Two students want to measure the acceleration a of a cart rolling down an inclined plane. The cart starts at rest and travels a distance s down the plane. The first student estimates the acceleration by measuring the instantaneous velocity v just as the cart has traveled s meters, and uses the formula a = v²/2s. The second student estimates the acceleration by measuring the time, in seconds, that the cart takes to travel s meters, and uses the formula a = 2s/t. Assume that s = 1 m, and that there is negligible uncertainty in s. Assume that v = 3.2 + 0.1 m/s and that t = 0.63 + 0.01 s. Assume that the measurements of v and t are independent. Compute the acceleration using the method of the first student. Call this estimate az. Find the uncertainty in a̟. a. b. Compute the acceleration using the method of the second shudent. Call this estimate az. Find the uncertainty in a,. Find the weighted average of a, and a, that has the smallest uncertainty. Find the C. uncertainty in this weighted average.
Two students want to measure the acceleration a of a cart rolling down an inclined plane. The cart starts at rest and travels a distance s down the plane. The first student estimates the acceleration by measuring the instantaneous velocity v just as the cart has traveled s meters, and uses the formula a = v²/2s. The second student estimates the acceleration by measuring the time, in seconds, that the cart takes to travel s meters, and uses the formula a = 2s/t. Assume that s = 1 m, and that there is negligible uncertainty in s. Assume that v = 3.2 + 0.1 m/s and that t = 0.63 + 0.01 s. Assume that the measurements of v and t are independent. Compute the acceleration using the method of the first student. Call this estimate az. Find the uncertainty in a̟. a. b. Compute the acceleration using the method of the second shudent. Call this estimate az. Find the uncertainty in a,. Find the weighted average of a, and a, that has the smallest uncertainty. Find the C. uncertainty in this weighted average.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Two students want to measure the acceleration a of a cart rolling down an inclined plane.
The cart starts at rest and travels a distance s down the plane. The first student estimates the
acceleration by measuring the instantaneous velocity v just as the cart has traveled s meters,
and uses the formula a = v²/2s. The second student estimates the acceleration by measuring
the time, in seconds, that the cart takes to travel s meters, and uses the formula a = 2s/t.
Assume that s = 1 m, and that there is negligible uncertainty in s. Assume that v = 3.2 + 0.1
m/s and that t = 0.63 + 0.01 s. Assume that the measurements of v and t are independent.
Compute the acceleration using the method of the first student. Call this estimate az.
Find the uncertainty in a̟.
a.
b. Compute the acceleration using the method of the second shudent. Call this estimate az.
Find the uncertainty in a,.
Find the weighted average of a, and a, that has the smallest uncertainty. Find the
C.
uncertainty in this weighted average.
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