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, 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) × 10-2 kg. Calculate the following quantities: 4. The value of the momentum component p = 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 (x23, 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) × 10-2 kg. Calculate the following quantities: 4. The value of the momentum component p = 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.

Modern Physics

3rd Edition

ISBN:9781111794378

Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Chapter1: Relativity I

Section: Chapter Questions

Problem 13P: The muon is an unstable particle that spontaneously decays into an electron and two neutrinos. If...

See similar textbooks

Similar questions

Explain why, when defining the length of a rod, it is necessary to specify that the positions of the ends of the rod are to be measured simultaneously.
The muon is an unstable particle that spontaneously decays into an electron and two neutrinos. If the number of muons at t = 0 is N0, the number at time t is given by , where τ is the mean lifetime, equal to 2.2 μs. Suppose the muons move at a speed of 0.95c and there are 5.0 × 104 muons at t = 0. (a) What is the observed lifetime of the muons? (b) How many muons remain after traveling a distance of 3.0 km?
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…
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) = (0.102 m, 0.112 m). You estimate 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 = 0.033333 s. The uncertainty of the frame rate of a video camera is VERY small. For the sake of this problem, use 8(At) = 1 x 10- s. The mass of the marble is (2.031 +0.001) × 10 kg.
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 (24 , Y24) = (0.102 m, 0.112 m). You estimate that you can measure the r 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 = 0.033333 s. The uncertainty of the frame rate of a video camera is VERY small. For the sake of this problem, use 8(At) = 1 x 10 s. The mass of the marble is (2.031 0.001) x 10 2 kg.
To estimate the velocity of a toy car you measure that it moves a distance of (20.0 +\- 0.03) meters in a time of (4.00 +\- 0.04) seconds. Use the rules for uncertainty propagation to obtain a value for the car’s associated uncertainty.
To estimate the velocity of a toy car you measure that it moves a distance of (20.0 +/- 0.03) meters in a time of (4.00 +\- 0.04) seconds. Use the rules for uncertainty propagation to obtain a value for the car’s velocity.
A car drives on a road and its position at timet (in hours) is (x(t), y(t)) where x and y are two differentiable functions that satisfy the equation æ(t)³ + y(t)³ = 9æ(t)y(t) +1 || (all distances in kilometers). A radar speed gun is placed in the origin. At time t = car and the radar speed gun increases with 50 kilometers per hour. Calculate x' (0). 0 the car is at the point (0, 1) and the distance between the
A fly with a mass of 23.7 mg is moving with a velocity of 6.7 m/s + 10%. What is the momentum of this fly? kgm/s What is the uncertainty in the momentum measurement? kgm/s At best, what is the uncertainty in the position of the fly? m Are we very certain with this measurement? Yes O No
Most real time clock chips use 32.678 KHz crystals (2^15), Why clock chips of 2^12 Hz or 2^18 Hz are not considered just as good?
Albert Einstein is pondering how to write his (soonto-be-famous) equation. He knows that energy E is a function of mass m and the speed of light c, but he doesn't know the functional relationship (E = m2c? E = mc4?). Pretend that Albert knows nothing about dimensional analysis, but since you are taking a fluid mechanics class, you help Albert come up with his equation. Use the step-by-step method of repeating variables to generate a dimensionless relationship between these parameters, showing all of your work. Compare this to Einstein's famous equation—does dimensional analysis give you the correct form of the equation?
A galaxy G is moving away radially with speed with respect to an observer O. The relation between X, the wavelength of light emitted at G, and λo, the wavelength observed at O, is 入。 λ = λe λε 1+B 1- B' = where ẞ v/c (c is the speed of light). For ẞ < 1 find a power series expansion of the above formula up to and including terms of order ẞ³.