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Jlenok [28]
3 years ago
6

You set out to design a car that uses the energy stored in a flywheel consisting of a uniform 101-kg cylinder of radius r that h

as a maximum angular speed of 470 rev/s. the flywheel must deliver an average of 2.40 mj of energy for each kilometer of distance. find the smallest value of r for which the car can travel 300 km without the flywheel needing to be recharged.
Physics
1 answer:
Ket [755]3 years ago
8 0
Ok, assuming "mj" in the question is Megajoules MJ) you need a total amount of rotational kinetic energy in the fly wheel at the beginning of the trip that equals
(2.4e6 J/km)x(300 km)=7.2e8 J
The expression for rotational kinetic energy is

E = (1/2)Iω²  

where I is the moment of inertia of the fly wheel and ω is the angular velocity.  
So this comes down to finding the value of I that gives the required energy.  We know the mass is 101kg.  The formula for a solid cylinder's moment of inertia is

 I = (1/2)mR²

We want (1/2)Iω² = 7.2e8 J and we know ω is limited to 470 revs/sec.  However, ω must be in radians per second so multiply it by 2π to get 
ω = 2953.1 rad/s
Now let's use this to solve the energy equation, E = (1/2)Iω²,  for I:
I = 2(7.2e8 J)/(2953.1 rad/s)² = 165.12 kg·m²

Now find the radius R,

 165.12 kg·m² = (1/2)(101)R²,
√(2·165/101) = 1.807m

R = 1.807m
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IceJOKER [234]

Answer:

It is a measure of the electric force per unit charge on a test charge.

Explanation:

The magnitude of the electric field is defined as the force per charge on the test charge.

Since we define electric field as the force per charge, it will have the units of  force divided by the unit of charge. This implies that the SI unit of electric field is given as Newton/Coulomb (N/C).

5 0
3 years ago
In a cell, the amount nutrition coming in equals the amount of waste going out. This is an example of _____.
babymother [125]
The answer is B) <span>equilibrium
hope this helps!=-)</span>
5 0
3 years ago
The wavelength of red helium-neon laser light in air is 632.8 nm.(a) What is its frequency?(b) What is its wavelength in glass t
inn [45]

(a) 4.74 \cdot 10^{14}Hz

The frequency of a wave is given by:

f=\frac{v}{\lambda}

where

v is the wave's speed

\lambda is the wavelength

For the red laser light in this problem, we have

v=c=3\cdot 10^8 m/s (speed of light)

\lambda=632.8 nm=632.8\cdot 10^{-9} m

Substituting,

f=\frac{3\cdot 10^8 m/s}{632.8 \cdot 10^{-9} m}=4.74 \cdot 10^{14}Hz

(b) 427.6 nm

The wavelength of the wave in the glass is given by

\lambda=\frac{\lambda_0}{n}

where

\lambda_0 = 632.8\cdot 10^{-9} m is the original wavelength of the wave in air

n = 1.48 is the refractive index of glass

Substituting into the formula,

\lambda=\frac{632.8\cdot 10^{-9}m}{1.48}=427.6\cdot 10^{-9}m=427.6 nm

(c) 2.02\cdot 10^8 m/s

The speed of the wave in the glass is given by

v=\frac{c}{n}

where

c = 3\cdot 10^8 m/s is the original speed of the wave in air

n = 1.48 is the refractive index of glass

Substituting into the formula,

v=\frac{3\cdot 10^8 m/s}{1.48}=2.02\cdot 10^8 m/s

5 0
3 years ago
In a popular classroom demonstration, a cotton ball is placed in the bottom of a strong test tube. A plunger fits inside the tub
mario62 [17]

Answer:

An increase in air temperature because of its compression.

Explanation:

The Gay-Lussac's Law states that a gas pressure is directly proportional to its temperature in an enclosed system to constant volume.  

P = kT  

<em>where P: is the gas pressure, T: is the gas temperature and k: is a constant.</em>

Therefore, due to Gay-Lussac's Law, when the plunger is pushed down very rapidly, the pressure of the air increase, which leads to its temperature increase. That is why cotton flashes and burns.      

I hope it helps you!

3 0
3 years ago
A 150 g baseball is traveling horizontally at 50 m/s. If the ball takes 20 ms to stop once it is in contact with the catcher’s g
Sliva [168]
To solve for force, you need to get the product of mass and acceleration. 
F = ma

Your given is:
m = 150g
a = ?
v = 50 m/s
t = 20ms

As you can see, you do not have acceleration yet. But if you read the problem you can come up with the formula of acceleration. 
Acceleration is the change in velocity over a period of time.

a = change in velocity/time

To get the change in velocity, you get the difference between the initial velocity and final velocity:

a =  \frac{vf-vi}{t}

The ball was moving initially at a velocity of 50 m/s and it came to a stop. This is your clue. If a ball comes to a stop then that means that the final velocity of the ball is 0 m/s. 

So we can put it into our formula now:

a = \frac{0m/s-50m/s}{20ms}

WAIT! As you can see, the units do not match. We have ms and s into our equation and that means you cannot proceed till they are the same. First we need to convert ms to s. 

20ms x \frac{1s}{1000ms} = \frac{20s}{1000} = 0.02s

So your new time is 0.02s. Now we put this time into the formula:


a = \frac{0m/s-50m/s}{0.02s}
a =  \frac{-50m/s}{0.02s}  = -2,500 m/ s^{2}

As you can see our acceleration is a negative value, this indicates that it decelerated or slowed down which makes sense because it was brought to a stop. 

So now we have our acceleration. Now using this, we can get our force. 

F= ma

Before we start doing this, you need to take note that the unit of force is N, but when you expand it, it is kg.m/ s^{2} but as you can see our mass given is in grams. So again, before you put them into the equation we need to change it into kg first. 

150g =  \frac{1kg}{1,000g}  =  \frac{150kg}{1,000}  = 0.150kg

Our new mass is 0.150kg. 

To make things clearer, let us write down all our new values:

m = 0.150kg
a = -2,500 m/ s^{2}

Now that all our units match, we can put that into our formula:

F= ma
F= (0.150kg)(-2,500m/s^{2})
F = -375kg.m/ s^{2}  or -375N

The value again is negative because it is going against the initial direction of the ball. But if your instructor just wants to get the value of force or the magnitude of the force, just disregard the sign. 



4 0
3 years ago
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