Each of the following equations was given by a student during an examination 1/2 mv^2=1/2 mv_0^2+√mgh v=v_0+at^2 ma=v^2 Do a dimensional analysis of each equation and explain why the equation can’t be correct. (Hint: Determine the dimensions on each side of the equation and compare them.)
Each of the following equations was given by a student during an examination 1/2 mv^2=1/2 mv_0^2+√mgh v=v_0+at^2 ma=v^2 Do a dimensional analysis of each equation and explain why the equation can’t be correct. (Hint: Determine the dimensions on each side of the equation and compare them.)
University Physics Volume 1
18th Edition
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:William Moebs, Samuel J. Ling, Jeff Sanny
Chapter1: Units And Measurement
Section: Chapter Questions
Problem 65P: A floating-point operation is a single arithmetic operation such as addition, subtraction,...
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- Each of the following equations was given by a student during an examination
- 1/2 mv^2=1/2 mv_0^2+√mgh
- v=v_0+at^2
- ma=v^2
Do a dimensional analysis of each equation and explain why the equation can’t be correct. (Hint: Determine the dimensions on each side of the equation and compare them.)
Expert Solution
Step 1
1)
The equation is given as,
Here, v0 and v denotes the initial and the final velocity, g denotes the acceleration due to gravity, h denotes the height, m denotes the mass.
The equation has three terms which are added. The dimension of each term should be same for the dimensional correctness of the equation. Let’s find the dimension of each term.
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