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:
14 m/s
Explanation:
u = 0, h = 10 m, g = 9.8 m/s^2
Use third equation of motion
v^2 = u^2 + 2 g h
Here, v be the velocity of ball as it just strikes with the ground
v^2 = 0 + 2 x 9.8 x 10
v^2 = 196
v = 14 m/s
A vector is a quantity or phenomenon that has two independent properties: magnitude and direction.
Answer:
So coefficient of kinetic friction will be equal to 0.4081
Explanation:
We have given mass of the block m = 0.5 kg
The spring is compressed by length x = 0.2 m
Spring constant of the sprig k = 100 N/m
Blocks moves a horizontal distance of s = 1 m
Work done in stretching the spring is equal to 
This energy will be equal to kinetic energy of the block
And this kinetic energy must be equal to work done by the frictional force
So 


So coefficient of kinetic friction will be equal to 0.4081