Answer:
r =[tex]\frac{ 1 \pm \sqrt{ \frac{m}{M} } }{1 - \frac{m}{M} }[/tex]
Explanation:
Let's apply the universal gravitation law to the body (c), we use the indications 1 for the planet and 2 for the moon
∑ F = 0
-F_{1c} + F_{2c} = 0
F_{1c} = F_{2c}
let's write the force equations
[tex]G \frac{m_c M}{r^2} = G \frac{m_c m}{(d-r)^2}[/tex]
where d is the distance between the planet and the moon.
[tex]\frac{M}{r^2} = \frac{m}{(d-r)^2}[/tex]
(d-r)² = [tex]\frac{m}{M} \ \ r^2[/tex]
d² - 2rd + r² = \frac{m}{M} \ \ r^2
d² - 2rd + r² (1 - [tex]\frac{m}{M}[/tex]) = 0
(1 - [tex]\frac{m}{M}[/tex]) r² - 2d r + d² = 0
we solve the second degree equation
r = [2d ± [tex]\sqrt{ 4d^2 - 4 ( 1 - \frac{m}{M} ) }[/tex] ] / 2 (1- [tex]\frac{m}{M}[/tex])
r = [2d ± 2d [tex]\sqrt{ \frac{m}{M} }[/tex]] / 2d (1- [tex]\frac{m}{M}[/tex])
r =[tex]\frac{ 1 \pm \sqrt{ \frac{m}{M} } }{1 - \frac{m}{M} }[/tex]
there are two points for which the gravitational force is zero
The distance between object from planet will be "[tex]\frac{R}{[1+\sqrt{\frac{m}{M} } ]}[/tex]".
According to the question,
Let,
Object is "x" m from planet center = R - xGravitational force = 0Mass of object = m₁As we know,
→ [tex]Prerequisites-Gravitational \ force = \frac{GMm}{r^2}[/tex]
Now,
→ [tex]\frac{GMm_1}{x^2} = \frac{Gmm_1}{(R-x)^2}[/tex]
→ [tex]\frac{(R-x)^2}{x^2} = \frac{m}{M}[/tex]
→ [tex]\frac{R-x}{x} =\sqrt{\frac{m}{M} }[/tex]
→ [tex]x = \frac{R}{[1+ \sqrt{\frac{m}{M} } ]}[/tex]
Thus the answer above is appropriate.
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Find the momentum of a 15 kg object traveling at 7 m/s
What is the momentum
What is the velocity
What is the mass
What equation did you use to solve?
Find the momentum of a 15 kg object traveling at 7 m/s.
The momentum of an object is found by using the following formula:
[tex]\displaystyle p=mv[/tex]
P is the momentum and is measured in kg · m/sm is the mass and is measured in kgv is the velocity and is measured in m/sIn this question, the object is 15 kg and is travelling at 7 m/s. That means the mass is 15 kg and the velocity is 7 m/s.
Since all the needed variables are found, substitute it into the equation:
[tex]\displaystyle p=mv \rightarrow p=15 \times 7[/tex]
Multiply:
[tex]\displaystyle p=105\ kg \times m/s[/tex]
__________________________________________________________
What is the momentum? 105 kg · m/s
What is the velocity? 7 m/s
What is the mass? 15 kg
What equation did you use to solve? p = mv
__________________________________________________________
Which of the following is generally true for people in their old age?
Answer:As people get older, most become better able to regulate negative feelings and emphasize the positive.
Explanation: With age, your skin thins and becomes less elastic and more fragile, and fatty tissue just below the skin decreases. You might notice that you bruise more easily. Decreased production of natural oils might make your skin drier. Wrinkles, age spots and small growths called skin tags are more common.
Rhodium is in period 5 of the periodic table. What does this tell you about this element
Answer:
. It is an extraordinarily rare, silvery-white, hard, corrosion-resistant, and chemically inert transition metal. It is a noble metal and a member of the platinum group.
Explanation:
Car B is rounding the curve with a constant speed of 54 km/h, and car A is approaching car B in the intersection with a constant speed of 72 km/h. The x-y axes are attached to car B. The distance separating the two cars at the instant depicted is 40 m. Determine:
This question is incomplete, the complete question is;
Car B is rounding the curve with a constant speed of 54 km/h, and car A is approaching car B in the intersection with a constant speed of 72 km/h. The x-y axes are attached to car B. The distance separating the two cars at the instant depicted is 40 m. Determine: the angular velocity of Bxy rotating frame (ω).
Answer:
the angular velocity of Bxy rotating frame (ω) is 0.15 rad/s
Explanation:
Given the data in the question and image below and as illustrated in the second image;
distance S = 40 m
V[tex]_B[/tex] = 54 km/hr
V[tex]_A[/tex] = 72 km/hr
α = 100 m
now, angular velocity of Bxy will be;
ω[tex]_B[/tex] = V[tex]_B[/tex] / α
so, we substitute
ω[tex]_B[/tex] = ( 54 × 1000/3600) / 100
ω[tex]_B[/tex] = 15 / 100
ω[tex]_B[/tex] = 0.15 rad/s
Therefore, the angular velocity of Bxy rotating frame (ω) is 0.15 rad/s
Solve the below problems being sure to provide the correct significant figures.
1) 1000 ÷ 4.886 = __________
2) 240 ÷ 12.3 = __________
3) 80 x 4.6 = __________
4) 4.527 x 30 = __________
5) 86 x 63.855 x 8000 = __________
6) 700 x 91.186 = __________
7) 7.1 x 348 = __________
8) 50 ÷ 29.1 = __________
9) 98.773 x 24.891 x 409 = __________
10) 0.065 x 3 x 3007 = __________
Answer:
1) 204.6663938
2) 19.51219512
3) 368
4) 135.81
5) 43932240
6) 63830.2
7) 2470.8
8) 1.718213058
9) 1005550.526
10) 586.365
Most of the questions you asked were in repeating decimal form.
Explanation:
Can two waves have the
same wavelength but different amplitudes?
Explain
Answer:
I think Yes because they could have different amounts of energy.
Explanation:
5.
2075 Set A Q.No. 20 2070 Supp. Set B Q.No. 2 B What
happens to the kinetic energy of photo electrons when
intensity of light is doubled?
[2]
Answer:
The energy of each photon can be transformed into kinetic energy and as this energy does not change, the energy of both photoelectrons remains constant,
Explanation:
The photoelectric effect was explained by Einstein, who assumed that the lz is made up of particles called photons each of a given energy, therefore the photoelectric effect can be explained as a collision of particles.
From this explanation we see that the intensity is proportional to the number of existing particles, when we double the intensity we double the number of particles, but the energy of each particle does not change, therefore if we use the conservation of energy.
The energy of each photon can be transformed into kinetic energy and as this energy does not change, the energy of both photoelectrons remains constant, only the number of electrons expelled changes.
PLEASE HELP The United States spends over $20 billion a year on space exploration through NASA. Do you think that this has been worth the cost? In three to five sentences, provide two specific examples of things we have learned from space exploration, and explain how these examples influence your opinion.(4 points)
Answer: I think $20 billion a year it’s worth the cost. The reasoning behind that is because we can conduct research on various things that could help out humanity. Therefore we can conclude that’s spending billions of dollars every year is worth it.
Explanation:
How can Newton’s laws of motion and the law of gravitation predict the motion of an object, and how can frames of reference be used to describe that motion?
discuss two reasons why people find transition between school and university
Answer:
Is that your answer
which causes magnets to stick to metal
Answer:
Steel
Explanation:
Steel is a metal that magnets stick to because iron can be found inside steel
Answer:Magnets stick to any metal that contains iron, cobalt or nickel.
Explanation:Iron is found in steel, so steel attracts a magnet and sticks to it. Stainless steel, however, does not attract a magnet.
The average mean distance of Saturn from the sun is
Answer:
From an average distance of 886 million miles (1.4 billion kilometers), Saturn is 9.5 astronomical units away from the Sun. One astronomical unit (abbreviated as AU), is the distance from the Sun to Earth. From this distance, it takes sunlight 80 minutes to travel from the Sun to Saturn.
we have that from the Question"The average mean distance of Saturn from the sun is" it can be said that Tthe average mean distance of Saturn from the sun is
A distance of 1427 x 10^6 km or 886 696 691 milesFrom the Question we are told
The average mean distance of Saturn from the sun is
Generally
The Sun is the star of the milky way galaxy and its distance from every planet in the milky way determines in one way or another its properties and in-habitability
Saturn being a Planet of the milky way we see that Saturn is a significant distance away from sun
A distance of 1427 x 10^6 km or 886 696 691 miles
Therefore
The average mean distance of Saturn from the sun is
A distance of 1427 x 10^6 km or 886 696 691 miles
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A 41.0-kg crate, starting from rest, is pulled across level floor with a constant horizontal force of 135 N. For the first 15.0 m the floor is essentially frictionless, whereas for the next 12.0 m the coefficient of kinetic friction is 0.320. (a) Calculate the work done by all the forces acting on the crate, during the entire 27.0 m path. (b) Calculate the total work done by all the forces. (c) Calculate the final speed of the crate after being pulled these 27.0 m.
Answer:
Explanation:
From the information given;
mass of the crate m = 41 kg
constant horizontal force = 135 N
where;
[tex]s_1 = 15.0 \ m \\ \\ s_2 = 12.0 \ m[/tex]
coefficient of kinetic friction [tex]u_k[/tex] = 0.28
a)
To start with the work done by the applied force [tex](W_f)[/tex]
[tex]W_F = F\times (s_1 +s_2) \times cos(0) \ J[/tex]
[tex]W_F = 135 \times (12 +15) \times cos(0) \ J \\ \\ W_F = (135 \times 37 )J \\ \\ W_F =4995 \ J[/tex]
Work done by friction:
[tex]W_{ff} = -\mu\_k\times m \times g \times s_2 \\ \\ W_{ff} = -0.320 \times 41 \times 9.81 \times 12 \ J \\ \\ W_{ff} = -1544.49 \ J[/tex]
Work done by gravity:
[tex]W_g = mg \times (s_1+s_2) \times cos (90)} \ J \\ \\ W_g = 0 \ j[/tex]
Work done by normal force;
[tex]W_n = N \times (s_1 + s_2) \times cos (90) \ J[/tex]
[tex]W_n = 0 \ J[/tex]
b)
total work by all forces:
[tex]W = F \times (s_1 + s_2) + \mu_k \times m \times g \times s_2 \times 180 \\ \\ W = 135 \times (15+12) \ J - 0.320 \times 41 \times 9.81 \times 12[/tex]
W = 2100.5 J
c) By applying the work-energy theorem;
total work done = ΔK.E
[tex]W = \dfrac{1}{2}\times m \times (v^2 - u^2)[/tex]
[tex]2100.5 = 0.5 \times 41 \times v^2[/tex]
[tex]v^2 = \dfrac{2100.5}{ 0.5 \times 41 }[/tex]
[tex]v^2 = 102.46 \\ \\ v = \sqrt{102.46} \\ \\ \mathbf{v = 10.1 \ m/s}[/tex]
TRUE OR FALSE
2 QUESTIONS
NEED HELP ASAP
THX :)
LOTS OF POINTS :>
Answer: Both False
Explanation:
Our Milky Way Galaxy is a spiral galaxy. Some spiral galaxies are what we call "barred spirals" because the central bulge looks elongated
Irregualuar glaxyices are all over the place
On a cold winter day, a steel metal fence post feels colder than a wooden fence post of identical size because: a. The specific heat capacity of steel is higher than the specific heat capacity of wood. b. The specific heat capacity of steel is lower than the specific heat capacity of wood. c. Steel has the ability to resist a temperature change better than wood. d. The mass of steel is less than wood so it loses heat faster. Selected:e. Two of the above statements are true.
Answer:
The specific heat capacity of steel is lower than the specific heat capacity of wood
Explanation:
THERE IS ONLY 1 ON MY assignment i geot dis right please brainlyist
The specific heat capacity of steel is lower than the specific heat of a piece of wood. Therefore, option (2) is correct.
What is the specific heat capacity?Specific heat can be defined as the heat energy required to change the temperature of one unit mass of a substance of a constant volume by 1 °C. The S.I. unit of the specific heat capacity of a material is KJ/Kg.
The thermal capacity of a material is defined as a physical property of a substance. The amount of heat is given to a given mass to create a change in unit temperature.
The mathematical expression of specific heat capacity can be written as :
Q = m C ΔT Where C is the heat capacity.
The specific heat capacity is an intensive property of a substance as it does not depend upon the size of the material.
A steel metal fence post feels colder than a wooden fence post of similar size because the specific heat of steel is lower than the specific heat capacity of wood.
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What would happen if the molecules in a sample moving entirely ?
Answer:
Molecular scale. The story begins a long time ago
when the idea that molecules are in constant motion
was first discovered. Part of the evidence that you can
see in everyday life was discovered by Robert Brown
about 150 years ago when he used a microscope to
watch how tiny dust particles move.
So how fast do molecules move? It all depends upon
the molecule and its state: molecules in a solid state
move slower than in a liquid state, and much slower
than gas molecules. One estimate puts gas molecules
in the range of 1,100 mph at room temperature. Cool
them down to almost absolute zero and they slow
down to less than 0.1 mph (slower than the average
couch potato). The fact that they are always moving
makes it a challenge to see molecules and make stuff
out of them, but it’s a challenge that scientists
work hard to figure out.
Explanation:
A class is learning about states of matter. The students set up the investigation in the diagram.
Which kinds of energy are needed in this investigation to change the state of matter of the owl made of wax?
A block and a ball have the same mass and move with the same initial velocity across a floor and then encounter identical ramps. The block slides without friction and the ball rolls without slipping. 1)Which one makes it furthest up the ramp
Answer:
Both.
Explanation:
Given that a block and a ball have the same mass and move with the same initial velocity across a floor and then encounter identical ramps. The block slides without friction and the ball rolls without slipping. 1)Which one makes it furthest up the ramp ?
Since both of them have the same mass and the same initial velocity, then, they will both have the same kinetic energy.
That is,
K.E = 1/2mv^2
Friction is a force that opposes motion. And since the frictional force is zero,
Both of them will accelerate from Newton's law.
F = ma
We can therefore conclude that both of them will make it further up the ramp.
The gravitational potential energy of an object is defined as the energy it has due to its position in a gravitational field. A ball with a weight of 50 N is lifted to a height of 1 meter. Which graph correctly represents the change in gravitational potential energy (shaded in blue) as it is lifted to this height?
Answer:
athletic
Explanation:
because internet system has been down since we were in few days
Two students Tim and Alane travel to South Dakota. Tim stands on Earth’s surface and enjoys some sunshine. At the same time, Alane descends into a gold mine where neutrinos are detected, Although the photon at the surface and the neutrinos in the mine arrive at the same time, they have had very different histories. Describe the differences.
Answer:
Explanation:
Neutrinos are otherwise called leptons. They are principal particles. A lepton is a rudimentary half-spin molecule that doesn't go through solid reactions. Neutrinos are not usually charged and exceptionally light weighted so they once in a while interface with other matter. Neutrinos are light weighted. Their mass is around 10⁻⁷ kg. A neutrino possesses a small radius, too little to ever be estimated. A little span and very less mass make them imperceptible. Since neutrinos have next to no mass. they travel at almost the speed of light and thus they arrive at the outside of the Sun in only 2 seconds, dissimilar to photons which take convoluted ways to arrive at the Sun's surface in a huge number of years.
The photon and neutrino, both were made in the Sun's center yet on various occasions. The neutrino is only a couple of minutes old though the photon is around 1,000,000 years of age. At the point when the photon was made in the Sun's center. it needed to venture out to the outside of the Sun. in any case, rather because of its hefty mass and cooperation with other matter, it headed out a crisscross way to the surface. Ordinarily, it was repulsed and it was sent back to the middle where it needed to begin once more. It required a large number of years for a photon to arrive at the outside of the Sun.
Nonetheless, when it arrived at the Sun's surface, it required just 8.8 minutes for the photon to arrive at Earth. The neutrino was anyway made only a couple of minutes prior in the Sun's center. Since it has an entirely irrelevant mass, little size, and no charge, it didn't interface with its environmental factors. So it just required 2 seconds for the neutrino to arrive at the Sun's surface. When it arrived at the Sun's surface, it arrived at the earth in about 8.8 minutes. with the photon. So both, photon and neutrino have various histories as the two of them were made at a hole of around 1,000,000 years.
what determines the magnification of an imagev
measure:what the current values of
Answer:
The magnification of an image is equal to the ratio of the image height to the object height.
an iron Tyre of diameter 50cm at 288k is to be shrank on to a wheel of diameter 50.35cm.To what temperature must the tyre be heated so that it will slip over the wheel with a radial gap of 0.5mm.Linear expansivity of iron is 0.000012k-1
Answer:
The answer should be D
Explanation:
(will give brainliest to whoever is first and gives reason) A mass is spun in a circle with a frequency of 40Hz. What is the period of its rotation?
Answer:
[tex]\huge\boxed{T = 0.025\ seconds}[/tex]
Explanation:
Given:
Frequency = f = 40 Hz
Required:
Time period = T = ?
Formula:
[tex]\sf T = 1 / f[/tex]
Solution:
T = 1 / 40
T = 0.025 seconds
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807Interactive Solution 8.29 offers a model for this problem. The drive propeller of a ship starts from rest and accelerates at 2.38 x 10-3 rad/s2 for 2.04 x 103 s. For the next 1.48 x 103 s the propeller rotates at a constant angular speed. Then it decelerates at 2.63 x 10-3 rad/s2 until it slows (without reversing direction) to an angular speed of 2.42 rad/s. Find the total angular displacement of the propeller.
Answer:
Δθ = 15747.37 rad.
Explanation:
The total angular displacement is the sum of three partial displacements: one while accelerating from rest to a certain angular speed, a second one rotating at this same angular speed, and a third one while decelerating to a final angular speed.Applying the definition of angular acceleration, we can find the final angular speed for this first part as follows:[tex]\omega_{f1} = \alpha * \Delta t = 2.38*e-3rad/s2*2.04e3s = 4.9 rad/sec (1)[/tex]
Since the angular acceleration is constant, and the propeller starts from rest, we can use the following kinematic equation in order to find the first angular displacement θ₁:[tex]\omega_{f1}^{2} = 2* \alpha *\Delta\theta (2)[/tex]
Solving for Δθ in (2):[tex]\theta_{1} = \frac{\omega_{f1}^{2}}{2*\alpha } = \frac{(4.9rad/sec)^{2}}{2*2.38*e-3rad/sec2} = 5044.12 rad (3)[/tex]
The second displacement θ₂, (since along it the propeller rotates at a constant angular speed equal to (1), can be found just applying the definition of average angular velocity, as follows:[tex]\theta_{2} =\omega_{f1} * \Delta_{t2} = 4.9 rad/s * 1.48*e3 s = 7252 rad (4)[/tex]
Finally we can find the third displacement θ₃, applying the same kinematic equation as in (2), taking into account that the angular initial speed is not zero anymore:[tex]\omega_{f2}^{2} - \omega_{o2}^{2} = 2* \alpha *\Delta\theta (5)[/tex]
Replacing by the givens (α, ωf₂) and ω₀₂ from (1) we can solve for Δθ as follows:[tex]\theta_{3} = \frac{(\omega_{f2})^{2}- (\omega_{f1}) ^{2} }{2*\alpha } = \frac{(2.42rad/s^{2}) -(4.9rad/sec)^{2}}{2*(-2.63*e-3rad/sec2)} = 3451.25 rad (6)[/tex]
The total angular displacement is just the sum of (3), (4) and (6):Δθ = θ₁ + θ₂ + θ₃ = 5044.12 rad + 7252 rad + 3451.25 rad ⇒ Δθ = 15747.37 rad.Sam moves an 800 N wheelbarrow 5 meters in 15 seconds. How much work did he do?
Answer:
work done= force × displacement
=800×5
=4000J
Explanation:
The amount of work done is the result of the magnitude of force applied and the displacement of the body due to the force applied. Therefore, work done is defined as the product of the applied force and the displacement of the body.
How does the REE change as a person ages?
Explain
I go to k12 too and i am writing this test now too. I am like pretty sure my answer is correct. I guess we can kinda help eachother with this assignment cuz i am sorta stuck too.
The older a person gets, the greater REE he has.I dont know i hope this helped a bit I know its not much i need help with this too.
In a test of an energy-absorbing bumper, a 2800-lb car is driven into a barrier at 5 mi/h. The duration of the impact is 0.4 seconds. When the car rebounds from the barrier [in the opposite direction], the magnitude of its velocity is 1.5 mi/h. Use the principle of impulse and momentum to determine the magnitude of the average horizontal force (lb) exerted on the car during the impact.
Answer:
F = 2074.13 lb
Explanation:
Given that,
Mass of car, m = 2800 lb = 1270.059 kg
Initial speed, u = 5 mi/h = 2.2352 m/s
Final speed, v = - 1.5 mi/h = -0.67056 m/s (in opposite direction)
Time, t = 0.4 s
We need to find the magnitude of the average horizontal force (lb) exerted on the car during the impact. It can be calculated as :
[tex]F=m\times \dfrac{v-u}{t}\\\\F=1270.059\times \dfrac{-0.67056 -2.2352 }{0.4}\\\\F=9226.21\ N[/tex]
or
F = -2074.13 lb
So, the required force is 2074.13 lb.
A ball is sitting at the top of a ramp. As the ball rolls down the ramp, the potential energy of the ball decreases, what happens to the potential energy as the ball moves
Answer:
the potential energy decreases as it is converted to kinetic energy.
Explanation:
As things move, their potential energy converts to kinetic energy to power them along. When a ball rolls down the top of a ramp, all the potential energy it accumulated at the top of the ramp converts to kinetic energy to help it roll down. In other words, its potential energy decreases as its kinetic energy increases.
(5 Points)
a) At ground level, the pressure of the helium in a balloon is 1x105
Pa. The volume occupied by the helium is 9.6m The balloon is
released and it rises quickly through the atmosphere. Calculate
the pressure of the helium when it occupies a volume of 12m3.
(3 Marks)
b) A box is 15m below the surface of the sea. The density of sea-
water is 1020 kg/m.
Calculate the pressure on the box due to the sea-water.
(2 Marks)
Answer:
1. [tex]P_{2}[/tex] = 8 x [tex]10^{4}[/tex] Pa
2. P = 1.5 x [tex]10^{5}[/tex] N/[tex]m^{2}[/tex]
Explanation:
1. From Boyles' law;
[tex]P_{1}[/tex][tex]V_{1}[/tex] = [tex]P_{2}[/tex][tex]V_{2}[/tex]
[tex]P_{1}[/tex] = 1 x [tex]10^{5}[/tex] Pa
[tex]V_{1}[/tex] = 9.6 [tex]m^{3}[/tex]
[tex]V_{2}[/tex] = 12 [tex]m^{3}[/tex]
Thus,
1 x [tex]10^{5}[/tex] x 9.6 = [tex]P_{2}[/tex] x 12
[tex]P_{2}[/tex] = [tex]\frac{100000 x 9.6}{12}[/tex]
= 80000
[tex]P_{2}[/tex] = 8 x [tex]10^{4}[/tex] Pa
2. Pressure, P = ρhg
where: ρ is the density of the fluid, h is the height/ depth and g is the acceleration due to gravity (9.8 m/[tex]s^{2}[/tex]).
Thus,
P = 1020 x 15 x 9.8
= 149940
P = 1.5 x [tex]10^{5}[/tex] N/[tex]m^{2}[/tex]
You can hear sounds transmitted through alr, water, or steel but not through the empty vacuum of space. What type of wave carries sound?
gravity
light
mechanical
electromagnetic