Table 1 - Position and number of oscillations for a mass-spring Mass of disc(s) + platform (g) ±0.5 g Position of the platform (cm) +0.3 cm 51.4 151.2 251.0 351.4 451.2 551.6 31.1 42.8 55.3 66.8 77.1 88.2 system with different hanging masses. # of oscillations for 1 minute ±1 86 62 51 44 39 36 Using the data from Table 1 in the experimental details, calculate "the uncertainty of the square of the period of oscillation (in s²) for a hanging mass of 151.2 g" using the propagation of error method. You must consider the uncertainty on the time measured and the number of oscillations given in the experimental details. Round your answer to 3 decimal places.

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Chapter5: Energy
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Note the square of the period of oscillation for a hanging mass of 151.2 g is 0.937s^2..... (calculate it to get more decimals)

1) Suspended mass on a spring
We record the results for the extension of the spring and the oscillation of the mass-spring system
in Table 1.
In this classic physics experiment, we want to find the properties of a conical-shape spring. We
examine the spring and measure its mass to be (154.5 ± 0.5) g. We attach the spring vertically to a
rod then attach a small hook with a platform to the spring. The platform allows us to stack small
discs on it to change the mass that is attached to the spring. A long ruler is attached to the rod
Table 1- Position and number of oscillations for a mass-spring system with different hanging masses.
Mass of disc(s) +
platform (g)
+ 0.5 g
Position of the
# of oscillations
platform (cm)
+ 0.3 сm
for 1 minute
which allows us to measure the position of the platform. The complete setup (with spring, platform,
ruler, and discs) is shown in Figure 1.
+ 1
51.4
31.1
86
151.2
42.8
62
251.0
55.3
51
351.4
66.8
44
451.2
77.1
39
551.6
88.2
36
Using the data from Table 1 in the experimental details, calculate "the uncertainty of
the square of the period of oscillation (in s2) for a hanging mass of 151.2 g" using the
propagation of error method. You must consider the uncertainty on the time
measured and the number of oscillations given in the experimental details. Round
your answer to 3 decimal places.
Fig. 1- Setup of a vertical mass on a spring experiment
We want to measure several relationships of the mass-spring system including the position of the
platform with respect to the added mass and the number oscillations during a fixed time
interval. We line the top of the spring with a reference position on the ruler and measure the initial
position of the platform (like seen in the figure). We then start adding discs to the platform one by
one and make several measurements. For each added disc, we record using either our ruler, a
balance, or a chronometer:
1) The mass of the disc(s) + platform (with uncertainty ± 0.5 g)
2) The new position of the platform (with uncertainty ± 0.3 cm)
2) The # of oscillations (with uncertainty + 1) for a time of one minute (with uncertainty + 0.5 s)
Transcribed Image Text:1) Suspended mass on a spring We record the results for the extension of the spring and the oscillation of the mass-spring system in Table 1. In this classic physics experiment, we want to find the properties of a conical-shape spring. We examine the spring and measure its mass to be (154.5 ± 0.5) g. We attach the spring vertically to a rod then attach a small hook with a platform to the spring. The platform allows us to stack small discs on it to change the mass that is attached to the spring. A long ruler is attached to the rod Table 1- Position and number of oscillations for a mass-spring system with different hanging masses. Mass of disc(s) + platform (g) + 0.5 g Position of the # of oscillations platform (cm) + 0.3 сm for 1 minute which allows us to measure the position of the platform. The complete setup (with spring, platform, ruler, and discs) is shown in Figure 1. + 1 51.4 31.1 86 151.2 42.8 62 251.0 55.3 51 351.4 66.8 44 451.2 77.1 39 551.6 88.2 36 Using the data from Table 1 in the experimental details, calculate "the uncertainty of the square of the period of oscillation (in s2) for a hanging mass of 151.2 g" using the propagation of error method. You must consider the uncertainty on the time measured and the number of oscillations given in the experimental details. Round your answer to 3 decimal places. Fig. 1- Setup of a vertical mass on a spring experiment We want to measure several relationships of the mass-spring system including the position of the platform with respect to the added mass and the number oscillations during a fixed time interval. We line the top of the spring with a reference position on the ruler and measure the initial position of the platform (like seen in the figure). We then start adding discs to the platform one by one and make several measurements. For each added disc, we record using either our ruler, a balance, or a chronometer: 1) The mass of the disc(s) + platform (with uncertainty ± 0.5 g) 2) The new position of the platform (with uncertainty ± 0.3 cm) 2) The # of oscillations (with uncertainty + 1) for a time of one minute (with uncertainty + 0.5 s)
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