Complete these calculations of uncertainty propagation and submit them for the pre-la assignment. You must show your work in your submission. Your video analysis of the motion of a marble gives it position in frame 23 as (x23, Y23) (0.134 m, 0.120 m) and its position in frame 24 as (x24, Y24) : mate that you can measure the x and y positions with uncertainty +0.003 m. The frame ra of the video is 30 frames/s, which means the time interval between frames is At = 0.033 333 The uncertainty of the frame rate of a video camera is VERY small. For the sake of this pro lem, use 8(At) =1 x 10-6 s. The mass of the marble is (2.031 ±0.001) × 10-2 kg. Calcula the following quantities: (0.122 m, 0.112 m). You est

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Complete these calculations of uncertainty propagation and submit them for the pre-lab
assignment. You must show your work in your submission.
Your video analysis of the motion of a marble gives it position in frame 23 as (x23. Upa) :
(0.134m,
mate that you can measure the x and y positions with uncertainty ±0.003 m. The frame rate
of the video is 30 frames/s, which means the time interval between frames is At = 0.033 333 s.
The uncertainty of the frame rate of a video camera is VERY small. For the sake of this prob-
lem, use 8(At) = 1 x 10-6 s. The mass of the marble is (2.031 ± 0.001) × 10-2 kg. Calculate
the following quantities:
0.120 m) and its position in frame 24 as (x24, Y24)
(0.122m, 0.112 m). You esti-
Xi+1 – X;
1. The value of the velocity component v =
and its uncertainty,
At
2. The value of the velocity component Vy
Yi+1-Yi and its uncertainty,
|
At
/v2+v and its uncertainty,
mv, and its uncertainty,
5. The value of the momentum component P, = mv, and its uncertainty, and
6. The value of the kinetic energy K = !mv? = !m(v? + v?) and its uncertainty.
3. The value of the velocity magnitude v =
4. The value of the momentum component Px
%3D
%3D
(34
Transcribed Image Text:Complete these calculations of uncertainty propagation and submit them for the pre-lab assignment. You must show your work in your submission. Your video analysis of the motion of a marble gives it position in frame 23 as (x23. Upa) : (0.134m, mate that you can measure the x and y positions with uncertainty ±0.003 m. The frame rate of the video is 30 frames/s, which means the time interval between frames is At = 0.033 333 s. The uncertainty of the frame rate of a video camera is VERY small. For the sake of this prob- lem, use 8(At) = 1 x 10-6 s. The mass of the marble is (2.031 ± 0.001) × 10-2 kg. Calculate the following quantities: 0.120 m) and its position in frame 24 as (x24, Y24) (0.122m, 0.112 m). You esti- Xi+1 – X; 1. The value of the velocity component v = and its uncertainty, At 2. The value of the velocity component Vy Yi+1-Yi and its uncertainty, | At /v2+v and its uncertainty, mv, and its uncertainty, 5. The value of the momentum component P, = mv, and its uncertainty, and 6. The value of the kinetic energy K = !mv? = !m(v? + v?) and its uncertainty. 3. The value of the velocity magnitude v = 4. The value of the momentum component Px %3D %3D (34
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