Answer:
the correct result is r = 3.71 10⁸ m
Explanation:
For this exercise we will use the law of universal gravitation
F = 
We call the masses of the Earth M, the masses of the moon m and the masses of the rocket m ', let's set a reference system in the center of the Earth, the distance from the Earth to the moon is d = 3.84 108 m
rocket force -Earth
F₁ = - \frac{m' M }{r^2}
rocket force - Moon
F₂ = - \frac{m' m }{(d-r)^2}
in the problem ask for what point the force has the relation
2 F₁ = F₂
let's substitute
2 
(d-r) ² = 
r²
d² - 2rd + r² = \frac{m}{2M} r²
r² (1 -\frac{m}{2M}) - 2rd + d² = 0
Let's solve this quadratic equation to find the distance r, let's call
a = 1 - \frac{m}{2M}
a = 1 - 
= 1 - 6.15 10⁻³
a = 0.99385
a r² - 2d r + d² = 0
r = 
r = [2d ± 2d 
] / 2a
r = 
(1 ± √ (1.65 10⁻³)) = (1 ± 0.04)
r₁ = \frac{d}{a} 1.04
r₂ = \frac{d}{a} 0.96
let's calculate
r₁ = 
1.04
r₁ = 401.8 10⁸ m
r₂ = \frac{3.84 10^8}{0.99385} 0.96
r₂ = 3.71 10⁸ m
therefore the correct result is r = 3.71 10⁸ m
Answer:
25. Approximately 8.1 meters
26. North 1.31 km, and East 2.81 km
Explanation:
25.
Notice that the displacements: 6 meters east and 5.4 south create the legs of a right angle triangle. The hypotenuse of that triangle will be the distance (d) needed to cover in order to get the ball in the hole in one putt. That is:
which can be rounded to 8.1 m.
26.
Notice that the 3.1 km at an angle of 25 degrees north of east, is the hypotenuse of a right angle triangle that has for legs the east and north components of that distance.
We can find the leg corresponding to the east displacement using the cosine function (that relates adjacent side with hypotenuse):
and we can calculate the north component using the sine function that relates the opposite side to the angle with the hypotenuse.
Answer:
The amount of potential energy that was initially stored in the spring is 88.8 J.
Explanation:
Given that,
Mass of block = 1.60 kg
Angle = 30.0°
Distance = 6.55 m
Speed = 7.50 m/s
Coefficient of kinetic friction = 0.50
We need to calculate the amount of potential energy
Using formula of conservation of energy between point A and B
Put the value into the formula
Hence, The amount of potential energy that was initially stored in the spring is 88.8 J.
Answer:
C/100 = (F-32) / 180
or, C/5 = (F-32)/9
Explanation:
relation between any two scales is given by:
(X- lower fixed point ) / (upper fixed point -lower fixed point)
where X is any temperature
The work-energy theorem explains the idea that the net work - the total work done by all the forces combined - done on an object is equal to the change in the kinetic energy of the object. After the net force is removed (no more work is being done) the object's total energy is altered as a result of the work that was done.
This idea is expressed in the following equation:
is the total work done
is the change in kinetic energy
is the final kinetic energy
is the initial kinetic energy
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