Answer:
a) T² = (
) r³
b) veloicity the dependency is the inverse of the root of the distance
kinetic energy depends on the inverse of the distance
potential energy dependency is the inverse of distance
angular momentum depends directly on the root of the distance
Explanation:
1) for this exercise we will use Newton's second law
F = ma
in this case the acceleration is centripetal
a = v² / r
the linear and angular variable are related
v = w r
we substitute
a = w² r
force is the universal force of attraction
F = 
we substitute

w² = 
angular velocity is related to frequency and period
w = 2π f = 2π / T
we substitute

the final equation is
T² = () r³
b) the speed of the orbit can be found
v = w r
v = 
v = 
in this case the dependency is the inverse of the root of the distance
Kinetic energy
K = ½ M v²
K = ½ M GM / r
K = ½ GM² 1 / r
the kinetic energy depends on the inverse of the distance
Potential energy
U =
U = -G mM / r
dependency is the inverse of distance
Angular momentum
L = r x p
for a circular orbit
L = r p = r Mv
L =
L =
The angular momentum depends directly on the root of the distance
Answer:
A). 1.9 cm
Explanation:
m = Mass of brick = 12 kg
g = Acceleration due to gravity = 9.81 m/s²
r = Radius of hose
A = Area = 
F = Force = 
Let us assume that the pressure required to lift the brick would be atmospheric pressure

The radius of the hose should be 1.9 cm
Answer:
31.831 Hz.
Explanation:
<u>Given:</u>
The vertical displacement of a wave is given in generalized form as

<em>where</em>,
- A = amplitude of the displacement of the wave.
- k = wave number of the wave =

= wavelength of the wave.- x = horizontal displacement of the wave.
= angular frequency of the wave =
.- f = frequency of the wave.
- t = time at which the displacement is calculated.
On comparing the generalized equation with the given equation of the displacement of the wave, we get,

therefore,

It is the required frequency of the wave.
Answer:
the average force 11226 N
Explanation:
Let's analyze the problem we are asked for the average force, during the crash, we can find this from the impulse-momentum equation, but this equation needs the speeds and times of the crash that we could look for by kinematics.
Let's start looking for the stack speeds, it has a free fall, from rest (Vo=0)
Vf² = Vo² - 2gY
Vf² = 0 - 2 9.8 7.69 = 150.7
Vf = 12.3 m / s
This is the speed that the battery likes when it touches the beam. They also give us the distance it travels before stopping, let's calculate the time
Vf = Vo - g t
0 = Vo - g t
t = Vo / g
t = 12.3 / 9.8
t = 1.26 s
This is the time to stop
Now let's use the equation that relates the impulse to the amount of movement
I = Δp
F t = pf-po
The amount of final movement is zero because the system stops
F = - po / t
F = - mv / t
F = - 1150 12.3 / 1.26
F = -11226 N
This is the average force exerted by the stack on the vean