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:
350 N/m
Explanation:
If we are assuming the stretch does not exceed the elastic range of the material, then by Hooke's law the spring constant of the cord is simply the ratio between the force 70N acting on the cord to stretch 20cm or 0.2m
k = 70 / 0.2 = 350 N/m
The spring constant is 350 N/m
Answer:
19 N
Explanation:
From the question given above, the following data were obtained:
Pressure (P) = 1.9 kPa
Length (L) = 10 cm
Force (F) =?
Next, we shall convert 1.9 KPa to N/m². This can be obtained as follow:
1 KPa = 1000 N/m²
Therefore,
1.9 KPa = 1.9 KPa × 1000 N/m² / 1 KPa
1.9 KPa = 1900 N/m²
Thus, 1.9 KPa is equivalent to 1900 N/m².
Next, we shall convert 10 cm to m. This can be obtained as follow:
100 cm = 1 m
Therefore,
10 cm = 10 cm × 1 m / 100 cm
10 cm = 0.1 m
Thus, 10 cm is equivalent to 0.1 m
Next, we shall determine the area of the square. This can be obtained as follow:
Length (L) = 0.1 m
Area of square (A) =?
A = L²
A = 0.1²
A = 0.01 m²
Thus, the area of the square is 0.01 m².
Finally, we shall determine the force that must be exerted on the sensor in order for it to turn red. This can be obtained as follow:
Pressure (P) = 1900 N/m²
Area (A) = 0.01 m²
Force (F) =?
P = F/A
1900 = F / 0.01
Cross multiply
F = 1900 × 0.01
F = 19 N
Therefore, a force of 19 N must be exerted on the sensor in order for it to turn red.
