COLLEGE PHYSICS
2nd Edition
ISBN: 9781464196393
Author: Freedman
Publisher: MAC HIGHER
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Chapter 1, Problem 45QAP
To determine
To show:
The dimensions in the equations are consistent.
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The period T of a simple pendulum is the amount of time required for it to undergo one complete oscillation. If the length of the pendulum is L� and the acceleration of gravity is gg, then T� is given by
T=2πLpgq
Find the powers p� and q� required for dimensional consistency.
Enter your answers numerically separated by a comma.
Physical units in mechanics are usually some combination of the dimensions time T, mass M, and length L. Consider the
physical quantities m, r, u, a, and t with dimensions [m] = M, [r] = L, [u] = LT-, [a] = LT-2, and [1] = T.
Enter the dimensional expression of the quantity on the right-hand side of each equation. Your answers may contain only M, L,
T, and exponents.
Assume that each of the following equations is dimensionally consistent.
Lo = mur
[Lo] =
W = mar
[W] =
T
A rectangular box for a new product is designed in such a way that the three dimensions always have a particular relationship defined by the variable x. The volume of the box can be written as (6x^3)+(31x^2)+(53x)+30, and the height is always x+2. What are the width and length of the box?
Chapter 1 Solutions
COLLEGE PHYSICS
Ch. 1 - Prob. 1QAPCh. 1 - Prob. 2QAPCh. 1 - Prob. 3QAPCh. 1 - Prob. 4QAPCh. 1 - Prob. 5QAPCh. 1 - Prob. 6QAPCh. 1 - Prob. 7QAPCh. 1 - Prob. 8QAPCh. 1 - Prob. 9QAPCh. 1 - Prob. 10QAP
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- A surveyor measures the distance across a straight river by the following method (Fig. P1.6). Starting directly across from a tree on the opposite bank, she walks d = 100 m along the riverbank to establish a baseline. Then she sights across to the tree. The angle from her baseline to the tree is 0 = 35.0. How wide is the river? Figure P1.6arrow_forwardConsider the physical quantities m,s,v,a, and t with dimensions [m]=M,[s]=L,[v]=LT1 and [a]=LT2 . Assuming each of the following equations is dimensionally consistent, find the dimension of the quantity on the left-hand side of the equation: (a)F=ma;(b)K=0.5mv2;(c)p=mv;(d)W=mas;(e)L=mvrarrow_forwardThree displacement vectors of a croquet ball are shown in Figure P1.44, where |A|=20.0units, |B|=40.0units, and |C|=30.0units. Find (a) the resultant in unit-vector notation and (b) the magnitude and direction of the resultant displacement. Figure P1.44arrow_forward
- A person going for a walk follows the path shown in Figure P1.51. The total trip consists of four straight-line paths. At the end of the walk, what is the persons resultant displacement measured from the starting point? Figure P1.51arrow_forwardRoughly how many heartbeats are there in a lifetime?arrow_forwardConsider the equation y=mt+b, where the dimension of y is length and the dimension of t is time, and mand bare constants. What are the dimensions and SI units of (a) mand (b) b ?arrow_forward
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