Answer:
See explanation
Explanation:
We have a mass 
revolving around an axis with an angular speed 
, the distance from the axis is 
. We are given:
![\omega = 10 [rad/s]\\r=0.5 [m]\\m=13[Kg]](https://tex.z-dn.net/?f=%5Comega%20%3D%2010%20%5Brad%2Fs%5D%5C%5Cr%3D0.5%20%5Bm%5D%5C%5Cm%3D13%5BKg%5D)
and also the formula which states that the kinetic rotational energy of a body is:
.
Now we use the kinetic energy formula
where 
is the tangential velocity of the particle. Tangential velocity is related to angular velocity by:
After replacing in the previous equation we get:
now we have the following:
therefore:
then the moment of inertia will be:
![I = 13*(0.5)^2=3.25 [Kg*m^2]](https://tex.z-dn.net/?f=I%20%3D%2013%2A%280.5%29%5E2%3D3.25%20%5BKg%2Am%5E2%5D)
Answer:
E=252J
Explanation:
The total mechanical energy of an object or system is given by:
E mech=K+U
Where K is the kinetic energy of the object and U is the potential energy of the object. The carriage, sitting motionless at the top of the hill, has only potential energy in the form of gravitational potential energy.
Gravitational potential energy is given by:
Ug=mgh
Where m is the mass of the object, g is the gravitational acceleration constant, and h is the height of the object above some specific reference point, in this case the ground 21 m below.
The weight of a stationary object at the surface of the earth is equal to the force of gravity acting on the object.
W=→Fg=mg
We are given that the carriage weighs 12 N, therefore mg=12N.
Ug=12N⋅21m
⇒Ug=252Nm=252J
Hope it helped, God bless you!
Complete question:
What is the peak emf generated by a 0.250 m radius, 500-turn coil is rotated one-fourth of a revolution in 4.17 ms, originally having its plane perpendicular to a uniform magnetic field 0.425 T. (This is 60 rev/s.)
Answer:
The peak emf generated by the coil is 15.721 kV
Explanation:
Given;
Radius of coil, r = 0.250 m
Number of turns, N = 500-turn
time of revolution, t = 4.17 ms = 4.17 x 10⁻³ s
magnetic field strength, B = 0.425 T
Induced peak emf = NABω
where;
A is the area of the coil
A = πr²
ω is angular velocity
ω = π/2t = (π) /(2 x 4.17 x 10⁻³) = 376.738 rad/s = 60 rev/s
Induced peak emf = NABω
= 500 x (π x 0.25²) x 0.425 x 376.738
= 15721.16 V
= 15.721 kV
Therefore, the peak emf generated by the coil is 15.721 kV
The result of the Mexican victory was that fallen defenders
became heroes to the cause of Texan independence.<span> The Battle of
the Alamo took place between February 23 and March 6, 1836 and became the
central episode of the Texas
Revolution . After this thirteen-day battle, the
Mexican troops of General President Antonio
Lopez de Santa Anna began an attack on San Antonio de
Bexar, the current San Antonio in Texas. The Battle of the Alamo fought the
army of Mexico against
a group of Texan rebels, mostly American settlers. More than four thousand
men from Santa Ana stood in front of
the Alamo Fort , the last stronghold of the rebels, which
barely reached 187. The Alamo was not a fortress prepared to withstand a siege.
It is believed that all the rebels of the Alamo died in the siege, but Santa
Anna came to lose up to about 900 men during the days that lasted the fight. However,
the worst result for Santa Ana was precisely the resistance that the Texan
rebels had in the Alamo, which fostered the fighting spirit of the Texans. A
few days later, on March 14, 1836, Texas became independent from Mexico and a
month later, Santa Ana was imprisoned.</span>
