Physics Homework Chapter 17

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1. A current of 79.0 mA exists in a metal wire.
(a) How many electrons flow past a given cross section of the wire in 10.8 min?
_____electrons
(b) In what direction do the electrons travel with respect to the current?
-The magnitude is zero.
-opposite direction   
-same direction




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2. The current supplied by a battery in a portable device is typically 0.183 A. Find the number of electrons passing through the device in two hours.
 
_____electrons


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3. An electric heater carries a current of 17.0 A when operating at a voltage of 3.30 X 10²V. What is the resistance of the heater?

_____Ω


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4. Nichrome wire of cross-sectional radius 0.781 mm is to be used in winding a heating coil. If the coil must carry a current of 10.00 A when a voltage of 2.70 X10^{2</ sup> V is applied across its ends, find the following.}
(a) the required resistance of the coil
_____Ω
(b) the length of wire you must use to wind the coil
_____m


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5. A wire of diameter 0.550 mm and length 30.0 m has a measured resistance of 3.00 Ω. What is the resistivity of the wire?
_____Ω · m


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6. A potential difference of 10 V is found to produce a current of 0.45 A in a 3.6 m length of wire with a uniform radius of 0.35 cm. Find the following values for the wire:

(a) the resistance
_____Ω

(b) the resistivity
_____ Ω· m



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7. If a certain silver wire has a resistance of 3.00 Ω at 15.0°C, what resistance will it have at 29.0°C?
_____Ω


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8. Suppose your waffle iron is rated at 1.25 kW when connected to a 1.80 X 10^{2</ sup> V source.}

(a) What current does the waffle iron carry?
_____A
(b) What is its resistance?
_____ Ω


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9.If electrical energy costs 12 cents, or $0.12, per kilowatt-hour, then what would the following events cost?
(a) burning a 40 W light bulb for 24 h straight
$_____  
(b) operating an electric oven for 4.0 h if it carries a current of 20.0 A at 220 V
$_____


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10. A high-voltage transmission line with a resistance of 0.30 /km carries a current of 1040 A. The line is at a potential of 660 kV at the power station and carries the current to a city located 160 km from the station.
(a) What is the power loss due to resistance in the line?
_____W
(b) What fraction of the transmitted power does this loss represent?
_____%


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Solutions for Chapter 2 "College Physics: Open Stax College" (Position, Velocity, Acceleration )

Questions are adapted from "College Physics: Open Stax College" (pg 81) and are used on WebAssign Under the title: "110(2.1) Position, Velocity, Acceleration, (Homework)"

For more Physics Solutions: See my Physics Page

Question
1. Find the following for path "D" in the figure

a) the total distance traveled
b) the distance from start to finish
c) the displacement from start to finish

Solution
a) distance (scalar) from 9 to 3, then from 3 to 5.
(9 -3) + (5-3) = 8(m)

b) Only magnitude needs to be indicated. Direction doesn't matter.
distance from start to finish (straight line) = 9- 5= 4(m)

c) displacement is a vector (must indicate direction)
displacement = Δx = x_f - x_i = 5 - 9 = -4m

Question
2. With the ability to measure the motion of land masses, continental drift has become an established fact. The North American and European continents are drifting apart at a rate of about 3cm/y. At this rate how long will it take them to drift 750 km further apart than at present?
______ yr

Solution
Uknown: "t"
Δx = 750 km (750,000 m)v = 3cm/y (0.03m/y)
NOTE: convert units to match (meter for distance, meters/year for velocity)
from equation: v = Δx/t
Solve for "t"
t = Δx/v
t = 750,000/0.03 (y) = 25,000,000 (y)

Question 3. A student drove to the university from her home and noted that the odometer reading of her car increased by 16.0 km. The trip took 17.0 min.

(a) What was her average speed?
_____ km/h

(b) If the straight-line distance from her home to the university is 10.3 km in a direction 25.0º south of east, what was her average velocity?
_____ km/h (25˚ S of E)

(c) If she returned home by the same path 7 h 30 min after she left, what were her average speed
_____ Km/h

(d) and velocity for the entire trip?
_____ km/h

Solution

a)
Known:
Distance: 16 km (odometer)
time: 17 min = 17/60 hours = 0.283333 hours

unknown: average speed:
speed = distance / time

speed = 16/0.28333 (km/h) = 57.4712526 km/h

b) velocity = displacement/time   v=Δx/t
displacement is 10.3 km (in the direction of 25˚ S of E)
t  = 0.28333 hours

v = 10.3/0.28333 = 36.35336 km/h

c) 

d = 16 X 2 = 32km

t = 7.5 h

v = d/t = 32/7.5 = 4.2667 km/h

d)
v=Δx/tΔx = x_f - x_{i = 0 - 0 = 0 km (she started and ended at the same position)}

_{v = 0/7.5 = 0 km}

_Question

4. A commuter backs her car out of her garage with an acceleration of 1.50 m/s2.

(a) How long does it take her to reach a speed of 2.4 m/s?
_____ s

(b) If she then brakes to a stop in 0.800 s, what is her deceleration?
_____ m/s<sup>2

Solution</sup> a)
v_f = 2.4m/s
vi = 0 m/s
a = 1.5 m/s²
a = Δv/t = (v_f - v_i)/t
Solve for "t"
t = (v_f - v_i)/a = (2.4 - 0) /1.5 = 1.6 seconds

b)
vf = 0
vi = 2.4 m/s
t = 0.8 s

a = Δv/t = (v_f - v_i)/t = (0 - 2.4) /0.8 = -3 m/s<sup>2

Question 5.</sup>  Assume that an MX missile goes from rest to a suborbital speed of 9.50 km/s in 30.0 s (the actual speed and time are classified).
a) What is its average acceleration in m/s²
_____
b) and in multiples of g?
_____

Soultion a) 
v_f = 9.5km/s = 9,500 m/s
vi = 0 m/s
t = 30 sec
a = Δv/t = (v_f - v_i)/t = (9500 - 0)/30 = 316.67 m/s²

b) g = 9.8 m/s²
 in multiples of "g"
a/g = 316.67 / 9.8 = 32.3129 g

Physics Homework Chapter 16

NOTE: This page will be constantly updated between now and January 27th (at which time all of Chapter 16 homework will be complete and posted).

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1. A uniform electric field of magnitude 440 N/C pointing in the positive x-direction acts on an electron, which is initially at rest. The electron has moved 3.00 cm.

(a) What is the work done by the field on the electron?
_____J

(b) What is the change in potential energy associated with the electron?
_____J

(c) What is the velocity of the electron?
magnitude
_____m/s
direction: (+x, +y, -x, -y)?

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2. Two point charges are on the y-axis. A 2.5 µC charge is located at y = 1.40 cm, and a -2.06 µC charge is located at y = -1.60 cm.

(a) Find the total electric potential at the origin.
_____V

(b) Find the total electric potential at the point having coordinates (1.50 cm, 0).
_____V

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3. A metal sphere of radius 5.00 cm is initially uncharged. How many electrons would have to be placed on the sphere to produce an electric field of magnitude 1.35 X 10⁵ N/C at a point 8.18 cm from the center of the sphere?
_____electrons

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4. The two charges in the figure below are separated by d = 1.50 cm.
(Let q1 = −18.5 nC and q2 = 28.5 nC.)

(a) Find the electric potential at point A.
_____kV

(b) Find the electric potential at point B, which is halfway between the charges.
_____kV

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>

5.Consider the following figure.

(a) Find the electric potential, taking zero at infinity, at the upper right corner (the corner without a charge) of the rectangle in the figure. (Let y = 2.8 cm and x = 6.5 cm.)
_____J/C

(b) Repeat if the 2.00-µC charge is replaced with a charge of −2.00 µC.
_____J/C

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6.
(a) When a 15.00-V battery is connected to the plates of a capacitor, it stores a charge of 24.0 µC. What is the value of the capacitance?
_____µF

(b) If the same capacitor is connected to a 12.00-V battery, what charge is stored?
_____µC

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7. An air-filled parallel-plate capacitor has plates of area 2.70 cm2 separated by 2.50 mm. The capacitor is connected to a 24.0 V battery.
(a) Find the value of its capacitance.
____pF

(b) What is the charge on the capacitor?
_____pC

(c) What is the magnitude of the uniform electric field between the plates?
_____N/C

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8. Given a 1.50 µF capacitor, a 7.00 µF capacitor, and a 18.00 V battery, find the charge on each capacitor if you connect them in the following ways.

(a) in series across the battery
_____µC

(b) in parallel across the battery
1.50 µF capacitor
_____µC
7.00 µF capacitor
_____µC

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9.Find the following. (Let C1 = 38.40 µF and C2 = 32.40 µF.)

(a) the equivalent capacitance of the capacitors in the figure above
_____µF

(b) the charge on each capacitor
on the right 38.40 µF capacitor       _____µC
on the left 38.40 µF capacitor         _____µC
on the 32.40 µF capacitor              _____µC
on the 6.00 µF capacitor                _____µC

(c) the potential difference across each capacitor
on the right 38.40 µF capacitor       _____V
on the left 38.40 µF capacitor         _____V
on the 32.40 µF capacitor              _____V
on the 6.00 µF capacitor                _____V

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10. For the system of capacitors shown in the figure below, find the following. (Let C1 = 1.00 µF and C2 = 2.00 µF.)

(a) the equivalent capacitance of the system
_____µF

(b) the charge on each capacitor
on C1                                  _____µC
on C2                                  _____ µC
on the 6.00 µF capacitor      _____µC
on the 2.00 µF capacitor      _____µC

(c) the potential difference across each capacitor
across C1                                   _____V
across C2                                   _____V
across the 6.00 µF capacitor       _____V
across the 2.00 µF capacitor       _____V

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Physics Vector Notation

This video explains î and ĵ Symbolic vector notation in physics.

Physics Homework Chapter 15

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1.  A 7.66 nC charge is located 1.87 m from a 4.46 nC point charge.

(a) Find the magnitude of the electrostatic force that one charge exerts on the other.
 ______ N

(b) Is the force attractive or repulsive?





2. A charged particle A exerts a force of 2.55 μN to the right on charged particle B when the particles are 13.0 mm apart. Particle B moves straight away from A to make the distance between them 16.9 mm. What vector force does particle B then exert on A?
_____ μN to the left





3.A small sphere of mass m = 7.60 g and charge q1 = 29.9 nC is attached to the end of a string and hangs vertically as in the figure. A second charge of equal mass and charge q2 = −58.0 nC is located below the first charge a distance d = 2.00 cm below the first charge as in the figure.

(a) Find the tension in the string.
_____N

(b) If the string can withstand a maximum tension of 0.180 N, what is the smallest value d can have before the string breaks?
_____cm

4. A small sphere of charge q1 = 0.808 µC hangs from the end of a spring as in figure (a). When another small sphere of charge q2 = −0.612 µC is held beneath the first sphere as in figure (b), the spring stretches by d = 3.78 cm from its original length and reaches a new equilibrium position with a separation between the charges of r = 5.15 cm. What is the force constant of the spring?
_____N/m

5. Calculate the magnitude and direction of the Coulomb force on each of the three charges shown in the figure below.

6.00 µC charge:
magnitude
_____N direction

1.50 µC charge:
magnitude
_____N direction

−2.00 µC charge:
magnitude
_____N
direction





6. A small object of mass 3.82 g and charge -18.4 µC is suspended motionless above the ground when immersed in a uniform electric field perpendicular to the ground. What are the magnitude and direction of the electric field?

magnitude
_____N/C
direction





7. An electric field of magnitude 5.25  105 N/C points due west at a certain location. Find the magnitude and direction of the force on a −4.20 µC charge at this location.

magnitude    
_____N
direction





8. An electron is accelerated by a constant electric field of magnitude 315 N/C.

(a) Find the acceleration of the electron.
_____m/s^2

(b) Use the equations of motion with constant acceleration to find the electron's speed after 9.50  10-9 s, assuming it starts from rest.
_____m/s





9. A proton accelerates from rest in a uniform electric field of 600 N/C. At some later time, its speed is 1.38  106 m/s.

(a) Find the magnitude of the acceleration of the proton.
_____m/s2

(b) How long does it take the proton to reach this speed?
_____µs

(c) How far has it moved in that interval?
_____m

(d) What is its kinetic energy at the later time?
_____J

3


Before beginning on Problem #10, it may be useful to watch a video that explains vector notation
vector notation is the use of the symbols "î and ĵ" to indicate a direction (apart from a magnitude).


10. Three point charges are located on a circular arc as shown in the figure below. (Let r = 3.76 cm. Let to the right be the +x direction and up along the screen be the +y direction.)















(a) What is the total electric field at P, the center of the arc?
             →
 (Vector)E = ______ î  +  _____ ĵ

(b) Find the electric force that would be exerted on a −4.8 nC point charge placed at P.
              →
 (Vector) F = _____ î + _____ ĵ






11. In the figure below, determine the point (other than infinity) at which the total electric field is zero.

_____m to the left of −2.5 × 10−6 C charge

12. A uniform electric field of magnitude E = 410 N/C makes an angle of θ = 66.0° with a plane surface of area A = 4.00 m2 as in the figure below. Find the electric flux through this surface.

_____N · m2/C

NOTE: in video #12, I make a claim that I think the textbook misrepresents the facts. After looking a second time, I feel I may have actually misinterpreted the textbook. The explanation in the textbook is actually correct (if read in the entirety -- and read slowly).


13. An electric field of intensity 4.5 kN/C is applied along the x-axis. Calculate the electric flux through a rectangular plane 0.350 m wide and 0.700 m long if the following conditions are true.

a. The plane is parallel to the y-z plane
_____ N*m²/C

b. The plane is parallel to the x-y plane
_____ N*m²/C

c. The plane contains the y-axis, and its normal makes an angle of 35° with the x-axis
_____ N*m²/C