Geocentric Theory
In astronomy, the geocentric model is a superseded description of the Universe with Earth at the center. Under the geocentric model, the Sun, Moon, stars, and planets all orbited Earth
Heliocentric Theory
Heliocentrism is the astronomical model in which the Earth and planets revolve around the Sun at the center of the Solar System. Historically, heliocentrism was opposed to geocentrism, which placed the Earth at the center
G-Theory is the earth is the center of the universe.
H-Theory is the sun is the center of the universe.
Answer:
a) T = 2.26 N, b) v = 1.68 m / s
Explanation:
We use Newton's second law
Let's set a reference system where the x-axis is radial and the y-axis is vertical, let's decompose the tension of the string
sin 30 = 
cos 30 = 
Tₓ = T sin 30
T_y = T cos 30
Y axis
T_y -W = 0
T cos 30 = mg (1)
X axis
Tₓ = m a
they relate it is centripetal
a = v² / r
we substitute
T sin 30 = m
(2)
a) we substitute in 1
T = 
T = 
T = 2.26 N
b) from equation 2
v² = 
If we know the length of the string
sin 30 = r / L
r = L sin 30
we substitute
v² = 
v² = 
For the problem let us take L = 1 m
let's calculate
v = 
v = 1.68 m / s
Stopped at the end of the tracks by a spg-damper system, as shown in fig. 1
Explanation:
y = y₀ + v₀ t + ½ at²
For the first ball:
0 = h + v₀ t − 4.9t²
For the second ball:
0 = h − 4.9 (t−1)²
a) If h = 20.0, find v₀.
0 = 20 − 4.9 (t−1)²
t = 3.02 s
0 = 20 + v₀ (3.02) − 4.9 (3.02)²
v₀ = 8.18 m/s
Graph:
desmos.com/calculator/uk1wzkxybt
If v₀ is given, find h.
First, find t in terms of v₀:
h + v₀ t − 4.9t² = h − 4.9 (t−1)²
v₀ t − 4.9t² = -4.9 (t−1)²
v₀ t − 4.9t² = -4.9 (t² − 2t + 1)
v₀ t − 4.9t² = -4.9t² + 9.8t − 4.9
v₀ t = 9.8t − 4.9
(9.8 − v₀) t = 4.9
t = 4.9 / (9.8 − v₀)
Therefore:
h = 4.9 (4.9 / (9.8 − v₀) − 1)²
bi) If v₀ = 6.0 m/s:
h = 4.9 (1 / (9.8 − 6.0) − 1)²
h = 2.66 m
bii) If v₀ = 9.5 m/s:
h = 4.9 (1 / (9.8 − 9.5) − 1)²
h = 26.7 m
c) As found in part a, the time it takes for the first ball to land is:
t = 4.9 / (9.8 − v₀)
If v₀ is greater than 9.8 m/s, the time becomes negative, which isn't possible. Therefore, vmax = 9.8 m/s. At this speed, the ball would reach its highest point after 1 second, the same time that the second ball is dropped. Two balls dropped at the same time from different heights cannot land at the same time.
d) If v₀ is less than 4.9 m/s, the time for the first ball to land becomes less than 1 second. Which means it will have already landed before the second ball is dropped. Therefore, vmin = 4.9 m/s.
