Answer:
( Angular Velocity = ( About ) 230 rad / s,
( Linear Speed = ( About ) 40.25 m / s,
( Acceleration = ( About ) 9290 m /
Explanation:
Here we want the angular velocity in radians per second, the linear velocity and acceleration.
The diameter = .35 meters, and thus we can conclude that the radius be half of that, or .175 meters. For part ( a ), or the calculation of the angular velocity, it is given that the diameter rotates at 2200 revolutions per minute - but we need to convert this into radians per second.
We can say that there are 2π radians for every minute, and for every minute there are 60 seconds. Therefore -
( a ) w = 2,200 rpm( 2π rads / rev )( 1 min / 60 sec )...
Hence, w = ( About ) 230 rad / s
_____
For this second part we can calculate the the linear velocity by multiplying the angular velocity ( omega ) by the radius r -
( b ) v = w( r ) - Substitute,
v = ( 230 rad / sec )( .175 m )...
v = ( About ) 40.25 m / s
_____
And for this last bit here, to find the acceleration we can simply take the angular velocity ( omega ) squared, by the radius r -
( c ) = w^2( r ),
= ( ( 230 rad / sec )^2 )( .175 m )...
= ( About ) 9290 m /
Answer:
The illumination on the book before the lamp is moved is 9 times the illumination after the lamp is moved.
Explanation:
The distance of the book before the lamp is moved,
The distance of the book after the lamp is moved,
Illumination can be given by the formula,
Illumination before the lamp is moved,
Illumination after the lamp is moved,
The illumination on the book before the lamp is moved is 9 times the illumination after the lamp is moved.
Answer:
a) The rocket reaches a maximum height of 737.577 meters.
b) The rocket will come crashing down approximately 17.655 seconds after engine failure.
Explanation:
a) Let suppose that rocket accelerates uniformly in the two stages. First, rocket is accelerates due to engine and second, it is decelerated by gravity.
1st Stage - Engine
Given that initial velocity, acceleration and travelled distance are known, we determine final velocity (), measured in meters per second, by using this kinematic equation:
(1)
Where:
- Acceleration, measured in meters per square second.
- Travelled distance, measured in meters.
- Initial velocity, measured in meters per second.
If we know that ,
and
, the final velocity of the rocket is:
The time associated with this launch (), measured in seconds, is:
2nd Stage - Gravity
The rocket reaches its maximum height when final velocity is zero:
(2)
Where:
- Initial speed, measured in meters per second.
- Final speed, measured in meters per second.
- Gravitational acceleration, measured in meters per square second.
- Initial height, measured in meters.
- Final height, measured in meters.
If we know that ,
,
and
, then the maximum height reached by the rocket is:
The rocket reaches a maximum height of 737.577 meters.
b) The time needed for the rocket to crash down to the launch pad is determined by the following kinematic equation:
(2)
Where:
- Initial height, measured in meters.
- Final height, measured in meters.
- Initial speed, measured in meters per second.
- Gravitational acceleration, measured in meters per square second.
- Time, measured in seconds.
If we know that ,
,
and
, then the time needed by the rocket is:
Then, we solve this polynomial by Quadratic Formula:
,
Only the first root is solution that is physically reasonable. Hence, the rocket will come crashing down approximately 17.655 seconds after engine failure.