COLLEGE PHYSICS
2nd Edition
ISBN: 9781464196393
Author: Freedman
Publisher: MAC HIGHER
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Chapter 1, Problem 45QAP
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The dimensions in the equations are consistent.
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The period (T) of a simple pendulum is given by the formula T = 2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity. Using dimensional analysis, determine the expression for the dimension of g in terms of the fundamental dimensions of mass (M), length (L), and time (T).
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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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- One student uses a meterstick to measure the thickness of a textbook and obtains 4.3 cm 0.1 cm. Other students measure the thickness with vernier calipers and obtain four different measurements: (a) 4.32 cm 0.01 cm. (b) 4.31 cm 0.01 cm, (c) 4.24 cm 0.01 cm, and (d) 4.43 cm 0.01 cm. Which of these four measurements, if any, agree with that obtained by the first student?arrow_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_forwardA 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_forward
- A sidewalk is to be constructed around a swimming pool that measures (10.0 0.1) m by (17.0 0.1) m. If the sidewalk is to measure (1.00 0.01) m wide by (9.0 0.1) cm thick, what volume of concrete is needed and what is the approximate uncertainty of this volume?arrow_forwardA 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_forwardUse the rules for significant figures to find the answer to the addition problem 21.4 + 15 + 17.17 + 4.003. (See Section 1.4).arrow_forward
- Consider 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_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_forwardFigure P1.6 shows a frustum of a cone. Match each of the three expressions (a) (r1 + r2)[h2 + (r2 r1)2]1/2, (b) 2(r1 + r2), and (c) h(r12 + r1r2 + r22)/3 with the quantity it describes: (d) the total circumference of the flat circular faces, (e) the volume, or (f) the area of the curved surface. Figure P1.6arrow_forward
- (a) Suppose the displacement of an object is related to time according to the expression x = Bt2. What are the dimensions of B? (b) A displacement is related to time as x = A sin (2ft), where A and f are constants. Find the dimensions of A. Hint: A trigonometric function appearing in an equation must be dimensionless.arrow_forward(a) Suppose the displacement of an object is related to time according to the expression x = Bt2. What are the dimensions of B? (b) A displacement is related to time as x = A sin (2ft), where A and f are constants. Find the dimensions of A. Hint: A trigonometric function appearing in an equation must be dimensionless.arrow_forwardThe period of a pendulum is the time it takes the pendulum to swing back and forth once. If the only dimensional quantities that the period depends on are the acceleration of gravity, g, and the length of the pendulum, l, what combination of g and l must the period be proportional to? (Acceleration has SI units of m/s^2)arrow_forward
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