If the kinetic energy of each ball is equal to that of the other,
then
(1/2) (mass of ppb) (speed of ppb)² = (1/2) (mass of gb) (speed of gb)²
Multiply each side by 2:
(mass of ppb) (speed of ppb)² = (mass of gb) (speed of gb)²
Divide each side by (mass of gb) and by (speed of ppb)² :
(mass of ppb)/(mass of gb) = (speed of gb)²/(speed of ppb)²
Take square root of each side:
√ (ratio of their masses) = ( 1 / ratio of their speeds)²
By trying to do this perfectly rigorously and elegantly, I'm also
using up a lot of space and guaranteeing that nobody will be
able to follow what I have written. Let's just come in from the
cold, and say it the clear, easy way:
If their kinetic energies are equal, then the product of each
mass and its speed² must be the same number.
If one ball has less mass than the other one, then the speed²
of the lighter one must be greater than the speed² of the heavier
one, in order to keep the products equal.
The pingpong ball is moving faster than the golf ball.
The directions of their motions are irrelevant.
<span>When an object moves in a circle, the acceleration points toward the center of the circle. This acceleration is called centripetal acceleration.
We can use a simple equation to find centripetal acceleration.
a = v^2 / r
We can use this same equation to find the speed of the car.
v^2 = a * r
v = sqrt { a * r }
v = sqrt{ (1.50)(9.80 m/s^2)(11.0 m) }
v = 12.7 m/s
The speed of the roller coaster is 12.7 m/s</span>
Answer:
The net magnetic field ta the center of square is
.
Explanation:
Current, I = 12 A , side ,a = 10 cm = 0.1 m
Let the magnetic field due to the one side is B.
The magnetic field is given by
Net magnetic field at the center of the square is
B' = 4 B
Answer:
<em>The comoving distance and the proper distance scale</em>
<em></em>
Explanation:
The comoving distance scale removes the effects of the expansion of the universe, which leaves us with a distance that does not change in time due to the expansion of space (since space is constantly expanding). The comoving distance and proper distance are defined to be equal at the present time; therefore, the ratio of proper distance to comoving distance now is 1. The scale factor is sometimes not equal to 1. The distance between masses in the universe may change due to other, local factors like the motion of a galaxy within a cluster. Finally, we note that the expansion of the Universe results in the proper distance changing, but the comoving distance is unchanged by an expanding universe.
