Determine whether or not each of the following statement is true. If a statement is true, prove it. If the statement is false, provide a counterexample and explain how it constitutes a counterexample. Diagrams can be useful in explaining such things. If the electric potential in a certain region of space is constant, then the charge enclosed by any closed surface completely contained within that region is zero.

Answers

Answer 1

Answer:

True

Explanation:

This is a representation of Gauss law.

Gauss’s law does hold for moving charges, and in this respect Gauss’s law is more general than Coulomb’s law. In words, Gauss’s law states that: The net outward normal electric flux through any closed surface is proportional to the total electric charge enclosed within that closed surface. The law can be expressed mathematically using vector calculus in integral form and differential form, both are equivalent since they are related by the divergence theorem, also called Gauss’s theorem.

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Which if, any, of these statements are true? (More than one may be true.) Assume the batteries are ideal. Check all that apply. A battery supplies the energy to a circuit. A battery is a source of potential difference; the potential difference between the terminals of the battery is always the same. A battery is a source of current; the current leaving the battery is always the same.
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Starting from rest, a basketball rolls from the top to the bottom of a hill, reaching a translational speed of 6.1 m/s. Ignore frictional losses. (a) What is the height of the hill? (b) Released from rest at the same height, a can of frozen juice rolls to the bottom of the same hill. What is the translational speed of the frozen juice can when it reaches the bottom?
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Consider your moment of inertia about a vertical axis through the center of your body, both when you are standing straight up with your arms flat against your sides, and when you are standing straight up holding your arms straight out to your sides. Estimate the ratio of the moment of inertia with your arms straight out to the moment of inertia with your arms flat against your sides. (Assume that the mass of an average adult male is about 80 kg, and that we can model his body when he is standing straight up with his arms at his sides as a cylinder. From experience in men's clothing stores, a man's average waist circumference seems to be about 34 inches, and the average chest circumference about 42 inches, from which an average circumference can be calculated. We'll also assume that about 20% of your body's mass is in your two arms, and that each has a length L = 1 m, so that each arm has a mass of about m = 8 kg.)

The volume control on a stereo is designed so that three clicks of the dial increase the output by 10 dB. How many clicks are required to increase the power output of the loudspeakers by a factor of 100?

Answers

Answer:

300 clicks...

Explanation:

Output on 3 clicks = 10 dB

Increasing 10 by a factor of 100 equals 1000 dB so,

Its simple math, clicks will also increase in the same ratio and it shall take 300 clicks to increase the volume by a factor of 100.

Certain insects can achieve seemingly impossible accelerations while jumping. the click beetle accelerates at an astonishing 400g over a distance of 0.52 cm as it rapidly bends its thorax, making the "click" that gives it its name. part a assuming the beetle jumps straight up, at what speed does it leave the ground? part b how much time is required for the beetle to reach this speed? part c ignoring air resistance, how high would it go?

Answers

(a) The launching velocity of the beetle is 6.4 m/s

(b) The time taken to achieve the speed for launch is 1.63 ms

(a) The beetle starts from rest and accelerates with an upward acceleration of 400 g and reaches its launching speed in a distance 0.53 cm. Here g is the acceleration due to gravity.

Use the equation of motion,

$v^2=u^2+2as$

Here, the initial velocity of the beetle is u, its final velocity is v, the acceleration of the beetle is a, and the beetle accelerates over a distance s.

Substitute 0 m/s for u, 400 g for a, 9.8 m/s² for g and 0.52×10⁻²m for s.

$v^2=u^2+2as\n = (0 m/s)^2+2 (400)(9.8 m/s^2)(0.52*10^-^2 m)\n =40.768 (m/s)^2\n v=6.385 m/s$

The launching speed of the beetle is 6.4 m/s.

(b) To determine the time t taken by the beetle for launching itself upwards is determined by using the equation of motion,

$v=u+at$

Substitute 0 m/s for u, 400 g for a, 9.8 m/s² for g and 6.385 m/s for v.

$v=u+at\n 6.385 m/s = (0 m/s) +400(9.8 m/s^2)t\n t = (6.385 m/s)/(3920 m/s^2) = 1.63*10^-^3s=1.63 ms$

The time taken by the beetle to launch itself upwards is 1.62 ms.

(c) After the beetle launches itself upwards, it is acted upon by the earth's gravitational force, which pulls it downwards towards the earth with an acceleration equal to the acceleration due to gravity g. Its velocity reduces and when it reaches the maximum height in its path upwards, its final velocity becomes equal to zero.

Use the equation of motion,

$v^2=u^2+2as$

Substitute 6.385 m/s for u, -9.8 m/s² for g and 0 m/s for v.

$v^2=u^2+2as\n (0m/s)^2=(6.385 m/s)^2+2(-9.8m/s^2)s\n s=((6.385 m/s)^2)/(2(9.8m/s^2)) =2.08 m$

The beetle can jump to a height of 2.1 m

We have that for the Question the Speed,Time and Height are

u=6.38m/s
T=13sec
h=2m

From the question we are told

Certain insects can achieve seemingly impossible accelerations while jumping.

the click beetle accelerates at an astonishing 400g over a distance of 0.52 cm as it rapidly bends its thorax, making the "click" that gives it its name.

Speed,Time and Height

Generally the equation for the average velocity is mathematically given as

$v^2-u^2=-2ah\n\nTherefore\n\nu=√(2*400*9.8*0.0052)\n\n$

u=6.38m/s

Generally the equation for the Time of flight is mathematically given as

$T=(2u)/(g)\n\nTherefore\n\nT=(2(6.38))/(9.8)$

T=13sec

Generally the equation for the air resistance is mathematically given as

$v^2-u^2=2gh\n\nTherefore\n\nh=(6.38^2)/(2*9.8)\n\$

h=2m

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At a stop light, a truck traveling at 10.5 m/s passes a car as it starts from rest. The truck travels at constant velocity and the car accelerates at 3 m/s2. How much time does the car take to catch up to the truck?

Answers

Answer:

t = 7 sec.

Explanation:

As the car and the truck travel the same distance, assuming a constant acceleration, we can describe the movement of the truck and the car with these equations for this same displacement:

x(truck) = v*t (1)

x(car) = $(1)/(2)*a*t^(2) (2)$

As the left sides of (1) and (2) are equal each other, the same must be true for the right sides:

v*t = $(1)/(2)*a*t^(2)$

Solving for t, replacing v= 10.5 m/s and a= 3 m/s², we have:

$t = (2*v)/(a) = (2*10.5 m/s)/(3 m/s2) = 7 sec.$

⇒ t = 7 sec.

In an electric circuit, resistance and current are ____A. directly proportional
B. inversely proportional
C. have no effect on each other

Answers

In an electric circuit, resistance and current are ____

A. directly proportional

B. inversely proportional

C. have no effect on each other

Explanation:

A 50n brick is suspended by a light string from a 30kg pulley which may be considered a solid disk with radius 2.0m. the brick is released from rest and falls to the floor below as the pulley rotates. it takes 4 seconds for the brick to hit the floor. i) what is the tension in newtons in the string well the brick is falling? ii) what is the magnitude of the angular momentum in kg*m^2/s of the pulley at the instant the brick hits the floor?

Answers

Brick is held at a position which is at height 2 m from the floor

Now it is released from rest and hit the floor after t = 4 s

Now the acceleration of the brick is given by

$y = v_i* t + 0.5 at^2$

$2 = 0 + 0.5 * a * 4^2$

$a = 0.25 m/s^2$

Now in order to find the tension in the string

we can use Newton's law

$F_(net) = ma$

$mg - T = ma$

$50 - T = (50)/(9.8)*0.25$

$T = 48.72 N$

part b)

Now for the pulley

moment of inertia= $(1)/(2)mr^2$

m = 30 kg

R = 2 m

I = $(1)/(2)*30*2^2$

I = 60 kg m^2

Now the angular speed just before brick collide with the floor

$w = (v)/(r)[\tex]</p><p>here we have</p><p>[tex]v = v_i + a* t$

$v = 0 + 0.25 * 4$

v = 1 m/s

Now we will have

L = angular momentum = I w = $I*(v)/(R)$

L = 60 * $(1)/(2)$

L = 30 kg m^2/s

Analysis of the relationship between the fuel economy (mpg) and engine size (liters) for 35 models of cars produces the regression model ModifyingAbove mpg with caret equals 36.44 minus 3.829 times Engine size. If a car has a 5 liter engine, what does this model suggest the gas mileage would be?