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3 years ago

When you push a toy car it eventually stops this is due to something called

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Much of what we know about the world today is built upon the work of Sir Isaac Newton, a scientist who lived in the 17th and 18th centuries. He built upon the earlier work of Galileo to develop laws for how motion works in the world. He summarized his work in three laws.

First Law: A moving object tends to keep moving at the same speed and in the same direction unless a force acts on it. An object at rest tends to stay at rest unless a force acts on it.

What does this mean?

It's pretty obvious that a stopped object doesn't move unless someone moves it. The second sentence, however, is harder to believe. It says that objects in motion tend to stay in motion unless stopped by a force. Said another way, until someone or something makes an effort to stop them, they'll keep moving. This tendency of an object to keep moving is called inertia. This is sometimes hard to see in the real world. When you throw a ball, it's going to stop when it hits the ground, even if it rolls for a while. This is because the air that the ball moves through pushes back on it and exerts a force. This pushing back is called friction. The ground also exerts a frictional force as the surface of the ball rubs against the surface of the ground. Without friction a thrown ball would roll forever.

How can I test it?

It's easy to test the first part. Set a ball in a stable position. It doesn't move. If you set it on a hill, it will roll down. That's because gravity exerts a downward force on it.

Now let's build something to test the second part.

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A flywheel is a mechanical device used to store rotational kinetic energy for later use. Consider a flywheel in the form of a un

Kamila [148]

Answer:

a) 6738.27 J

b) 61.908 J

c) $\frac{4492.18}{v_{car} ^{2} }$

Explanation:

The complete question is

A flywheel is a mechanical device used to store rotational kinetic energy for later use. Consider a flywheel in the form of a uniform solid cylinder rotating around its axis, with moment of inertia I = 1/2 mr2.

Part (a) If such a flywheel of radius r1 = 1.1 m and mass m1 = 11 kg can spin at a maximum speed of v = 35 m/s at its rim, calculate the maximum amount of energy, in joules, that this flywheel can store?

Part (b) Consider a scenario in which the flywheel described in part (a) (r1 = 1.1 m, mass m1 = 11 kg, v = 35 m/s at the rim) is spinning freely at its maximum speed, when a second flywheel of radius r2 = 2.8 m and mass m2 = 16 kg is coaxially dropped from rest onto it and sticks to it, so that they then rotate together as a single body. Calculate the energy, in joules, that is now stored in the wheel?

Part (c) Return now to the flywheel of part (a), with mass m1, radius r1, and speed v at its rim. Imagine the flywheel delivers one third of its stored kinetic energy to car, initially at rest, leaving it with a speed vcar. Enter an expression for the mass of the car, in terms of the quantities defined here.

moment of inertia is given as

$I$ = $\frac{1}{2}$ $mr^{2}$

where m is the mass of the flywheel,

and r is the radius of the flywheel

for the flywheel with radius 1.1 m

and mass 11 kg

moment of inertia will be

$I$ = $\frac{1}{2}$ $*11*1.1^{2}$ = 6.655 kg-m^2

The maximum speed of the flywheel = 35 m/s

we know that v = ωr

where v is the linear speed = 35 m/s

ω = angular speed

r = radius

therefore,

ω = v/r = 35/1.1 = 31.82 rad/s

maximum rotational energy of the flywheel will be

E = $Iw^{2}$ = 6.655 x $31.82^{2}$ = 6738.27 J

b) second flywheel has

radius = 2.8 m

mass = 16 kg

moment of inertia is

$I$ = $\frac{1}{2}$ $mr^{2}$ = $\frac{1}{2}$ $*16*2.8^{2}$ = 62.72 kg-m^2

According to conservation of angular momentum, the total initial angular momentum of the first flywheel, must be equal to the total final angular momentum of the combination two flywheels

for the first flywheel, rotational momentum = $Iw$ = 6.655 x 31.82 = 211.76 kg-m^2-rad/s