Answer:
x = D (M/M-m) 2.41
Explanation:
a) Let's apply Newton's second law to find the summation of force, where each force is given by the law of universal gravitation
F = g m₁m₂ / r²
Σ F = 0
F1- F2 = 0
F1 = F2
We set the reference system in the body of greatest mass (M) the planet
F1 = g m₁ M / x²
F2 = G m1 m / (D-x)²
G m₁ M / x² = G m₁ m / (D-x)²
M (D-x)² = m x²
MD² -2MD x + M x² = m x²
x² (M-m) -2MD x + MD² = 0
We solve the second degree equation
x = [2MD ±√ (4M²D² - 4 (M-m) MD²)] / 2 (M-m)
x = {2MD ± 2D √ (M² + (M-m) M)} / 2 (M-m)
x = D {M ± Ra (2M²-mM)} / (M-m)
x = D (M ± M √ (2-m/M)) / (M-m)
x = D (M / (M-m)) (1 ±√ (2-m/M)
Let's analyze this result, the value of M-m >> 1, so if we take the negative root, the value of x would be negative, it is out of the point between the two bodies, so the correct result must be taken with the positive root
x = D (M / (M-m)) (1 + √2)
x = D (M/M-m) 2.41
b) X = 2/3 D
x = D (M/M-m) 2.41
2/3 D = D (M/(M-m)) 2.41
2/3 (M-m) = M 2.41
2/3 M - 2/3 m = 2.41 M
1.743 M = 0.667 m
M/m = 0.667/1.743
M/m = 0.38
Answer:
Explanation:
The distance traveled by the sound wave between the beats of the wing is its wavelength, since it is defined as the distance traveled by a periodic disturbance that propagates in a cycle, is defined as:
Where v is the speed of sound and f the frequency of the wing beats
Answer:
The volume of a cylindrical conduit,
where is the inner radius, is the outer radius, h is the length.
First of all, we would covert each parameter into centimeters.
length of the conduit,
outer radius,
inner radius,
Insert the values in the volume formula,
Hence, the volume of metal in the conduit is 510. 12 cubic centimeters.
There are three different forms of potential energy. The rock hanging above the ground has a form of stored energy called gravitational potential energy. ... The higher an object is above the ground or the greater its mass, the more gravitational potential energy it has.
Answer:
m
Explanation:
Consider the motion of the boat across the stretch from west to east direction :
= velocity of boat = 15 mph
= length of the stretch = 1.01 miles
= Time taken to reach the opposite end
Time taken to reach the opposite end is given as
h
sec (Since 1 h = 3600 sec)
sec
= speed of river = 2.04 m/s
= distance traveled downstream
Distance traveled downstream is given as
m