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Consider the equation $v=\frac{1}{3} z x t^{2}$ . The dimensions of the variables $v, x,$and $t$ are $[\mathrm{L}] / \mathrm{T} ],[\mathrm{L}],$ and $[\mathrm{T}],$ respectively. The numerical factor 3 is dimensionless. What must be the dimensions of the variable $z,$ such thatboth sides of the equation have the same dimensions? Show how youdetermined your answer.
$z$ dimension is $\frac{1}{[T]^{3}}$
Physics 101 Mechanics
Chapter 1
Introduction and Mathematical Concepts
Physics Basics
University of Washington
Simon Fraser University
University of Sheffield
University of Winnipeg
Lectures
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Oh, hello there. Hope you're doing well today. We have exciting new problem here. So we have a is equal to 1/3 Z eggs T square, all right. And this problem we're gonna be solving for the units or the unit dimensions of Z and how we were going to do that. We know that the as dimensions of oh, over TV Minister, little brackets around this, no one teaches shorts up their dimensions. And so those length t is Time and X has dimensions of playing so that there is mill and T has demon dimensions of time. All right, we're gonna resolving for the dimensions of Z groups. All right, so we can play all these dimensions in for their values. And since 1/3 is a dimension less value, you need me that it's just kind of a factor in there too. Make the math work out nicely. Um, we It doesn't have any actual dimensions, though. So if we plug in the dimensions to the equation Yeah, Ling, divided by time, is equal to see which we're solving for X, which is equal length and T square origin's gonna be equal to the dimension of time square. Okay, Hopefully, um well, from here on out, we can just solve for Z. Uh, using some I want you right here so we can divide both sides by el thes Those air gonna cancel and the next week and divide four sides by time squared. So I will read. Write that down here. You get one over time. Huge brain. This is already, um that's right, Sugar. It's already provided by, uh, this week to the teacher. The first, right. We're inviting anybody cheese squared. That's gonna give us We're over t cubed. That is going to be equal. Gesine. And there you have it. Who? That was super helpful. Um, good luck on your homework and see you next time.
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