Classical Dynamics of Particles and Systems
5th Edition
ISBN: 9780534408961
Author: Stephen T. Thornton, Jerry B. Marion
Publisher: Cengage Learning
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Chapter 1, Problem 1.4P
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(a) (AB)t = BtAt (b) (AB)−1 = B−1 A−1
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Four capacitors are connected as shown in the figure below. (Let C = 12.0 μF.)
a
C
3.00 με
Hh.
6.00 με
20.0 με
HE
(a) Find the equivalent capacitance between points a and b.
5.92
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(b) Calculate the charge on each capacitor, taking AV ab = 16.0 V.
20.0 uF capacitor 94.7
6.00 uF capacitor 67.6
32.14
3.00 µF capacitor
capacitor C
☑
με
με
The 3 µF and 12.0 uF capacitors are in series and that combination is in parallel with the 6 μF capacitor. What quantity is the same for capacitors in parallel? μC
32.14
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You are correct that the charge on this capacitor will be the same as the charge on the 3 μF capacitor. μC
In the pivot assignment, we observed waves moving on a string stretched by hanging
weights. We noticed that certain frequencies produced standing waves. One such
situation is shown below:
0 ст
Direct Measurement
©2015 Peter Bohacek I.
20
0 cm 10
20
30
40
50
60
70
80
90
100
Which Harmonic is this?
Do NOT include units!
What is the wavelength of this wave in cm with only no decimal places?
If the speed of this wave is 2500 cm/s, what is the frequency of this harmonic (in Hz, with
NO decimal places)?
Four capacitors are connected as shown in the figure below. (Let C = 12.0 µF.)
A circuit consists of four capacitors. It begins at point a before the wire splits in two directions. On the upper split, there is a capacitor C followed by a 3.00 µF capacitor. On the lower split, there is a 6.00 µF capacitor. The two splits reconnect and are followed by a 20.0 µF capacitor, which is then followed by point b.
(a) Find the equivalent capacitance between points a and b. µF(b) Calculate the charge on each capacitor, taking ΔVab = 16.0 V.
20.0 µF capacitor
µC
6.00 µF capacitor
µC
3.00 µF capacitor
µC
capacitor C
µC
Chapter 1 Solutions
Classical Dynamics of Particles and Systems
Ch. 1 - Prob. 1.1PCh. 1 - 1.2. Prove Equations 1.10 and 1.11 from...Ch. 1 - Prob. 1.3PCh. 1 - Show
(a) (AB)t = BtAt (b) (AB)−1 = B−1 A−1
Ch. 1 - Prob. 1.5PCh. 1 - Prob. 1.6PCh. 1 - Consider a unit cube with one corner at the origin...Ch. 1 - Prob. 1.8PCh. 1 - For the two vectors
find
A − B and |A –...Ch. 1 - A particle moves in a plane elliptical orbit...
Ch. 1 - Prob. 1.11PCh. 1 - Let a, b, c be three constant vectors drawn from...Ch. 1 - X is an unknown vector satisfying the following...Ch. 1 - Prob. 1.14PCh. 1 - Prob. 1.15PCh. 1 - What surface is represented by r a = const, that...Ch. 1 - Obtain the cosine law of plane trigonometry by...Ch. 1 - Obtain the sine law of plane trigonometry by...Ch. 1 - Prob. 1.19PCh. 1 - 1-20. Show that
Ch. 1 - Show (see also Problem 1–11) that
Ch. 1 - Prob. 1.22PCh. 1 - Use the εijk notation and derive the identity
(A ×...Ch. 1 - Prob. 1.24PCh. 1 - Find the components of the acceleration vector a...Ch. 1 - Prob. 1.26PCh. 1 - If r and are both explicit functions of time,...Ch. 1 - Show that
Ch. 1 - Prob. 1.29PCh. 1 - Prob. 1.30PCh. 1 - Show that
(a)
(b)
(c)
Ch. 1 - Show that (2arr+2brr)dt=ar2+br2+const. where r is...Ch. 1 - Show that (rrrrr2)dt=rr+C where C is a constant...Ch. 1 - Prob. 1.34PCh. 1 - Prob. 1.35PCh. 1 - Prob. 1.36PCh. 1 - Prob. 1.37PCh. 1 - Prob. 1.38PCh. 1 - A plane passes through the three points (x, y, z)...Ch. 1 - For what values of a are the vectors A = 2ai − 2j...
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- A spectra is a graph that has amplitude on the Y-axis and frequency on the X-axis. A harmonic spectra simply draws a vertical line at each frequency that a harmonic would be produced. The height of the line indicates the amplitude at which that harmonic would be produced. If the Fo of a sound is 125 Hz, please sketch a spectra (amplitude on the Y axis, frequency on the X axis) of the harmonic series up to the 4th harmonic. Include actual values on Y and X axis.arrow_forwardSketch a sign wave depicting 3 seconds of wave activity for a 5 Hz tone.arrow_forwardSketch a sine wave depicting 3 seconds of wave activity for a 5 Hz tone.arrow_forward
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- 6). What is the magnitude of the potential difference across the 20-02 resistor? 10 Ω 11 V - -Imm 20 Ω 10 Ω 5.00 10 Ω a. 3.2 V b. 7.8 V C. 11 V d. 5.0 V e. 8.6 Varrow_forward2). How much energy is stored in the 50-μF capacitor when Va - V₁ = 22V? 25 µF b 25 µF 50 µFarrow_forward9). A series RC circuit has a time constant of 1.0 s. The battery has a voltage of 50 V and the maximum current just after closing the switch is 500 mA. The capacitor is initially uncharged. What is the charge on the capacitor 2.0 s after the switch is closed? R 50 V a. 0.43 C b. 0 66 C c. 0.86 C d. 0.99 C Carrow_forward
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