The ball's moment of inertia around the circle's centre is 1.14 kg/m². 0.0195 Nm of torque is required to maintain the ball's rotational angular velocity.
Are joules a type of moment unit?How come the SI unit of work is While both appear to have the same formula, the difference between the Joule and the SI unit of Moment of force (torque) is that the former includes a perpendicular distance while the latter just includes a distance. The joule is the SI unit for measuring work or energy.
I = mr²
where m is the mass of the ball and r is the radius of the circle. Substituting the given values, we get:
I = (0.65 kg) × (1.3 m)² = 1.14 kg·m²
τ = Fr
where F is the force exerted on the ball by air resistance and r is the radius of the circle. Substituting the given values, we get:
τ = (0.015 N) × (1.3 m) = 0.0195 N·m
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places a stick in a pond. when she looked down at the stick, it appeared to be broken at the point where the stick entered the water. this was caused by:
This phenomenon is caused by the refraction of light as it passes from one medium (air) to another (water).
Light refraction breaks the stick where it reaches the water. Light refracts when it goes from air to water. Light changes speed and direction when it flows from air to water. Refraction causes this alteration. The angle light enters the water determines refraction.
In this situation, the stick appears to move because light rays from the submerged section bend or refract as they transit from water to air. This optical illusion makes the stick look shattered at the water's surface.
Light refraction at the air-water contact makes the stick seem shattered.
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a negatively charged rubber rod is brought near the knob of a positively charged electroscope. the result is that:
The correct option is D) Negative
The negative charges pass on to the electroscope due to induction which causes the electroscope leaves to move further apart.
Induction refers to the process of producing an electromotive force (EMF) in a conductor due to a change in the magnetic field around it. This principle is known as Faraday's Law of Induction. The EMF produced by induction can be used to generate an electric current in a conductor. Induction is the basis for the operation of transformers, generators, and many other electrical devices.
In the process of induction, a changing magnetic field is produced when a current is flowing through a wire. This changing magnetic field induces a voltage in a nearby conductor. If the conductor is part of a closed circuit, an electric current will flow, creating an electromotive force.
Therefore, The correct option is D) Negative
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I don't understand how to even begin to solve this, can someone help?
Answer:
Liquid: A state of matter that consists of loose, free moving particles which form the shape set by the boundaries of the container in which the liquid is in. This happens because the motion of the individual particles within a liquid is much less restricted than in a solid. One may notice that some liquids flow readily whereas some liquids flow slowly. A liquid's relative resistance to flow is viscosity.
Solid: A state of matter with tightly packed particles which do not change the shape or volume of the container that it is in. However, this does not mean that the volume of a solid is a constant. Solids can expand and contract when temperatures change. This is why when you look up the density of a solid, it will indicate the temperature at which the value for density is listed. Solids have strong intermolecular forces that keep particles in close proximity to one another. Another interesting thing to think about is that all true solids have crystalline structures. This means that their particles are arranged in a three-dimensional, orderly pattern. Solids will undergo phase changes when they come across energy changes.
Gas: A state of matter where particles are spread out with no definite shape or volume. The particles of a gas will take the shape and fill the volume of the container that it is placed in. In a gas, there are no intermolecular forces holding the particles of a gas together since each particle travels at its own speed in its own direction. The particles of a gas are often separated by great distances.
Explanation:
QUESTION 4 A 200 kg rock lies on the surface of a planet with mass, M. The gravitational force, F exerted by the planet on the rock is 1200 N. The radius of the the planet is 700 Calculate the mass, M of the planet
4.4 kg is the mass, M of the planet.
m=200 kg
M=?
F= 1200 N.
r= 700m
G=6.674×10^−11
F=GMm/r²
M=Fr²/Gm
M=5.8×10^8/1.310^−8
M=4.4 kg
Mass is used in physics to express inertia, a fundamental characteristic of all matter. Essentially, it is a mass of matter's resistance to changing its direction or speed in response to the application of a force. The change that an applied force produces is smaller the more mass a body has. The kilogram, the unit of mass in the International System of Units, corresponds to 6.62607015 1034 joule seconds using Planck's constant (SI). One joule is produced by multiplying one kilogram by one square meter per second. The kilogram is determined by exact measurements of Planck's constant since the second and the meter have previously been defined in terms of other physical constants.
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2. A school bus moves at a speed of 35 miles per hour (mph) for 20
miles. How long will it take for the bus to arrive at school?
Answer:
Time, t = 0.57 hours or 34 minutes and 12 seconds.
Explanation:
Given:
Speed of the school bus, s = 35 mi/hr
Distance covered by the bus, d = 20 miles
Speed(s) is equal to Distance over Time (s=d/t)
Meaning time is equal to distance over speed (t=d/s)
plugging our given information into the formula, we know Time is equal to 20 over 35 (t=20/35)
20/35=0.57, so
t = 0.57 hours
the time taken by the bus to reach school is 0.57 hours or 34 minutes and 12 seconds.
Answer:
Explanation:
Mathematically, speed is given by this formula;
Speed=distance/time
Making time the subject of formula, we have:
Time = distance/speed
Substituting the given parameters into the formula, we have;
Time = 20/35
Time = 0.571 hours.
A bird flies from the ground to a high branch in a tree. must the average speed of the bird for this motion be equal to the magnitude of the average velocity?
The average speed of a bird flying from the ground to a high branch in a tree may not necessarily be equal to the magnitude of the average velocity.
The average speed of an object is defined as the total distance traveled divided by the total time taken, disregarding the direction of motion. On the other hand, the average velocity considers both the magnitude and direction of motion, calculated as the displacement divided by the total time taken.
In the case of the bird flying from the ground to a high branch in a tree, the average speed is determined solely by the total distance covered divided by the total time taken. However, the average velocity takes into account the displacement, which includes the change in position from the starting point to the final point, along with the direction of motion. If the bird flies directly from the ground to the high branch without any significant lateral movement, then the magnitude of the average velocity would be equal to the average speed. However, if the bird follows a curved or non-direct path, the magnitude of the average velocity would not be equal to the average speed, as the direction of motion plays a role in determining the average velocity.
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why it is difficult to run fast in sand
Explanation:
The force exerted by our foot on the sand is less because time taken is large so it is difficult to run fast on sand.
hope it will help you
Identify each lettered part of the circuit, and explain what each part does.
(PLEASE HELP!) 20 POINTS!!!
The question is incomplete but the parts of the electric circuit have been outlined below.
What are the components of an electric circuit?An electric circuit is a path through which electric current flows, and typically consists of several components, including:
Power source: A device that provides the electric energy needed for the circuit to function, such as a battery, generator, or power supply.
Conductors: Materials that allow electric current to flow through them easily, such as copper wires.
Load: The device or component in the circuit that consumes or uses the electric energy, such as a light bulb, motor, or resistor.
Switch: A device that can be used to open or close the circuit, allowing or blocking the flow of electric current.
Control elements: Devices that can regulate or control the flow of electric current, such as diodes, capacitors, and transistors.
Connectors: Materials or devices used to connect the components of the circuit together, such as wire nuts, solder, or connectors.
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what is the acceleration of a car that goes from 0 to 20m/s in 7 seconds?
Answer:
2m/s^2
Explanation:
Clculate the acceleration:
V = u +at
20m/s = 0 + a*10s
a = 20m//10s
a = 2m/s²
From the data given , it is not possible to calculate the displacement , because no direction of motion is given
But it is possible to calculate the distance travelled
Distance = ut + ½ *a*t²
distance = 0 + ½ * 2m/s * 10²s
distance = 100m
If a 5.5 kg object experiences 15 N of force for .15 seconds what is the speed change
The speed change : Δv = 0.41 m/s
Further explanationGiven
mass = 5.5 kg
Force = 15 N
time = 0.15 s
Required
the speed change
Solution
Newton 2nd's law
Impulse and momentum
F = m.a
F = m . Δv/t
F.t = m.Δv
Input the value :
15 N x 0.15 s = 5.5 kg x Δv
Δv = 0.41 m/s
What is the combined resistance of 5ohms wire arranged in series with a parallel arrangement of 4ohms and 6ohms wires
No link or I'll report you
Answer:
This is a very straightforward problem, and not too difficult to do in your head. If we have two nearly equal resistances, the series resistance (Rs) is twice the average value (midpoint between the two) and the parallel resistance Rp) is approximately equal to half the midpoint value. So a rough initial guess might be 12 and 13 ohms, where Rs is 25 ohms but Rp is approximately 6.25 ohms. Since Rp needs to be lower, we can play around with resistor values. Here’s an easy shortcut:
Let’s start with the equation for two parallel resistors:
Rp = (R1 * R2)/(R1 + R2)
Since Rs = R1 + R2,
Rp = (R1 * R2)/Rs.
We can rewrite this as
Rp * Rs = R1 * R2
Plugging in our numbers (Rp = 6, Rs = 25), we see that R1 + R2 = 150. What two numbers in the vicinity of 12 and 13 have the product of 150 and a sum of 25? Immediately 10 and 15 come to mind! Easy enough!
A 91-kg hockey player on the austin bats team is at rest on the ice if he throws a 4 kg rock at 2.1 m/s. what is the resulting speed of the hockey player in m/s
это действие является рективным, формула которой такова: m1×v1 = – m2×v2
m1 - масса игрока
m2 - масса шайбы
v1 - скорость игрока
v2 - скорост шайбы.
отсюда, скорост игрокa: v1 = (m2×v2):m1 = 0.092 m/s
A sample of diamagnetic material is initially at rest in a uniform magnetic field. if no other forces are present, how will the sample move
The sample will move very slowly in the opposite direction of the applied magnetic field, but it will eventually come to a stop when it reaches equilibrium.
Diamagnetic materials, unlike ferromagnetic or paramagnetic materials, do not possess any permanent magnetic moment or net magnetic dipole moment. The magnetic force acting on the diamagnetic material is perpendicular to its velocity, and hence it cannot accelerate the material along the direction of the magnetic field.
Since the sample is made of diamagnetic material, it will have a very weak and temporary magnetic moment induced in it when placed in a magnetic field. This induced magnetic moment will be in the opposite direction to the applied magnetic field. Therefore, the sample will experience a force in the direction opposite to the applied magnetic field. However, this force will be very weak since the diamagnetic material has a weak magnetic susceptibility.
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11. When gathering glassware and equipment for an experiment, you should
a. Read all directions carefully to know what equipment is necessary
b. Examine all glassware to check for chips or cracks.
C. Clean any glassware that appears dirty
d. All of the above
Answer:
C
Explanation:
Option D is the correct answer.
What are the importance when gathering glassware and equipment for experiment?Usually in the research labs there were some rules and we have follow those for our safety measures. Some importance rules while doing experiments were:
Flammable materials should be used in open.Always must use the experimental equipment given.While gathering we must read all directions carefully to know the necessary of the equipment.Glassware should be checked whether it's broken or not before using the equipment.All the glassware and equipment using for experiment must be clean.Should ask our lead or instructor before and after the experiment.While using a test tube we should be away from other people.We should use tongs before picking up the heating material and heated equipment.For any clarifications and doubts we should always ask and listen to the instructor.Hence, option D is the correct answer.
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Make
a claim about what might happen to a
population of rabbits in a forest if a new
predator moved to the forest. Cite evidence
to support the claim and explain your
reasoning.
Answer: The rabbits will die off and the things that rabbits eat will overpopulate.
Explanation:
Sustainability of land use is involved in three parts. Which areas are these?A) reduce, reuse, recycle = wrongB) social, environment, economy = ?C) poverty, agriculture, health = ?maybe???D) biodiversity, environment, waste management = ?please answer correctly and its NOT "A) reduce, reuse, recycle"
How long would a pendulum on earth (where g = 9. 8 m/s2) have to be to have the same period as a spring with a mass of 10. 0 kg and a spring constant of 25 n/m
The pendulum would need to be approximately 3.92 meters long to have the same period as the given spring-mass system.
The period of a pendulum can be calculated using the formula:
T = 2π * sqrt(L / g)
where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.
To find the length of the pendulum that would have the same period as the given spring-mass system, we need to set their periods equal to each other and solve for L.
The period of the spring-mass system is given by:
T = 2π * sqrt(m / k)
where m is the mass and k is the spring constant.
Setting the two periods equal to each other:
2π * sqrt(L / g) = 2π * sqrt(m / k)
Simplifying the equation:
sqrt(L / g) = sqrt(m / k)
Squaring both sides:
L / g = m / k
Solving for L:
L = (m * g) / k
Substituting the given values, m = 10.0 kg, g = 9.8 m/s^2, and k = 25 N/m:
L = (10.0 kg * 9.8 m/s^2) / (25 N/m)
Calculating the value of L:
L = 3.92 m
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What happens to the force needed to stretch an elastic object?
Answer:
the force pulls each other cause its just physics
a nearsighted person wants to see an apple that is 7 meters away but can only clearly see objects that are at most 62 cm away from her eyes. eyeglasses made of diverging corrective lenses can help her to see the apple clearly. if her glasses are 2.5 cm in front of her eyes, what should be the power of these corrective lenses to allow her to see the apple?
The power of the diverging corrective lenses for a nearsighted person who wants to see an apple that is 7 meters away should be -40.1 diopters.
What will be the focal length of the diverging corrective lenses that can help her to see the apple clearly?The focal length of the diverging corrective lenses that can help her to see the apple clearly is determined as follows using the lens formula:
1/f = 1/v + 1/uwhere;
f is focal length of the lensv is the image distanceu is the object distancethe focal length of diverging lenses is always negative.
Hence in the formula above;
v = 2.5 cm or 0.025 m
u = 7 m
1/-f = 1/0.025 + 1/7
1/-f = 40 + 0.143
1/-f = 40.143
f = -0.025 m
The power of a lens, D = 1/f
Hence, the power of the lens = -40.1 diopters
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the block of mass m in the following figure slides on a frictionless surface
For the right block to balance the forces and remain steady, it needs to weigh 7.9 kg.
The force is an external agent which is applied to the body or an object to move it or displace it from one position to another position.
When there is no net force acting on the system, the two blocks stay in place. In this instance, the strain in the rope holding the two blocks together balances the pull of gravity on them. The sine of the angles, along with the masses of the blocks, can be used to calculate the tension in the rope.
\(T= (m_1 \times g) \times sin(\theta_1) + (m_2\times g) \times sin(\theta_2)\)
Substituting the known values:
\(T = (10 \times 9.8 )\times sin(23^o) + (m_2\times 9.8 )\times sin(40^o)\)
Solving for m₂:
\(m_2= \dfrac{(T- (10 \times 9.8 )\times sin(23^o)} { (9.8\times sin(40^o))}\)
The mass of the right block must be 7.9 kg for the two blocks to remain stationary.
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The question is -
Two blocks in the Figure below are at rest on frictionless surfaces What must be the mass of the right block so that the two blocks remain stationary? 4.9kg 6.1kg 7.9kg 9.8kg
consider some metal which has a work function of 2.16 ev for its surface. (a) find the cutoff wavelength for the photoelectric effect in this metal.
According to the given statement a work function of 2.16 ev for its surface then the cutoff wavelength for the photoelectric effect in this metal is 9.14 x 10^-7 meters.
We need to understand the function of the work function and how it relates to the photoelectric effect. The work function is the minimum energy required to remove an electron from the surface of a metal. The photoelectric effect occurs when photons of light with sufficient energy strike a metal surface and eject electrons, creating a current.
The cutoff wavelength is the shortest wavelength of light that can cause the photoelectric effect in a particular metal. To find the cutoff wavelength, we can use the formula:
λ cutoff = hc/Φ
Where λ cutoff is the cutoff wavelength, h is Planck's constant, c is the speed of light, and Φ is the work function of the metal.
Substituting the values given in the question, we get:
λ cutoff = (6.626 x 10^-34 J s x 3 x 10^8 m/s) / (2.16 eV x 1.6 x 10^-19 J/eV)
Simplifying, we get:
λ cutoff = 9.14 x 10^-7 m
Therefore, the cutoff wavelength for the photoelectric effect in this metal is 9.14 x 10^-7 meters.
This is a more than 100-word answer that explains the function of work function and how it relates to the photoelectric effect, and provides the formula and calculation to find the cutoff wavelength for the given metal.
To find the cutoff wavelength for the photoelectric effect in the metal with a work function of 2.16 eV, we need to use the following equation:
work function = (hc) / λ
where:
- work function is 2.16 eV (1 eV = 1.6 x 10^(-19) J)
- h (Planck's constant) = 6.63 x 10^(-34) J·s
- c (speed of light) = 3 x 10^8 m/s
- λ (cutoff wavelength)
First, convert the work function to joules:
work function (J) = 2.16 eV * 1.6 x 10^(-19) J/eV = 3.456 x 10^(-19) J
Next, rearrange the equation to solve for λ:
λ = (hc) / work function
Finally, plug in the values and solve:
λ = (6.63 x 10^(-34) J·s * 3 x 10^8 m/s) / 3.456 x 10^(-19) J
λ = 5.725 x 10^(-7) m
The cutoff wavelength for the photoelectric effect in this metal is approximately 5.725 x 10^(-7) m or 572.5 nm.
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Refer to Fig. 10.31(c). In situations in which R_sig is large, the high-frequency response of the source follower is determined by the low-pass circuit formed by R_sig and the input capacitance. An estimate of C_in can be obtained by using the Miller approximation to replace C_gs with an input capacitance C_eq = C_gs (1-k) where K is the gain from gate to source. Using the low-frequency value of K = g_m R^1_L (1 + g_m R^1_L) Find C_eq and hence C_in and an estimate of f_H.A directly coupled source follower without the bias detail; high-frequency equivalent circuit of the source follower; a simplified version of the equivalent circuit.
\(C_{eq}=\frac{C_{gs} }{1+g_{m}R^{1}_L }\)
\(C_{in}=\frac{C_{gs}(2+g_mR^1_L) }{1+g_mR^1_L}\)
\(f_{H}= \frac{1}{2\pi R_LC_{in} }\)
Step-by-step explanation:Based on Fig. 10.31(c), we can see that the high-frequency response of the source follower is affected by \(R_{sig}\) when it is large. In this case, the low-pass circuit formed by \(R_{sig}\) and the input capacitance determines the response.
To estimate \(C_{in}\), we can use the Miller approximation to replace \(C_{gs}\) with an input capacitance \(C_{eq} =C_{gs}(1-K)\) , where K is the gain from the gate to the source. The low-frequency value of K is given by \(K=g_mR^1_L(1+g_mR^1_L)\)
Using this information, we can find \(C_{eq}\) as follows:
\(C_{eq} =C_{gs}(1-K)\)
\(=\frac{C_gs (1 - g_m R^1_L )} {(1 + g_m R^1_L)}\)
\(=\frac{C_{gs}} {(1 + g_m R^1_L)}\)
From the above equation, we can estimate \(C_{in}\) by replacing \(C_{gs}\) with \(C_{eq}\). Therefore, we have:
\(C_{in} = C_{eq} + C_{gs}\)
\(= \frac{C_{gs}} {(1 + g_m R^1_L)} + C_{gs}\)
\(= \frac{C_{gs} (1 + g_m R^1_L + 1)}{(1 + g_m R^1_L)}\)
\(= \frac{C_{gs} (2 + g_m R^1_L)}{(1 + g_m R^1_L)}\)
To find an estimate of \(f_{H}\), we can use the simplified high-frequency equivalent circuit of the source follower, which consists of \(C_{in}\) in parallel with \(R_{L}\). We can then find the cutoff frequency \(f_{H}\) using the following equation:
\(f_H = \frac{1}{(2\pi R_L C_{in})}\)
Lastly, a simplified version of the equivalent circuit can be obtained by neglecting the bias detail. The simplified circuit will only include the signal path components, such as the input capacitance, the transconductance amplifier, and the output resistance.
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a positive and a negative charge are initially 4 cm apart. When they are moved closer together so that they are now only 1 cm apart, the force between them is
(a) 4 times smaller than before
(b) 4 times larger than before
(c) 8 times larger than before
(d) 16 times lager than before
Answer:
\( \boxed{\tt(b) \: 4 \: times \: larger \: than \: before}\)
What does Newton’s law of universal gravitation state?
Answer
Newton's law of gravitation, statement that any particle of matter in the universe attracts any other with the force varying directly the product of the masses and inversely as the square of the distance between them. ...
a fireman has mass m; he hears the fire alarm and slides down the pole with acceleration a (which is less than g in magnitude). (a) write an equation giving the vertical force he must apply to the pole. (b) if his mass is 90.0 kg and he accelerates at what is the magnitude of his applied force?
The equation F ≤ mg gives the vertical force he must apply to the pole. The magnitude of the force is 90.0 times the acceleration if the mass of the firemen is 90kg.
The given data is:
Mass of firemen = m
Acceleration = a
a.
There are two forces acting on the fireman. They are his weight (mg) acting downwards, and the force of friction (F) between the pole and the fireman acting upwards.
The fireman is sliding down the pole, and the force of friction must be less than the force of gravity acting toward the fireman or equal. Therefore, the equation giving the vertical force he must apply to the pole is,
F ≤ mg.
b.
If the fireman's mass is 90.0 kg and he accelerates at a rate of a.
The magnitude of his applied force can be calculated by:
a = F/m
To calculate the Forec, we can rearrange the equation as:
F = ma
F = (90.0 kg) x (a)
Therefore we can conclude that the magnitude of the force is 90.0 times the acceleration a.
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Please select the word from the list that best fits the definition
Choose the correct process for the description given:
oxygen is given off as a by-product
1) Cellular Respiration
2) Photosynthesis
Answer:
cellular respiration , note how it says oxygen
Which combustion product is a deadly gas that you cannot see or smell? O sulfur dioxide O carbon monoxide O carbon dioxide O sulfur monoxide
Answer:
carbon monoxide
Explanation:
A Nichrome wire (p=110x10-8 ) has a radius of 0.65mm. What length of wire is needed to obtain a resistance of 2?
A length of approximately 1.05 meters of Nichrome wire is needed to obtain a resistance of 2 ohms.
To calculate the length of Nichrome wire needed to obtain a resistance of 2 ohms, we can use the formula for the resistance of a wire:
R = (ρ × L) / A
Where:
R is the resistance,
ρ is the resistivity of the wire material,
L is the length of the wire, and
A is the cross-sectional area of the wire.
First, we need to calculate the cross-sectional area of the wire using the given radius:
Radius (r) = 0.65 mm = 0.65 × \(10^{-3}\) m
Cross-sectional area (A) = π × \(r^{2}\)
Substituting the values:
A = π × \([0.65(10^{-3}m)]^{2}\)
Next, rearrange the resistance formula to solve for the length (L):
L = (R × A) / ρ
Substituting the given resistance (R = 2 ohms), resistivity of Nichrome (ρ = 110 × \(10^{-8}\) ohm-m), and the calculated cross-sectional area (A), we can find the length (L):
L = (2 ohms × π × \([0.65(10^{-3}m)]^{2}\) / \([110(10^{-8} )]\) ohm-m)
Calculating the value:
L ≈ 1.05 meters
Therefore, a length of approximately 1.05 meters of Nichrome wire is needed to obtain a resistance of 2 ohms.
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A 0.25 kg book falls off a 2 m shelf on to a 0.5 m chair. What was the change in GPE?
The equation of GPE is mgH, where m is mass, g is gravitational acceleration, and H is the height.
If we're solving for the change in GPE, then:
∆\(U_{g}\) = mg∆H
Input our given values for m and g:
∆\(U_{g}\) = 0.25 * 9.80 * ∆H
The book falls from 2 meters high to 0.5 meters high, so:
∆\(U_{g}\) = 0.25 * 9.80 * (2.0 - 0.5)
∆\(U_{g}\) = 0.25 * 9.80 * 1.5
∆\(U_{g}\) = 3.675 (J)
Adjust for significant figures:
∆\(U_{g}\) = 3.7 (J)
The change in gravitational potential energy was 3.7 (J)
If you have any questions on anything I did to get to the answer, just ask!
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Planet X has a mass of M and a radius of R. Planet Y has a mass of 3M and a radius of 3R. Identical satellites orbit both planets at a distance R above their surfaces, as shown above. The planets are separated by such a large distance that the gravitational forces between them are negligible.
How does the magnitude of the gravitational force FY exerted by Planet Y on its satellite compare to the gravitational force FX exerted by Planet X on its satellite?
Answer:
\({FY} = \dfrac{3}{4} \times FX\)
Explanation:
The parameters given for the planets are;
The mass of planet X = M and the radius of planet X = R
The mass of planet Y = 3·M and the radius of planet Y = 3·R
The magnitude of the gravitational force of the planets on their satellites are given by the following equation;
\(F=G \times \dfrac{M_{1} \cdot m_{2}}{R^{2}}\)
Where;
M₁ = The mass of the first object = The mass of the planet
m₂ = The mass of the second object = The mass of the satellite
R = The distance between the centers of the two planets = The distance between the center of the planet and the satellite
G = The universal gravitational constant
The force between planet X and the satellite in its orbit = \(FX=G \times \dfrac{M \times m}{(2 \cdot R)^{2}} = G \times \dfrac{M \times m}{4 \cdot R^{2}}\)
The force between planet Y and the satellite in its orbit = \(FY=G \times \dfrac{3\cdot M \times m}{(4 \cdot R)^{2}} = G \times \dfrac{3\cdot M \times m}{16 \cdot R^{2}} = G \times \dfrac{ 3\cdot M \cdot m}{16 \cdot R^{2}}\)
Therefore;
\(\dfrac{FY}{FX} = \dfrac{G \times \dfrac{ 3\cdot M \cdot m}{16 \cdot R^{2}}}{G \times \dfrac{M \times m}{4 \cdot R^{2}}} = \dfrac{3}{16} \times \dfrac{4}{1} = \dfrac{3}{4}\)
\({FY} = \dfrac{3}{4} \times FX\)