Answer:
hmax = 1/2 · v²/g
Explanation:
Hi there!
Due to the conservation of energy and since there is no dissipative force (like friction) all the kinetic energy (KE) of the ball has to be converted into gravitational potential energy (PE) when the ball comes to stop.
KE = PE
Where KE is the initial kinetic energy and PE is the final potential energy.
The kinetic energy of the ball is calculated as follows:
KE = 1/2 · m · v²
Where:
m = mass of the ball
v = velocity.
The potential energy is calculated as follows:
PE = m · g · h
Where:
m = mass of the ball.
g = acceleration due to gravity (known value: 9.81 m/s²).
h = height.
At the maximum height, the potential energy is equal to the initial kinetic energy because the energy is conserved, i.e, all the kinetic energy was converted into potential energy (there was no energy dissipation as heat because there was no friction). Then:
PE = KE
m · g · hmax = 1/2 · m · v²
Solving for hmax:
hmax = 1/2 · v² / g
Area of a circle is
A= pi r^2
so
500m^2 = 3.14 r2
500/pi = r ^2
152.1549...=r^2
square root both sides
r=12.61566...
d=2r
d=25.2
to 3 sig fig
To solve the problem it is necessary to use the concepts related to the calculation of periods by means of a spring constant.
We know that by Hooke's law
Where,
k = Spring constant
x = Displacement
Re-arrange to find k,
Perioricity in an elastic body is defined by
Where,
m = Mass
k = Spring constant
Therefore the period of the oscillations is 0.685s
the wavelength is to be 56.67 cm and I know that i should be applying the double slit equation for destructive interference.
My guess would be because the gravity from the Earth's core is constantly pulling the ball towards the ground. It's like the moon. Why doesn't the moon just float away in space? Because Earth's gravitational pull keeps it rotating around it. Therefore, the ball will always be pulled towards the core which keeps it from from rolling forever due to friction. But i may be wrong, even though this a quite a good answer, hope it is right!
