An Olympic high diver has gravitational potential energy because of her height. As she dives, kinetic energy becomes of her energy just before she hits the water.
Gravitational potential energy is the energy possessed or acquired by an object due to a change in its position when it is present in a gravitational field. In simple terms, it can be said that gravitational potential energy is an energy that is related to gravitational force or to gravity.
Kinetic energy is the energy of motion, observable as the movement of an object, particle, or set of particles.
When the high diver is standing stable and not moving , that diver has a gravitational potential energy because of the height . The moment she dives , before hitting the water , from being stationary she gained some momentum and come in motion , due to motion her gravitational potential energy will change to kinetic energy before hitting the ground.
To learn more about Gravitational potential energy here
brainly.com/question/15978356
#SPJ4
A mass weighing 32 pounds stretches a spring 2 feet.
(a) Determine the amplitude and period of motion if the mass is initially released from a point 1 foot above the equilibrium position with an upward velocity of 6 ft/s.
(b) How many complete cycles will the mass have completed at the end of 4 seconds?
Answer:
![A = 1.803 ft](https://tex.z-dn.net/?f=A%20%3D%201.803%20ft)
Period =
seconds
8 cycles
Explanation:
A mass weighing 32 pounds stretches a spring 2 feet;
it implies that the mass (m) = ![\frac{w}{g}](https://tex.z-dn.net/?f=%5Cfrac%7Bw%7D%7Bg%7D)
m= ![\frac{32}{32}](https://tex.z-dn.net/?f=%5Cfrac%7B32%7D%7B32%7D)
= 1 slug
Also from Hooke's Law
2 k = 32
k = ![\frac{32}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B32%7D%7B2%7D)
k = 16 lb/ft
Using the function:
![\frac{d^2x}{dt} = - 16x\\\frac{d^2x}{dt} + 16x =0](https://tex.z-dn.net/?f=%5Cfrac%7Bd%5E2x%7D%7Bdt%7D%20%3D%20-%2016x%5C%5C%5Cfrac%7Bd%5E2x%7D%7Bdt%7D%20%2B%2016x%20%3D0)
(because of the initial position being above the equilibrium position)
( as a result of upward velocity)
NOW, we have:
![x(t)=c_1cos4t+c_2sin4t\\x^{'}(t) = 4(-c_1sin4t+c_2cos4t)](https://tex.z-dn.net/?f=x%28t%29%3Dc_1cos4t%2Bc_2sin4t%5C%5Cx%5E%7B%27%7D%28t%29%20%3D%204%28-c_1sin4t%2Bc_2cos4t%29)
However;
means
![-1 =c_1\\c_1 = -1](https://tex.z-dn.net/?f=-1%20%3Dc_1%5C%5Cc_1%20%3D%20-1)
also implies that:
![-6 =4(c_2)\\c_2 = - \frac{6}{4}](https://tex.z-dn.net/?f=-6%20%3D4%28c_2%29%5C%5Cc_2%20%3D%20-%20%5Cfrac%7B6%7D%7B4%7D)
![c_2 = -\frac{3}{2}](https://tex.z-dn.net/?f=c_2%20%3D%20-%5Cfrac%7B3%7D%7B2%7D)
Hence, ![x(t) =-cos4t-\frac{3}{2} sin 4t](https://tex.z-dn.net/?f=x%28t%29%20%3D-cos4t-%5Cfrac%7B3%7D%7B2%7D%20sin%204t)
![A = \sqrt{C_1^2+C_2^2}](https://tex.z-dn.net/?f=A%20%3D%20%5Csqrt%7BC_1%5E2%2BC_2%5E2%7D)
![A = \sqrt{(-1)^2+(\frac{3}{2})^2 }](https://tex.z-dn.net/?f=A%20%3D%20%5Csqrt%7B%28-1%29%5E2%2B%28%5Cfrac%7B3%7D%7B2%7D%29%5E2%20%7D)
![A=\sqrt{\frac{13}{4} }](https://tex.z-dn.net/?f=A%3D%5Csqrt%7B%5Cfrac%7B13%7D%7B4%7D%20%7D)
![A= \frac{1}{2}\sqrt{13}](https://tex.z-dn.net/?f=A%3D%20%5Cfrac%7B1%7D%7B2%7D%5Csqrt%7B13%7D)
![A = 1.803 ft](https://tex.z-dn.net/?f=A%20%3D%201.803%20ft)
Period can be calculated as follows:
= ![\frac{2 \pi}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B2%20%5Cpi%7D%7B4%7D)
=
seconds
How many complete cycles will the mass have completed at the end of 4 seconds?
At the end of 4 seconds, we have:
![x* \frac{\pi}{2} = 4 \pi](https://tex.z-dn.net/?f=x%2A%20%5Cfrac%7B%5Cpi%7D%7B2%7D%20%3D%204%20%5Cpi)
![x \pi = 8 \pi](https://tex.z-dn.net/?f=x%20%5Cpi%20%3D%208%20%5Cpi)
cycles
<span> </span>Most of the stars in the Milky Way will end their lives as white dwarfs
Answer:
hmm
Explanation:
By increasing the number of turns in the coil, strength of magnetic field, speed of rotation of the coil in the magnetic field and by decreasing the distance between the coil and the magnet the magnitude of the induced e.m.f. can be increased in generator/dynamo.