PHYSICS 1250 PACKAGE >CI<
PHYSICS 1250 PACKAGE >CI<
9th Edition
ISBN: 9781305000988
Author: SERWAY
Publisher: CENGAGE LEARNING (CUSTOM)
Question
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Chapter 16, Problem 16.42P

(a)

To determine

The value of A from scalar quantity 4(7+3) .

(a)

Expert Solution
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Answer to Problem 16.42P

The value of A from scalar quantity 4(7+3) is 40 .

Explanation of Solution

Given info: The scalar quantity A is 4(7+3) .

The formula to calculate scalar quantity A is,

A=a(b+c)

Here,

a is the scalar value.

b is the scalar value.

c is the scalar value.

Substitute 4 for a , 7 for b and 3 for c in the above expression.

A=4(7+3)=40

Conclusion:

Therefore, the value of A from scalar quantity 4(7+3) is 40 .

(b)

To determine

To write: The value of A,B and C in the vector quantity 700i^+3.00k^=Ai^+Bj^+Ck^ .

(b)

Expert Solution
Check Mark

Answer to Problem 16.42P

The value of A is 7 , B is 0 and C is 3 .

Explanation of Solution

Given info: The scalar quantity A is 4(7+3) and the vector quantity is 700i^+3.00k^=Ai^+Bj^+Ck^ .

The given vectors are,

700i^+3.00k^ and Ai^7+Bj^+Ck^

The given two vectors are said to be equal if the magnitude of one vector equals the magnitude of other vector and direction in all the three axes are equal.

Compare the respective coefficient of i^ , j^ and k^ ,

A=700B=0C=3.00

Conclusion:

Therefore, the value of A is 7 , B is 0 and C is 3 .

(c)

To determine

The proper way to get the answer and convince the student.

(c)

Expert Solution
Check Mark

Answer to Problem 16.42P

The comparison of the unit vectors on both sides of equation the given equation is the proper way to convince the student how we arrive at the answer.

Explanation of Solution

Given info: The scalar quantity A is 4(7+3) and the vector quantity is 700i^+3.00k^=Ai^+Bj^+Ck^ .

The dot product generates a scalar as output. The coefficients of same unit vector are multiplied and added to get the answer.

The unit vectors in three mutually perpendicular axes are i^ in x direction j^ in y direction and k^ in z direction.

The coefficients of i^ , j^ and k^ are compared to get the three unknowns.

The coefficient of j^ is 0 in 700i^+3.00k^ . So the value of B is 0. The coefficient of i^ is 700 in 700i^+3.00k^ . So the value of A is 700 and the coefficient of k^ is 3.00 in 700i^+3.00k^ . So the value of C is 3.00 .

Conclusion:

Therefore, the comparison of the unit vectors on both sides of equation the given equation is the proper way to convince the student how we arrive at the answer.

(d)

To determine

The values of A , B , C , D and E from the functional equality.

(d)

Expert Solution
Check Mark

Answer to Problem 16.42P

The value of A is 0 , B is 7.00 , C is 3rad/m , D is 4rad/s and E is 2rad .

Explanation of Solution

Given info: The scalar quantity A is 4(7+3) and the vector quantity is 700i^+3.00k^=Ai^+Bj^+Ck^ . The functional equality is A+Bcos(Cx+Dt+E)=7.00cos(3x+4t+2) .

Compare the given functional equality for the values of A , B , C , D and E .

The given functional equality is,

A+Bcos(Cx+Dt+E)=7.00cos(3x+4t+2)

Rewrite the above equation as,

A+Bcos(Cx+Dt+E)=0+7.00cos(3x+4t+2)

Compare the above expression.

A=0B=7.00C=3rad/mD=4rad/sE=2rad

Conclusion:

Therefore, the value of A is 0 , B is 7.00 , C is 3rad/m and D is 4rad/s .

(e)

To determine

The way to get the answer.

(e)

Expert Solution
Check Mark

Answer to Problem 16.42P

The comparison of the given functional equality is helped to get the answer A is 0 , B is 7.00 , C is 3rad/m and D is 4rad/s .

Explanation of Solution

Given info: The scalar quantity A is 4(7+3) and the vector quantity is 700i^+3.00k^=Ai^+Bj^+Ck^ . The functional equality is A+Bcos(Cx+Dt+E)=7.00cos(3x+4t+2) .

The given functional equality is,

A+Bcos(Cx+Dt+E)=7.00cos(3x+4t+2)

Add 0 on the R.H.S of the above equation.

A+Bcos(Cx+Dt+E)=0+7.00cos(3x+4t+2)

Compare the R.H.S and L.H.S of the above equality,

A=0B=7.00C=3rad/mD=4rad/sE=2rad

Conclusion:

Therefore, the comparison of the given functional equality is helped to get the answer A is 0 , B is 7.00 , C is 3rad/m and D is 4rad/s .

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Chapter 16 Solutions

PHYSICS 1250 PACKAGE >CI<

Ch. 16 - Which of the following statements is not...Ch. 16 - Prob. 16.7OQCh. 16 - Prob. 16.8OQCh. 16 - The distance between two successive peaks of a...Ch. 16 - Prob. 16.1CQCh. 16 - (a) How would you create a longitudinal wave in a...Ch. 16 - When a pulse travels on a taut string, does it...Ch. 16 - Prob. 16.4CQCh. 16 - If you steadily shake one end of a taut rope three...Ch. 16 - (a) If a long rope is hung from a ceiling and...Ch. 16 - Why is a pulse on a string considered to be...Ch. 16 - Does the vertical speed of an element of a...Ch. 16 - In an earthquake, both S (transverse) and P...Ch. 16 - A seismographic station receives S and P waves...Ch. 16 - Ocean waves with a crest-to-crest distance of 10.0...Ch. 16 - At t = 0, a transverse pulse in a wire is...Ch. 16 - Two points A and B on the surface of the Earth are...Ch. 16 - A wave is described by y = 0.020 0 sin (kx - t),...Ch. 16 - A certain uniform string is held under constant...Ch. 16 - A sinusoidal wave is traveling along a rope. The...Ch. 16 - For a certain transverse wave, the distance...Ch. 16 - Prob. 16.9PCh. 16 - When a particular wire is vibrating with a...Ch. 16 - The string shown in Figure P16.11 is driven at a...Ch. 16 - Consider the sinusoidal wave of Example 16.2 with...Ch. 16 - Prob. 16.13PCh. 16 - (a) Plot y versus t at x = 0 for a sinusoidal wave...Ch. 16 - A transverse wave on a siring is described by the...Ch. 16 - A wave on a string is described by the wave...Ch. 16 - A sinusoidal wave is described by the wave...Ch. 16 - A sinusoidal wave traveling in the negative x...Ch. 16 - (a) Write the expression for y as a function of x...Ch. 16 - A transverse sinusoidal wave on a string has a...Ch. 16 - Review. The elastic limit of a steel wire is 2.70 ...Ch. 16 - A piano siring having a mass per unit length equal...Ch. 16 - Transverse waves travel with a speed of 20.0 m/s...Ch. 16 - A student taking a quiz finds on a reference sheet...Ch. 16 - An Ethernet cable is 4.00 in long. The cable has a...Ch. 16 - A transverse traveling wave on a taut wire has an...Ch. 16 - A steel wire of length 30.0 m and a copper wire of...Ch. 16 - Why is the following situation impossible? An...Ch. 16 - Tension is maintained in a string as in Figure...Ch. 16 - Review. A light string with a mass per unit length...Ch. 16 - Prob. 16.31PCh. 16 - In a region far from the epicenter of an...Ch. 16 - Transverse waves are being generated on a rope...Ch. 16 - Sinusoidal waves 5.00 cm in amplitude are to be...Ch. 16 - A sinusoidal wave on a string is described by die...Ch. 16 - A taut tope has a mass of 0.180 kg and a length...Ch. 16 - A long string carries a wave; a 6.00-m segment of...Ch. 16 - A horizontal string can transmit a maximum power...Ch. 16 - The wave function for a wave on a taut siring is...Ch. 16 - A two-dimensional water wave spreads in circular...Ch. 16 - Prob. 16.41PCh. 16 - Prob. 16.42PCh. 16 - Show that the wave function y = eb(x vt) is a...Ch. 16 - Prob. 16.44PCh. 16 - Prob. 16.45APCh. 16 - The wave is a particular type of pulse that can...Ch. 16 - A sinusoidal wave in a rope is described by the...Ch. 16 - The ocean floor in underlain by a layer of basalt...Ch. 16 - Review. A 2.00-kg I Jock hangs from a rubber cord,...Ch. 16 - Review. A block of mass M hangs from a rubber...Ch. 16 - A transverse wave on a sting described by the wave...Ch. 16 - A sinusoidal wave in a string is described by the...Ch. 16 - Review. A block of mass M, supported by a string,...Ch. 16 - An undersea earthquake or a landslide can produce...Ch. 16 - Review. A block of mass M = 0.450 kg is attached...Ch. 16 - Review. A block of mass M = 0.450 kg is attached...Ch. 16 - Prob. 16.57APCh. 16 - Prob. 16.58APCh. 16 - A wire of density is tapered so that its...Ch. 16 - A rope of total mass m and length L is suspended...Ch. 16 - Prob. 16.61APCh. 16 - Prob. 16.62APCh. 16 - Review. An aluminum wire is held between two...Ch. 16 - Assume an object of mass M is suspended from the...Ch. 16 - Prob. 16.65CPCh. 16 - A string on a musical instrument is held under...Ch. 16 - If a loop of chain is spun at high speed, it can...
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