Answer:
7572 m/s
Explanation:
The force between two masses separated by a distance r is given as:
Where F is the attractive force between 2 masses, m1 and m2, r is the distance between the centres of the masses and G is the universal gravitation constant, which is
The mass of the earth () is far greater than the mass of the sputnik (
). Therefore
. The mass of the sputnik is neglected, therefore:
But F is actually centripetal acceleration, a = v²/r
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:
3.90 degrees
Explanation:
Let g= 9.81 m/s2. The gravity of the 30kg grocery cart is
W = mg = 30*9.81 = 294.3 N
This gravity is split into 2 components on the ramp, 1 parallel and the other perpendicular to the ramp.
We can calculate the parallel one since it's the one that affects the force required to push up
F = WsinΘ
Since customer would not complain if the force is no more than 20N
F = 20
So the ramp cannot be larger than 3.9 degrees
