the spring, as shown below.
i. Describe a procedure you could use, and the measurements you would make, to verify the value
obtained in part (c) using the setup shown above.
ii. Show how you would use the measurements described in part (d)-i to verify the value obtained in
part (c).
Transcribed Image Text:(a) Calculate the missing values from the table above. Show your work in the space below (b) On the axes below, plot the data points for the spring force F Label the axes, including the scale. Draw a straight line that best represents the data as a function of the acceleration a.. spring (c) i. Calculate the slope of your line. ii. Indicate what the slope calculated in part (c)-i represents. (d) One sphere and one spring are removed from the rotation apparatus. They are hung vertically so that the sphere is now suspended from the spring, as shown below. i. Describe a procedure you could use, and the measurements you would make, to verify the value obtained in part (c) using the setup shown above. ii. Show how you would use the measurements described in part (d)-i to verify the value obtained in part (c).
19.
cm 30, 25, 20, 15, 10, 5,
„10 ,15 |20 125 ,30 cm
The apparatus shown above consists of two identical springs of negligible mass, each with spring
constant k = 20.4 N/m and each attached at one end to a vertical rotating pole. Identical small spheres of
mass m are attached to the other ends of the springs. The spheres are constrained to horizontal motion
by horizontal guides of negligible friction, each of which has a ruler below it for measuring the radial
position r of the sphere. The system can be manually rotated about the pole's axis. In a lab experiment,
a student adjusts the rotational speed so that the spheres move to a desired radius r. For each such value
of r, the student measures the rotational period T. The student’'s partially completed data table is shown
below. The length of each unstretched spring is L = 0.15 m.
Radial
Acceleration Spring Force
Period
Trial
Position
T (s)
a. (m/s²)
Fspring (N)
r (m)
1
0.300
0.440
61.2
3.06
2
0.270
0.475
47.2
2.45
0.240
0.530
4
0.210
0.570
25.5
1.22
0.180
0.795
11.2
0.61
5.
Transcribed Image Text:19. cm 30, 25, 20, 15, 10, 5, „10 ,15 |20 125 ,30 cm The apparatus shown above consists of two identical springs of negligible mass, each with spring constant k = 20.4 N/m and each attached at one end to a vertical rotating pole. Identical small spheres of mass m are attached to the other ends of the springs. The spheres are constrained to horizontal motion by horizontal guides of negligible friction, each of which has a ruler below it for measuring the radial position r of the sphere. The system can be manually rotated about the pole's axis. In a lab experiment, a student adjusts the rotational speed so that the spheres move to a desired radius r. For each such value of r, the student measures the rotational period T. The student’'s partially completed data table is shown below. The length of each unstretched spring is L = 0.15 m. Radial Acceleration Spring Force Period Trial Position T (s) a. (m/s²) Fspring (N) r (m) 1 0.300 0.440 61.2 3.06 2 0.270 0.475 47.2 2.45 0.240 0.530 4 0.210 0.570 25.5 1.22 0.180 0.795 11.2 0.61 5.
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