You can define the height of zero to be at any level you want.
Then the equation will give the height of the ball above that level
at any time. If you define zero height as the position of your hand
just as you drop the ball, then the equation will give negative values
for any time after the drop. If you define zero height as the floor, then
the equation will give a value of zero at the instant of every bounce,
and positive values at any other time.
For a graph of (something vs. time), the x-axis is usually time, so the
y-intercept is the height of the ball at the drop, when time begins.
That's just the height from which it's dropped ... relative to whatever
height you decide to define as zero.
This is another application of Newton's second law of motion
Force = (mass) x (acceleration).
The quantities are a little more complicated in circular motion than
they are in plain old straight-line motion. In circular motion, the 'force'
is the centripetal force on the object, always pointing toward the center
of the circle. And the 'acceleration' is the centripetal acceleration, also
pointing toward the center of the circle, and equal to
(speed)² / (radius).
The only thing we really need to find is the centripetal acceleration, and
then we'll have everything needed to plug into the formula and calculate
the centripetal force.
Acceleration = (speed)² / (radius).
Speed = (distance) / (time) =
(3 circumferences) / (minute) =
(3 x 2pi x radius) / minute =
(6 pi x 8 meters) / (60 sec) = 0.8 pi m/s .
Acceleration = (speed)² / (radius) =
0.64 pi² m²/s² / (8 meters) = 0.08 pi² m/s² =
0.79 m/s² (rounded) .
Force = (mass) x (acceleration) =
(15 kg) x (0.79 m/s²) = 11.84 newtons
(about 2.66 pounds) .
I would not say that she "exerts this centripetal force". The fact of
the matter is much simpler: This is the force that something must
exert on her, pointing toward the center, in order to keep her revolving
around the center at that speed. It could be the friction between her
shoes and the platform, if she's standing on the merry-go-round.
It could be a rope tied between her ankle and something at the center
of the rotating platform. It could be the safety belt on the horse that
she's riding. Whatever it is, something has to constantly pull her toward
the center of the platform, with a force of 11.84 newtons, otherwise her
15kg body will not travel in that circular path.
My answer would be that<span> they transmit light between the two ends of the fiber and find wide usage in fiber-optic communications,</span>
Part a)
kinetic energy of the hammer will be
here we know that
m = 4 kg
v = 6 m/s
now by the equation of kinetic energy we have
Part b)
for finding the force we will have
here we know that
now from above equation we have
now by Newton's II law we have
so it requires 720 N.
