Answer:
m³/(kg⋅s²)
Explanation:
Hello.
In this case, since the involved formula is:
[tex]F=G*\frac{m_1m_2}{r^2}[/tex]
By writing a dimensional analysis with the proper algebra handling, we obtain:
[tex]N[=]G*\frac{kg*kg}{m^2}\\ \\kg*\frac{m}{s^2}[=]G *\frac{kg*kg}{m^2}\\\\G[=]\frac{kg*m*m^2}{kg^2*s^2}\\ \\G[=]\frac{m^3}{kg*s^2}[/tex]
Thus, answer is:
m³/(kg⋅s²)
Note that the [=] is used to indicate the units of G.
Best regards
A common method to measure thermal conductivity of a biomaterial is to insert a long metallic probe axially into the center of a long cylindrical container of the material. The probe is maintained at some uniform temperature Ti, and the outside of the container is maintained at a temperature To. Inside the metallic probe is an electrical heater for which the electrical power is measured. If the diameter of the probe maintained at 50°C is 1 cm, the outer diameter of the container maintained at 20°C is 4 cm, the length of the cylinder container is 60 cm, and the power input is 40.8 W, calculate the thermal conductivity of this material.
Answer:
The thermal conductivity of the biomaterial is approximately 1.571 watts per meter-Celsius.
Explanation:
Let suppose that thermal conduction is uniform and one-dimensional, the conduction heat transfer ([tex]\dot Q[/tex]), measured in watts, in the hollow cylinder is:
[tex]\dot Q = \frac{2\cdot k\cdot L}{\ln \left(\frac{D_{o}}{D_{i}} \right)}\cdot (T_{i}-T_{o})[/tex]
Where:
[tex]k[/tex] - Thermal conductivity, measured in watts per meter-Celsius.
[tex]L[/tex] - Length of the cylinder, measured in meters.
[tex]D_{i}[/tex] - Inner diameter, measured in meters.
[tex]D_{o}[/tex] - Outer diameter, measured in meters.
[tex]T_{i}[/tex] - Temperature at inner surface, measured in Celsius.
[tex]T_{o}[/tex] - Temperature at outer surface, measured in Celsius.
Now we clear the thermal conductivity in the equation:
[tex]k = \frac{\dot Q}{2\cdot L\cdot (T_{i}-T_{o})}\cdot \ln\left(\frac{D_{o}}{D_{i}} \right)[/tex]
If we know that [tex]\dot Q = 40.8\,W[/tex], [tex]L = 0.6\,m[/tex], [tex]T_{i} = 50\,^{\circ}C[/tex], [tex]T_{o} = 20\,^{\circ}C[/tex], [tex]D_{i} = 0.01\,m[/tex] and [tex]D_{o} = 0.04\,m[/tex], the thermal conductivity of the biomaterial is:
[tex]k = \left[\frac{40.8\,W}{2\cdot (0.6\,m)\cdot (50\,^{\circ}C-20\,^{\circ}C)}\right]\cdot \ln \left(\frac{0.04\,m}{0.01\,m} \right)[/tex]
[tex]k \approx 1.571\,\frac{W}{m\cdot ^{\circ}C}[/tex]
The thermal conductivity of the biomaterial is approximately 1.571 watts per meter-Celsius.
The mass of the basketball shown below is 4 times the mass of the baseball.
Basketball
Baseball
If the two balls are moving at the same speed, and the basketball and the baseball has a kinetic
energy of 10.0 J, what is the kinetic energy of the basketball?
2.5 J
5.03
10.03
20.0 J
Answer:
40.0 Joules. None of the answers is correctExplanation:
Kinetic energy of an object is expressed as;
KE = 1/2mv² where;
m is the mass of the object
V is the velocity of the object.
Let Ma be the mass of the basketball and Mb be the mass of baseball.
If the mass of the basketball shown below is 4 times the mass of the baseball, then Ma = 4Mb
KE of the basket ball = 1/2MaVa²
Va² = 2(KE)a/Ma ...... 1
KE of the baseball = 1/2MbVb²
Vb² = 2(KE)b/Mb .......... 2
Since their velocities are the same, hence Va²= Vb²
2(KE)a/Ma = 2(KE)b/Mb
Substituting Ma = 4Mb into the resulting expression.
2(KE)a/4Mb = 2(KE)b/Mb
2(KE)a/4 = 2(KE)b
Given Kinetic energy of baseball (KE)b = 10.0J, the expression becomes;
2(KE)a/4 = 2(10)
2(KE)a = 4*20
2(KE)a = 80
(KE)a = 80/2
(KE)a = 40.0J
Hence the kinetic energy of the basketball is 40.0Joules
In getting ready to slam-dunk the ball, a basketball player starts from rest and sprints to a speed of 5.45 m/s in 3.02 s. Assuming that the player accelerates uniformly, determine the distance he runs.
Recall that average velocity v is given by
v = ∆x/∆t
where ∆x is displacement and ∆t is time.
Under constant acceleration, average velocity is also equal to the average of the initial and final velocities,
v = (v₂ + v₁)/2
The player starts at rest, so v₁ = 0, and speeds up to v₂ = 5.45 m/s in a matter of ∆t = 3.02 s. So
∆x = (v₂ + v₁) ∆t / 2
∆x = (5.45 m/s) * (3.02 s) / 2
∆x ≈ 8.23 m
A water skier has a mass of 86 kg and accelerates at 2 m/s2. What is the net force acting on him?
Ο Α.
0.0233 N
2
B.
43 N
C. 84N
D.
172 N
Answer:
F = 172 N
Explanation:
Newton's second law of motion gives the amount of force acting on an object. Mathematically, it is given by :
F=ma
Put m =86 kg and a = 2 m/s²
So,
[tex]F=(86\times 2)\ N\\\\F=172\ N[/tex]
Hence, the net force is 172 N.
How much will a 200kg hippo accelerate if you push it with a force of 800 N?
Answer:
Explanation:
force = f, mass = m, acceleration = a
f = m a
m = 200 kg
f = 800 N
f = m a
800 = 200a
a = 800 / 200
a = 4
Hope this helps
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You are standing on a scale in an elevator that is moving upward with a constant velocity. The scale reads 600 N. The following table shows five options for what the scale reads when the elevator slows down as it comes to a stop, when it is stopped, and when it picks up speed on down. Which one of the five options correctly describes the scale's readings? Note that the symbol < means "less than" and > means "greater than."
Option Elevator slows down Elevator is stopped Elevator picks up speed
as it comes to a half on its way back down
(a) >600 N >600 N >600 N
(b) <600 N 600 N <600 N
c) >600 N 600 N <600 N
(d) <600 N <600 N <600 N
(e) <600 N 600 N >600 N
Answer:
C. >600 N 600 N <600 N
Explanation:
The scale's reading when when the elevator slows down as it comes to a stop, when it is stopped, and when it picks up speed on down is >600 N, 600 N, <600 N respectively.
To understand this we have to first understand weight.
What is weight?Weight is a product of mass and gravitational acceleration.Weight W = mg , where m = mass of an object , g = gravitational acceleration.The gravitational force increases as the height of an object increases.What happens to scale's reading when an elevator changes its position? The scale's reading is 600 N.When an elevator goes upwards and slows down , the Earth's gravity pulls it down so the force will be 600 N + force applied by earth so it will be >600 N.When an elevator stops it is at its natural height so, the force will be 600 N.When an elevator picks up speed on down, the force will be less than 600 N so it will be <600 N.So, the scale's reading is >600 N 600 N <600 N, hence the correct answer is option C.
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A car is driving at 85 km/h and the driver spots a stop sign ahead. What coefficient of friction is needed to stop the car at the stop sign if the stop sign is 900m away?
Answer:
μ = 0.0315
Explanation:
Since the car moves on a horizontal surface, if we sum forces equal to zero on the Y-axis, we can determine the value of the normal force exerted by the ground on the vehicle. This force is equal to the weight of the cart (product of its mass by gravity)
N = m*g (1)
The friction force is equal to the product of the normal force by the coefficient of friction.
F = μ*N (2)
This way replacing 1 in 2, we have:
F = μ*m*g (2)
Using the theorem of work and energy, which tells us that the sum of the potential and kinetic energies and the work done on a body is equal to the final kinetic energy of the body. We can determine an equation that relates the frictional force to the initial speed of the carriage, so we will determine the coefficient of friction.
[tex]\frac{1}{2} *m*v_{i}^{2}-(F*d)= \frac{1}{2} *m*v_{f}^{2}[/tex]
where:
vf = final velocity = 0
vi = initial velocity = 85 [km/h] = 23.61 [m/s]
d = displacement = 900 [m]
F = friction force [N]
The final velocity is zero since when the vehicle has traveled 900 meters its velocity is zero.
Now replacing:
(1/2)*m*(23.61)^2 = μ*m*g*d
0.5*(23.61)^2 = μ*9,81*900
μ = 0.0315
Xiang is comparing the strong nuclear force and the weak nuclear force.
Which describes the weak nuclear force only? Check all that apply.
is attractive
is repulsive
has an infinite range
has a very small range
is stronger than the gravitational force
is weaker than the electromagnetic forc
Answer:
answer is 2 and 6 on edge2020, sorry that its a week late
Explanation:
Answers:
B. is repulsive
F. is weaker than the electromagnetic force
Explanation:
Correct on Edge 2021
In a Young's double-slit experiment the separation distance y between the second-order bright fringe and the central bright fringe on a flat screen is 0.0177 m, when the light has a wavelength of 425 nm. Assume that the angles are small enough so that sin is approximately equal to tan . Find the separation y when the light has a wavelength of 560 nm.
Answer:
y = 0.0233 m
Explanation:
In a Young's Double Slit Experiment the distance between two consecutive bright fringes is given by the formula:
Δx = λL/d
where,
Δx = distance between fringes
λ = wavelength of light
L = Distance between screen and slits
d = Slit Separation
Now, for initial case:
λ = 425 nm = 4.25 x 10⁻⁷ m
y = 2Δx = 0.0177 m => Δx = 8.85 x 10⁻³ m
Therefore,
8.85 x 10⁻³ m = (4.25 x 10⁻⁷ m)L/d
L/d = (8.85 x 10⁻³ m)/(4.25 x 10⁻⁷ m)
L/d = 2.08 x 10⁴
using this for λ = 560 nm = 5.6 x 10⁻⁷ m:
Δx = (5.6 x 10⁻⁷ m)(2.08 x 10⁴)
Δx = 0.0116 m
and,
y = 2Δx
y = (2)(0.0116 m)
y = 0.0233 m
If the total time is 120 seconds and the total distance is 320 meters. Calculate
the average speed (show work)
Answer:
S=D/T
320/120= 2.66 miles
Explanation:
1
Find the x-component of this
vector:
Help Resources
0.250 m
18.4°
Skip
Remember, angles are measured from
the +X axis.
x-component (m)
Answer:
x-component = 0.237 [m]
Explanation:
In order to solve this problem in an easy way, we must first make a sketch of the vector and its respective angle with the X-axis, in the attached image we can see that sketch.
Since the X component of the vector is needed, this component can be found by means of the cosine of the angle and its hypotenuse.
x-component = 0.250*cos(18.4)
x-component = 0.237 [m]
Answer:
x = 0.237
y = -0.0789
Explanation:
A trough is 8m long and has ends which are isosceles triangles with height 3m and width (across the top) of 3m. The trough has a spout at the top of the tank with height 2m. The tank is full of water. (a) How much work is required to pump all of the water out of the tank? (NOTE that the density of water is rho = 1000 kg/m3 and the acceleration due to gravity is 9.8 m/s2 . (b) Suppose the pump breaks down after 4 × 105 J of work has been done. What is the depth of the remaining water in the tank
Answer:
(a) the work required to pump all of the water out is 1.0584 x 10⁶ J
(b) the depth of the remaining water in the tank is 1.87 m
Explanation:
Given;
length of trough, L = 8m
height of the isosceles triangle, h = 3m
width of the isosceles triangle, w = 3m
length of spout, b = 2m
The center mass of isosceles triangle is given by;
[tex]\frac{1}{3} \ of \ height \ of \ the \ triangle = \frac{1}{3} *3 = 1 \ m[/tex] (this is the height below the top of the trough)
The total height water will be pumped, H = 1m + b
H = 1m + 2m = 3m
Determine the volume of the trough;
Volume of the trough = area of the triangle x length of the trough
Volume of trough = [tex]\frac{1}{2}*3*3*(8) = 36 \ m^3[/tex]
(a) The work done in pumping all of the water out;
The work done in pumping all of the water out = potential energy of water at that height, H;
W = mgH
where;
m is mass of water
m = ρV
m = (1000 kg/m³) x (36 m³)
m = 36,000 kg
The work done = mgH
= 36,000 x 9.8 x 3
= 1.0584 x 10⁶ J
(b) after 4 × 10⁵ J of work has been done, the energy required to pump out the remaining water is given by;
ΔE = 1.0584 x 10⁶ J - 4 × 10⁵ J = 658,400 J
The depth of the remaining water is calculated as
658,400 J = mgh
where;
h is the height of the remaining water
658,400 = (36,000 x 9.8)h
658,400 = 352,800h
h = 658,400 / 352,800
h = 1.87 m
Given the hypothesis that the element zinc prevents cancer, which of the following procedures BEST exemplifies the nature of scientific investigation?
A- Analyze zinc, looking for different forms
B- Do research on zinc and its uses throughout history to determine if there is evidence that zinc prevents incidence of cancer
C- Rely on testimony of friends and relatives, as well as conduct a survey to see if there is a concentration of cancer in the people not taking zinc supplements
D- Give zinc supplements to a group of rats and not to another group. After a period of time, determine if there is a higher incidence of cancer in the control group
Answer:D
Explanation: i found the answer in an answer key!
Give zinc supplements to certain rats while withholding them from others. Determine whether the control group's cancer incidence has increased over time. Hence, option D is correct.
What is Scientific Investigation?Scientific investigation refers to the procedures and procedures used by scientists to create hypotheses, carry out experiments, collect and analyze data, and come to conclusions. Sometimes the evidence doesn't offer adequate answers, but it can raise fresh questions that need to be looked into. Scientific methods are employed by scientists primarily to conduct scientific research.
The steps in Scientific Investigation are :
Make some observationsAsk questions on basis of observationsMake a HypothesisCheck that HypothesisExtract ConclusionCommunicate the results.The hypothesis portion is the best way to define a hypothesis as a potential solution to a problem in science. Though it may be falsifiable, it is crucial that the hypothesis be rational. Observations that would contradict the hypothesis must be made if we want to show it to be false. In this case, we'll check to determine if the problem is with just one particular electrical item or with all of them.
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When a technician touches a _____ it is the most dangerous, and likely to cause serious injury. a. live conductor with his right hand and touches a ground with his left hand b. live wire with his hand but is standing on an insulated platform c. live wire with his right hand and accidentally touches his right elbow on the metal of the same unit d. ground with his thumb and a live wire with his index finger
Answer: live conductor with his right hand and touches a ground with his left hand
Explanation:
When a technician touches a live conductor with his right hand and touches a ground with his left hand, it is the most dangerous, and likely to cause serious injury.
This is because when the person touches the live conductor, there will be an electrical path which will allow current flow with the aid of the person's body. This is because the body of human being is a conductor. Therefore, when the technician touches the live conductor with his right hand and touches a ground with his left hand, an electrical path is created.
A.) A bullet accelerates at 8000 m/s2
as it
is fired from a 1.6m rifle. How much
time will it take to clear the barrel?
B.) How much velocity does that rifle
impart on the bullet?
Answer:
0.02 s
160 m/s
Explanation:
Given:
Δx = 1.6 m
v₀ = 0 m/s
a = 8000 m/s²
A) Find t.
Δx = v₀ t + ½ at²
1.6 m = (0 m/s) t + ½ (8000 m/s²) t²
t = 0.02 s
B) Find v.
v² = v₀² + 2aΔx
v² = (0 m/s)² + 2 (8000 m/s²) (1.6 m)
v = 160 m/s
Whatcan you say to care our mother earth
Answer:
You can say, use public transportation
Calculate the average speed of a car which moves 200 km in 10 hours.
Answer:
Average speed = (total distance) / (total time)
Total distance = 100 km + 200 km = 300 km
Total time = 2 hrs (first part) + 1/2 hr (stop) + 4 hrs (second part) = 6.5 hrs
Average speed = 300 / 6.5 = 46.154 km/hr (rounded)
Explanation:
The sound wave has a frequency of 426 Hz. What is the period? What is the wavelength?
Answer:
See below
Explanation:
Using the speed of sound in air as 343 m/s :
343 = wavelength * frequency
= wavelength * 426
wavelength = .81 meters
Period is just 1/frequency = .00235 seconds
You have four identical conducting spheres: A, B, C, and D. In each scenario below, sphere A starts with a charge of -Q, sphere C starts out with a charge of Q, and spheres B and D start out neutral. Then the spheres are touched to each other and separated in the order described. Any spheres not in contact are held very far away. For each scenario, give the final charge of sphere C as a whole number fraction of Q. For example, if you decide that the final charge of sphere C is -Q/7, enter \"-1\" in the numerator and \"7\" in the denominator. Remember! Before each scenario begins, spheres A, B, C, and D are reset to charges of -Q, 0, Q, and 0 again.
Scenario 1: A and B touch and are separated, then A and C touch and are separated, then A and D touch and are separated.
Scenario 2: A and D touch and are separated, then D and C touch and are separated, then D and A touch and are separated, then A and B touch and are separated.
Scenario 3: A and B touch and are separated, then B and D touch and are separated, then C and D touch and are separated.
Answer:
1) Q_c = - ½ Q , 2) Q_c = + ¼ Q , 3) Q_c= 3/8 Q
Explanation:
For this exercise we must use that equal charges repel and charges with different signs attract. When two objects are in contact, the charges are evenly distributed between them.
Scenario 1.
when the two spheres touch the charge -Q is distributed between them, when separating each sphere has a charge = -1/2 Q
as there are no more interacts sphere C its charge is
Q_c = - ½ Q
Scenario 2
when the two spheres touch the charge -Q is distributed between them, when separating each one has a charge
Q_a = Q_d = - ½ Q
now the sphere D and C touch the charge is Q_net = -1/2 Q + Q = + ½ Q
when separating each sphere has half the charge
Q_d = Q_c = + ¼ Q
since sphere C has no more interaction, its charge is
Q_c = + ¼ Q
Scenario 3
A and B touch the net charge is Q_net = - Q + 0 = - Q
when parting
Q_a = Q_b = - ½ Q
now B and D touch, the charge is Q_net = - ½ Q +0 = - ½ Q
when parting
Q_b = Q_d = - ¼ Q
finally C and D touch
the net charge is Q_net = Q- ¼ Q = ¾ Q
when separating each one is left with half the load
Q_c = Q_d = 3/8 Q
Q_c= 3/8 Q
Electric current passing through a human body can be dangerous, even fatal, depending on the amount of current, the duration of the current, and the region of the body through which the current passes. However, currents less than about 0.5 mA are typically imperceptible. A current caused by a low potential difference typically travels through the outer layer of the skin. The resistance of the skin therefore determines how much current flows for a given potential difference. The resistance can be influenced by a number of factors, including whether the skin is wet or dry. For example, suppose an electric current of 89.0 µA follows a path through the thumb and index finger. When the skin is dry, the resistance along this path is 4.70 ✕ 105 Ω. What voltage (in V) is required for this current, in the case of dry skin? V When the skin is wet, the resistance is lowered to 2,200 Ω. What voltage (in V) is required for the same current, in the case of wet skin? V
Answer:
V for dry skin = 41.83 volts
V for wet skin = 0.196 volts
Explanation:
The relationship between current and voltage is given as follows by Ohm's Law:
V = IR
where,
V = voltage
I = Current
R = Resistance
FOR DRY SKIN:
V = Vd = ?
I = 89 μA = 89 x 10⁻⁶ A
R = 4.7 x 10⁵ Ω
Therefore,
Vd = (89 x 10⁻⁶ A)(4.7 x 10⁵ Ω)
Vd = 41.83 volts
FOR WET SKIN:
V = Vw = ?
I = 89 μA = 89 x 10⁻⁶ A
R = 2200 Ω
Therefore,
Vd = (89 x 10⁻⁶ A)(2200 Ω)
Vd = 0.196 volts
Knowing that a ball traveled 16 feet in one second, how much will it travel in the first quarter second?
Answer:
4 Feet
Explanation:
Because A Quarter of 16 is 4
You really can't tell. You don't know if its speed was constant for the whole second, or whether it was accelerated, decelerated, intermittent, bouncing back and forth, etc. All you know is that after 1 second, it had moved 16 ft.
IF its speed was constant AND it moved in a straight line, THEN it moved 4 ft in the first quarter of that second.
If it rolled off of a roof and FELL 16 ft in the first second, then it fell 1 foot in the first quarter second.
A ball is thrown with velocity 30.m⋅s−1at an angle of 40.º below the horizontal. What is the magnitude of the horizontal component of the velocity? Give your answer to the nearest m⋅s−1 and do not include units with your answer.
Answer:
Explanation:
The horizontal component of the velocity is expresssed as;
Vx = Vcos θ
V is the velocity of the ball
θ is the angle of inclination to the horizontal
Given
V = 30m/s
θ = 40°
Vx = 30cos40°
Vx = 22.98
Hence the magnitude of the horizontal component of the velocity to the nearest m/s is 23
Elements are organized on the periodic table based on their properties. Which statement correctly predicts and explains the chemical reactivity of two metals?
Rubidium (Rb) is more reactive than strontium (Sr) because strontium atoms must lose more electrons.
Sodium (Na) is more reactive than magnesium (Mg) because sodium atoms must gain more electrons.
Calcium (Ca) is less reactive than potassium (K) because potassium atoms must lose more electrons.
Beryllium (Be) is less reactive than lithium (Li) because beryllium atoms must gain more electrons.
Answer:Rubidium or answer 1
Explanation:took quiz
Answer: Rubidium (Rb) is more reactive than strontium (Sr) because strontium atoms must lose more electrons.
Explanation: Look at the elements they are organized on the periodic table based on their properties. (A) correctly predicts and explains the chemical reactivity of two metals.
Suppose that 4 charged particles, all having a positive charge Q, are placed and fixed at the vertices of a square, where every side has a length a.
(a) What is the electric potential at the center of this arrangement? You can use any of the symbols already provided to you when typing your answer, in addition to the symbol ke and any numbers. [NOTE: The symbol ke must be typed with e as a subscript on k to receive credit. Simply typing "ke" will not suffice.]
(b) Now imagine that we introduce a new charge, called q. How much potential energy would this charge have if it were placed at the center of the square? You can use any of the symbols already provided to you when typing your answer, in addition to the symbol ke and any numbers.PE =
Answer:
+%_×¥+₩ £kshnow sjsni niadk lplz kfkd skidk skkkim
A student releases a marble from the top of a 130cm ramp. The marble increases speed steadily and reaches the bottom of the ramp with a speed of 140cm/s. Determine all unknowns and answer the following question.
How long did the marble take to reach the bottom of the ramp?
PLZ HELP ASAP
Explanation:
V=p/t
t=p/V
p=130cm
V=140cm/s
t=130/140s = 13/14s
Explain why scientists use the International System of Units (SI)
Answer:
Scientist use the IS system to keep measurements that are identical and equivalent for all scientists across the world. The metric system can also be broken down easier and much clearer than Imperial units. This also clears up confusion if all scientists are using the same units and leaves less room for accidents in transferring measurements.
Explanation:
A dog runs 3 miles and 4 miles west in 6 hours. What’s the dogs total distance and displacement ?
Complete question:
A dog runs 3 miles east and 4 miles west in 6 hours. What’s the dogs total distance and displacement ?
Answer:
The total distance covered by the dog is 7 miles
The displacement of the dog is 1 mile west
Explanation:
Given;
initial position of the dog = 3 miles east
final position of the dog = 4 miles west
time of motion, t = 6 hours
The total distance covered by the dog is given as;
Total distance = 3 miles + 4 miles = 7 miles
The displacement of the dog is given as;
displacement = final position of the dog - initial position of the dog
displacement = 4 miles west - 3 miles east = 1 mile west
how can we prove air in water
We can show that air is dissolved in water with the help of following activity: Take some water in a glass or metal container like pan and heat it. Just before water begins to boil, you will notice some bubbles at the inner surface of the pan. These bubbles come from the air dissolved in water.
Which of these would be the BEST way to illustrate the percentage of students receiving A's,
B's, C's, D's and F's on a recent test? *
Bar graph
Circle graph
Line graph
Scatter graph
Answer:
it’s circle graph
Explanation:
the best type of graph to use to show the percentages of a whole is a circle graph
A moon orbits a planet every 42 hours with a mean orbital radius of .002819 AU. The mass of the moon is 8.932 x 1022 kg. Using Newton’s modification to Kepler’s 3rd law, calculate the Mass of the Planet in kg.
Answer:
The mass of the planet is [tex]1.9407\times10^{27}\ kg[/tex]
Explanation:
Given that,
Time period = 42 hours = 151200 sec
Orbital radius = 0.002819 AU = 421716397.5 m
Mass of moon [tex]m=8.932\times10^{22}\ kg[/tex]
We need to calculate the mass of the planet
Using Kepler’s third law
[tex]T^2\propto a^3[/tex]
[tex]T^2=\dfrac{4\pi^2}{G(M+m)}\times a^3[/tex]
Where, a = orbital radius
T = time period
G = gravitational constant
M = mass of moon
m = mass of planet
Put the value into the formula
[tex](151200)^2=\dfrac{4\pi^2}{6.673\times10^{-11}(8.932\times10^{22}+m)}\times(421716397.5)^3[/tex]
[tex](8.932\times10^{22}+m)=\dfrac{4\pi^2}{6.673\times10^{-11}}\times\dfrac{(421716397.5)^3}{(151200)^2}[/tex]
[tex](8.932\times10^{22}+m)=1.94087\times10^{27}[/tex]
[tex]m=1.94087\times10^{27}-8.932\times10^{22}[/tex]
[tex]m=1.9407\times10^{27}\ kg[/tex]
Hence, The mass of the planet is [tex]1.9407\times10^{27}\ kg[/tex]
