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Your video analysis of the motion of a marble gives it position in frame 23 as (723, 923) = (0.134 m, 0.120 m) and its position in frame 24 as (x24, 924) = (0.122 m, 0.112 m). You esti- 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 10-6s. The mass of the marble is (2.031±0.001) x 10-2 kg. Calculate the following quantities: 1. The value of the velocity component U = Xi+1Xi At and its uncertainty, Yi+1-yi and its uncertainty, At v2+2 and its uncertainty, 2. The value of the velocity component vy 3. The value of the velocity magnitude v = 4. The value of the momentum component pr = mv, and its uncertainty, 5. The value of the momentum component Py = muy and its uncertainty, and 6. The value of the kinetic energy K = mv² = m(v² + v²) and its uncertainty. =

Your video analysis of the motion of a marble gives it position in frame 23 as (723, 923) = (0.134 m, 0.120 m) and its position in frame 24 as (x24, 924) = (0.122 m, 0.112 m). You esti- 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 10-6s. The mass of the marble is (2.031±0.001) x 10-2 kg. Calculate the following quantities: 1. The value of the velocity component U = Xi+1Xi At and its uncertainty, Yi+1-yi and its uncertainty, At v2+2 and its uncertainty, 2. The value of the velocity component vy 3. The value of the velocity magnitude v = 4. The value of the momentum component pr = mv, and its uncertainty, 5. The value of the momentum component Py = muy and its uncertainty, and 6. The value of the kinetic energy K = mv² = m(v² + v²) and its uncertainty. =

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Your video analysis of the motion of a marble gives it position in frame 23 as (x23, 923) = (0.134 m, 0.120 m) and its position in frame 24 as (x24, Y24) = (0.122 m, 0.112 m). You esti- 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 (At) = 1 x 10-6 s. The mass of the marble is (2.031 +0.001) x 10-2 kg. Calculate the following quantities: 1. The value of the velocity component U = Xi+1Xi At and its uncertainty, Yi+1 Yi = and its uncertainty, At 2. The value of the velocity component vy 3. The value of the velocity magnitude v = 4. The value of the momentum component p 5. The value of the momentum component Py = muy and its uncertainty, and 6. The value of the kinetic energy K = =mv² = m(v²+v²) and its uncertainty. v2+2 and its uncertainty, = mv, and its uncertainty,
Transcribed Image Text:Your video analysis of the motion of a marble gives it position in frame 23 as (x23, 923) = (0.134 m, 0.120 m) and its position in frame 24 as (x24, Y24) = (0.122 m, 0.112 m). You esti- 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 (At) = 1 x 10-6 s. The mass of the marble is (2.031 +0.001) x 10-2 kg. Calculate the following quantities: 1. The value of the velocity component U = Xi+1Xi At and its uncertainty, Yi+1 Yi = and its uncertainty, At 2. The value of the velocity component vy 3. The value of the velocity magnitude v = 4. The value of the momentum component p 5. The value of the momentum component Py = muy and its uncertainty, and 6. The value of the kinetic energy K = =mv² = m(v²+v²) and its uncertainty. v2+2 and its uncertainty, = mv, and its uncertainty,
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