A satellite of mass mis orbiting Earth in a stable circular orbit of radius R, (a) Speed of satellite is v = sqrt(G x Mg/R). (b) total mechanical energy is E = KE + PE. (c) the period of the satellite as orbit is T = 2 x pi x sqrt(R^3 / (G x Mg)).
(a) The speed of the satellite in its orbit can be derived using Kepler's second law of planetary motion, which states that a planet or satellite's orbital speed is inversely proportional to the square root of the distance from the center of the planet or satellite to the center of the primary body. This can be expressed mathematically as:
v = sqrt(G x Mg / R)
where v is the orbital speed of the satellite, G is the gravitational constant, Mg is the mass of Earth, and R is the radius of the satellite's orbit.
(b) The total mechanical energy of the satellite-Earth system in its orbit can be calculated using the formula for kinetic energy and the formula for gravitational potential energy. The kinetic energy of the satellite is given by:-
= KE
= 1/2 x m x v^2
The satellite's gravitational P.E. determined by:
= PE
= -G x Mg x m / R
The total mechanical energy of the satellite-Earth system is the sum of the kinetic energy and gravitational potential energy, so:
= E
= KE + PE
= 1/2 x m x v^2 - G x Mg x m / R
(c) The period of the satellite's orbit is the time it takes for the satellite to complete one full orbit around Earth. This can be calculated using the formula:-
= T
= 2 x pi x sqrt (R^3 / (G x Mg))
where T is the period of the orbit, G is the gravitational constant, Mg is the mass of Earth, and R is the radius of the satellite's orbit.
(d) If the new satellite has twice the mass of the original satellite, then its kinetic energy will be four times greater, since KE is proportional to m. However, the gravitational potential energy of the new satellite will also be four times greater, since PE is proportional to m. Since the total mechanical energy of the satellite-Earth system is the sum of the kinetic and gravitational potential energy, the total mechanical energy of the new satellite-Earth system will be the same as the total mechanical energy of the original satellite-Earth system. Therefore, the new satellite's orbital speed will be the same as the original satellite's orbital speed.
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In the playground game of tetherball, a ball tied to a rope circles a pole, wrapping the rope around the pole is it goes. Opponents compete to wrap the ball around the pole in one direction or the other; the game ends when the rope is entirely wrapped around the pole and the ball touches the pole. If you get the ball going around in one direction, as the rope shortens and the ball goes in smaller and smaller circles, the ball goes around with a shorter and shorter period.
Required:
Explain why this happens.
As the rope becomes shorter, the length of the rope is decreased and the centripetal force decreases according causing the ball to move in smaller circles.
What is centripetal force?The centripetal force is defined as the force that keeps an object moving in a circular path. Also, the centripetal force is equal to the tension in the rope and the tension in the rope depends on the length of the rope.
As the rope shortens, the tension in the rope decreases and the centripetal force on the ball decreases hence the ball moves in smaller and smaller circles, the ball goes around with a shorter and shorter period.
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A 51.0 kg crate, starting from rest, is pulled across a floor with a constant horizontal force of 225 N. For the first 10.0 m the floor is frictionless, and for the next 10.5 m the coefficient of friction is 0.17.
What is the final speed of the crate after being pulled these 20.5 meters?
Answer:
The final speed of the crate is 12.07 m/s.
Explanation:
For the first 10.0 meters, the only force acting on the crate is 225 N, so we can calculate the acceleration as follows:
[tex] F = ma [/tex]
[tex] a = \frac{F}{m} = \frac{225 N}{51.0 kg} = 4.41 m/s^{2} [/tex]
Now, we can calculate the final speed of the crate at the end of 10.0 m:
[tex] v_{f}^{2} = v_{0}^{2} + 2ad_{1} [/tex]
[tex] v_{f} = \sqrt{0 + 2*4.41 m/s^{2}*10.0 m} = 9.39 m/s [/tex]
For the next 10.5 meters we have frictional force:
[tex] F - F_{\mu} = ma [/tex]
[tex] F - \mu mg = ma [/tex]
So, the acceleration is:
[tex] a = \frac{F - \mu mg}{m} = \frac{225 N - 0.17*51.0 kg*9.81 m/s^{2}}{51.0 kg} = 2.74 m/s^{2} [/tex]
The final speed of the crate at the end of 10.0 m will be the initial speed of the following 10.5 meters, so:
[tex] v_{f}^{2} = v_{0}^{2} + 2ad_{2} [/tex]
[tex] v_{f} = \sqrt{(9.39 m/s)^{2} + 2*2.74 m/s^{2}*10.5 m} = 12.07 m/s [/tex]
Therefore, the final speed of the crate after being pulled these 20.5 meters is 12.07 m/s.
I hope it helps you!
help me besties PLEASE ;-;
Answer:
Current in resistors = 1.5 amp
Current in resistors = 0.18 amp
P = 93.75 watts
Explanation:
Given:
1. Three 5 ohm resistor(series)
Voltage = 10 volt
2. Three 5 ohm resistor(parallel)
Voltage = 9 volt
3. Three 5 ohm resistor(series)
Voltage = 6 volt
Find:
Current in resistors
Current in resistors
Total power of circuit
Computation:
1. Total resistor (Series) R = R1 + R2 + R3
Total resistor (Series) R = 5 + 5 + 5
Total resistor (Series) R = 15 ohm
I = V/R
Current in resistors = (15)/(10)
Current in resistors = 1.5 amp
2. Total resistor (Series) R = 1/[1/R1 + 1/R2 + 1/R3
Total resistor (Series) R = 1[1/5 + 1/5 + 1/5]
Total resistor (Series) R = 1.67 ohm
I = V/R
Current in resistors = (1.67)/(9)
Current in resistors = 0.18 amp
3. Total resistor (Series) R = R1 + R2 + R3
Total resistor (Series) R = 5 + 5 + 5
Total resistor (Series) R = 15 ohm
I = V/R
I = (15)/(6)
I = 2.5 amp
P = I²(R)
P = (2.5)²(15)
P = 93.75 watts
A rocket weighs 1.000. N on the surface of Earth. What is its weight at a distance of two Earth radii above the
surface of Earth?
P.5B
0 111.0 N
250.0 N
333.0 N
5000 N
Answer:
0 111.0N be cause the rest do not add up
One of the advantages of alternating current (ac) over direct current (dc) is the ease with which voltage levels can be increased or decreased.
a. True
b. False
Answer:
True
Explanation:
In an alternating current, voltage levels can be easily increased or decreased as per the requirements of the energy distribution in practical world.
Hence, the given statement is true
Can someone help me here
Answer:
1. grass Can survive by itself because it is not dependent on food, it is self-sustaining. and since grass it's not dependent on food it is a producer.
2. and 3. they would all decrease, since the prairie dogs are herbivores they eat basically plants such as grass and if half of the grass is gone then they would have less to eat and therefore decrease.
since ferrets eat prairie dogs, if the prairie dogs population decreases the ferrets would have less to eat and therefore decrease as well.
one of the predators of ferrets are foxes and if the ferrets decrease then the fox would also decrease since it will have less to eat.
4. if we would continue advancing years soon the ferret, prairie dogs and foxes would be no more because if there is less grass they would keep on decreasing over the years until they would be extinct.
a shiny object reflects light. will a shiny object make a shadow when light shine on it? explain your answer
Answer:
yes I think it is possible
1+1=69 how is it possible
Answer:
you add 67 to 1+1 is this clear also chicken nuggets
Answer:
i dont know
Explanation:
A 69.5-kg person throws a 0.0475-kg snowball forward with a ground speed of 31.5 m/s. A second person, with a mass of 57.5 kg, catches the snowball. Both people are on skates. The first person is initially moving forward with a speed of 2.35 m/s, and the second person is initially at rest. What are the velocities of the two people after the snowball is exchanged
Answer:
- After throwing the snow, velocity of the thrower is 2.33 m/s
- the velocity of the receiver is 0.026 m/s
Explanation:
Given the data in the question;
Using conservation of momentum,
Initial thrower has a momentum of mv; [tex]m_{total[/tex]v
(69.5 kg + 0.0475 kg) × 2.35 m/s = 163.4366 kg.m/s
Now, When he throws it at 31.5 m/s, these constitutes a momentum of;
(0.0475 kg )(31.5 m/s) = 1.49625 kg.m/s
hence his momentum now is: 163.4366 - 1.49625 = 161.94035 kg.m/s
To get his velocity, we say;
161.94035 = mv
{ he lost weight of the snow ball so, m = 69.5 kg )
161.94035 = 69.5 × v
v = 161.94035 / 69.5
v = 2.33 m/s
Therefore, After throwing the snow, velocity of the thrower is 2.33 m/s
Next is the Receiver;
the receiver will gain momentum of 1.49625 kg.m/s
he has no momentum initially and after he catches the snow ball;
1.49625 kg.m/s = mv
1.49625 kg.m/s = ( 57.5 kg + 0.0475 kg ) × v
1.49625 kg.m/s = 57.5475 kg × v
v = ( 1.49625 kg.m/s ) / 57.5475 kg
v = 0.026 m/s
Therefore, the velocity of the receiver is 0.026 m/s
7. The work done in picking the same chair up 1 meter would be about
A. 4J
B. 40J
C. OJ
D. 400J
Someone please help me...
the distance from the Earth to the sun equals 1 AU. Neptune is 30 AU from the sun. How far is Neptune from the Earth?
Answer:
1 astronomical unit, or AU, is the average distance from the Earth to the Sun; that's about 150 million km. So, Neptune's average distance from the Sun is 30.1 AU. Its perihelion is 29.8 AU, and it's aphelion is 30.4 AU.
Short Answer: it is 29
Explanation:
sorry if its wrong
Answer:
29
Explanation:
I just took a test! not only that but the other person who answered this question had the corrected answer.
A police siren of frequency fsiren is attached to a vibrating platform. The platform and siren oscillate up and down in simple harmonic motion with amplitude Ap and frequency fp. Use v for the speed of sound. Part A Find the maximum sound frequency that you would hear at a position directly above the siren. At what point in the motion of the platform is the minimum frequency heard
Answer:
he maximum frequency occurs when the denominator is minimum
f’= f₀ [tex]\frac{343}{343 + v_s}[/tex]
Explanation:
This is a doppler effect exercise, where the sound source is moving
f = fo [tex]\frac{v}{v-v)s}[/tex] when the source moves towards the observer
f ’=f_o [tex]\frac{v}{v+v_{sy}}[/tex] Alexandrian source of the observer
the maximum frequency occurs when the denominator is minimum, for both it is the point of maximum approach of the two objects
f’= f₀ [tex]\frac{343}{343 + v_s}[/tex]
A car crashes into a wall with an impulse of 40,000 kg.m/s. The collision took 2 seconds. How much force did the wall exert?
Answer:
i hate physics lol but its 20,000N
Explanation:
. Estimate the buoyant force that air exerts on you. (To do this, you can estimate your volume by knowing your weight and by assuming that your weight density is a bit less than that of water.)
Answer:
[tex]0.886[/tex] N buoyant force is exerted by air
Explanation:
My weight is [tex]75[/tex] Kg
Weight = mass * gravity
As we know
Buoyant Force is equal to the product of density * acceleration due to gravity and volume of the body
Assuming weight density is a bit less than that of water or equal to water i.e [tex]997.77[/tex] kg/m3
Volume is equal to mass / density
[tex]= 75[/tex] Kg * g/[tex]997.777[/tex]
[tex]= 0.0751[/tex] * g
Buoyant Force
= Volume * g * density
[tex]= 0.0751 * 9.8 * 1.2041[/tex]kg/m3
[tex]= 0.886[/tex] N
A train whistle produces a sound at a frequency of 600 Hz. If the train is moving toward a stationary observer at a constant speed, which of the following may be the frequency of the whistle as detected by the observer?
Bob and Sally sit on a 4 m long see-saw that has its fulcrum smack in the center of the board. If 50 kg Sally is sitting at one end of the plank, where should 70 kg Bob sit on the other side relative to the fulcrum so the net Torque is zero?
Answer:
1.43m
Explanation:
Given data
m1= 50kg
m2=70kg
We are told that Sally m1= 50 sat at one end which is 2m from the center
Hence, the summation of clockwise moment = summation of anticlockwise moment
See the attached image for your reference
50*2= 70*x
100= 70x
x= 100/70
x=1.43m
Hence the mass m2 will be at the 1.43m mark for the net torque to be zero
Thomson observed that cathode beams can pass undeflected through crossed electric and magnetic fields. Which of the following quantities must then be common to the particles making up these beams? A. Mass B. Size C. Magnitude of charge D. Sign of charge E. Sign and magnitude of charge F. Velocity
Answer:
e must have the charge of the particle
Explanation:
In this experiment, the particles that the cathode rays are found where from an electric field and another magnetic field, for the particle to pass without deviating the magnetic force must have the same modulus of the entricar force, and be in the opposite direction.
the expression for the magnetic force is
F_m = q v xB
the expression for the electric force is
F_e = q E
when warning the check two formulas we must have the charge of the particle
(20 points) You are at the center of a boat and have been rowing the boat for a long time. You weigh only 80 kg and your 120 kg buddy Bubba has been riding at the front of your 60 kg, 4 m long boat. You come to a stop in the water and then switch places. A) What is the center of mass before you switch places
Answer:
Explanation:
From the given information:
Let the first weight be [tex]m_ 1[/tex] = 80 kg
The weight of the buddy be [tex]m_2[/tex] = 120 kg
The weight of Bubba be [tex]m_3[/tex] = 60 kg
Also, since you and Budda are a distance of 4m to each other, then the length to which both meet buddy will be:
[tex]x_1 = x_3 = \dfrac{4}{2} \\ \\ = 2[/tex]
The length of the boat be [tex]x_2[/tex] = 4 m
∴
We can find the center of mass of the system by using the formula:
[tex]X_{CM} = \dfrac{m_1x_1+m_2x_2+m_3x_3}{m_1+m_2+m_3} \\ \\ X_{CM} = \dfrac{(80 \times 2)+(120\times4)+(60\times2)}{80+120+60} \\ \\ X_{CM} = \dfrac{160+480+120}{260} \\ \\ \mathbf{X_{CM} = 2.923}[/tex]
Sound wave with of frequency of 300 HZ is traveling with a wavelength of 1 m what is the speed?
Answer:
300m/s
Explanation:
f = c/λ
f = frequency
c = speed
λ = wave length
f = c/λ
300 = c/1
c = 300m/s
Cindy follows her dog around a circle having a radius of 7.40 m.
a) What distance did she travel?
b) The trip took 54 seconds. What was her speed?
c) What was the magnitude of her velocity?
Answer:
a)=46.49 m
b)=0.861 m/s
c)=0.274 m/s
Explanation:
I am quite confuse with ans C . If it is correct but I can explain .lol
3.
Two Cars, A and B, (starting, at the same time, from the same point) are moving
with average speeds of 40 km/h and 50 km/h, respectively, in the same direction.
Find how far will Car B be from Car A after 3 hours.
Answer:
car B will be 30 Km ahead of car A.
Explanation:
We'll begin by calculating the distance travelled by each car. This is illustrated below:
For car A:
Speed = 40 km/h
Time = 3 hours
Distance =?
Speed = distance / time
40 = distance / 3
Cross multiply
Distance = 40 × 3
Distance = 120 Km
For car B:
Speed = 50 km/h
Time = 3 hours
Distance =?
Speed = distance / time
50 = distance / 3
Cross multiply
Distance = 50 × 3
Distance = 150 Km
Finally, we shall determine the distance between car B an car A. This can be obtained as follow:
Distance travelled by car B (D₆) = 150 Km
Distance travelled by car A (Dₐ) = 120 Km
Distance apart =?
Distance apart = D₆ – Dₐ
Distance apart = 150 – 120
Distance apart = 30 Km
Therefore, car B will be 30 Km ahead of car A.
A car starting from rest moves with constant acceleration of 2.0 m/s2 for 10 s, then travels with
constant speed lor another 10 s, and then finally slows to a slop will conslanl acceleration of
-2.0 m/s2. How far does it travel?
Answer:
Secondary SchoolPhysics 5+3 ptsA body starts from rest and moves with a uniform acceleration.
a solid sphere and a hollow sphere with equal mass are rotated about an axis through their centers. both spheres experience equal torque. which sphere will reach a speed of 10 rad/s first? Explain your answer.
Answer:
Solid sphere
Explanation:
According to the given situation, the solid sphere would contain the less moment of inertia because it would carry large mass that closed to the axis of rotation
Also if there is a less moment of inertia so there would be high angular acceleration under a torque
α = τ/I
So the solid sphere would reach a speed of 10 rad/s first
35 POINTSS!!! PLSSSS HELLPPP!!!
Work is the transfer of power from one object to another.
Please select the best answer from the choices provided
T
F
Answer:
T
beacuse:
Energy can be transferred from one object to another by doing work. ... When work is done, energy is transferred from the agent to the object, which results in a change in the object's motion (more specifically, a change in the object's kinetic energy).
Two satellites are monitored as they orbit the Earth; satellite X is eight (8) times as far from the Earth's center as is satellite Y. Using Kepler's 3rd Law, by what factor is the the period (or revolution) of satellite X that of satellite Y
Answer:
[tex]\frac{T_x}{T_y} = 22.63[/tex]
Explanation:
Kepler's third law is an application of Newton's second law for circular motion
T² = K a³
let's apply this expression for each satellite
satellite X
Tₓ² = K aₓ³
satellite Y
[tex]T_y^2 = K a_y^3[/tex]
the relation of the periods is
[tex]\frac{T_x}{T_y} = \sqrt{ (\frac{a_x}{a_y} )^3 }[/tex]
they indicate us
aₓ = 8 a_y
substitutes
[tex]\frac{T_x}{T_y} = 8^{3/2}[/tex]
[tex]\frac{T_x}{T_y} = 22.63[/tex]
S
In a game of pool, the cue ball rolls toward the stationary eight ball with a velocity of 1.35,
and they collide. The mass of the cue ball is 170 grams, and the mass of the eight ball is
156 grams. The velocity of the cue ball immediately after the collision is 0.060
What is the velocity of the eight ball immediately after the collision?
Your answer should have three significant figures.
m
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The velocity of the eight ball immediately after the collision is 1.41 m/s.
What is the final velocity of the eight ball after the collision?
The final velocity of the eight ball after the collision is calculated by applying the principle of conservation of linear momentum;
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
where;
m₁ is the mass of the cue ballu₁ is the initial velocity of the cue ballm₂ is the mass of the eight ballu₂ is the initial velocity of the eight ballv₁ is the final velocity of the cue ballv₂ is the final velocity of the eight ball(0.17)(1.35) + (0.156)(0) = (0.17)(0.06) + (0.156v₂)
0.2295 = 0.0102 + 0.156v₂
0.156v₂ = 0.2193
v₂ = 1.41 m/s
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PLEASE HELP ME WITH THIS ONE QUESTION
A piston has a volume change of 7 x 10^-6 m^3. Assuming atmospheric pressure is 101,325 J, what is the work needed to change the piston volume?
Correct question:
A piston has a volume change of 7 x 10^-6 m^3. Assuming atmospheric pressure is 101,325 Pa, what is the work needed to change the piston volume?
Answer:
The work needed to change the piston volume is 0.709 J
Explanation:
Given;
volume of the piston, V = 7 x 10⁻⁶ m³
atmospheric pressure, P = 101,325 Pa
The work needed to change the piston volume is calculated as follows;
W = PV
W = (7 x 10⁻⁶ m³) x (101,325 Pa)
W = 0.709 J
Therefore, the work needed to change the piston volume is 0.709 J
All EM waves (light waves) travel at the same speed through the vacuum of space. If the different types of waves are distinguished by their frequency, what basic characteristic of the waves determines their difference
Answer:
Their different wavelengths.
Explanation:
trust me
All EM waves (light waves) travel at the same speed through the vacuum of space. If the different types of waves are distinguished by their frequency, the basic characteristic of the waves that determine their difference is the wavelength of the electromagnetic waves.
What is Wavelength?It can be understood in terms of the distance between any two similar successive points across any wave for example wavelength can be calculated by measuring the distance between any two successive crests.
It is the total length of the wave for which it completes one cycle.
The wavelength is inversely proportional to the frequency of the wave as from the following relation.
C = νλ
where c is the speed of light
ν is the frequency of the wave
λ is the wavelength of the wave
As we know electromagnetic waves (light waves) travel at the same speed through the vacuum of space which is the speed of light which is 3×10⁸ meter/second
All EM waves (light waves) travel at the same speed through the vacuum of space. If the different types of waves are distinguished by their frequency, the basic characteristic of the waves that determine their difference is the wavelength of the electromagnetic waves.
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Which one of the statements below is true about mechanical waves?
They must travel in empty space.
They can travel in a vacuum.
Both sound and light are examples of mechanical waves.
They require a medium to travel through.
Answer:
The answer is B
Explanation:
How far could you walk backwards in one hour? Use your speed from the 10m test to calculate the answer. Show your work or you will not receive credit.
Answer: Sweetheart i'm not walking backward for an hour for your little assignment
Explanation: Do it yourself lazy! Have a great day!