The time it takes for the mass to reach the new equilibrium position is approximately 0.15 seconds.
To calculate the time it takes for the mass to reach the new equilibrium position, you will need to know the spring constant of the spring. The spring constant, denoted by the letter k, is a measure of the spring's stiffness, and it is related to the force required to stretch the spring by a certain distance. If the spring constant is not given, it can not be calculated.
Once you have the spring constant, you can use the equation:
T = 2π √(m/k) where,
T is the period of oscillation (the time it takes for the mass to complete one full cycle of motion) m is the mass of the object attached to the spring k is the spring constant.The spring constant (k) can be found by using the equation:
F = kx where,
F is the force applied to the spring x is the distance the spring is stretched from its equilibrium position, and k is the spring constant.In this case, the force is equal to the weight of the mass, which is m*g, where m is the mass and g is the acceleration due to gravity.
mg = kx
or, k = (m*g)/x
or, k = (1.65 kg * 9.8 m/s^2) / 0.215 m = 74.65 kg/s^2
Now that we know the spring constant, we can use the equation:
T = 2π √(m/k)
To find the time it takes for the mass to reach the new equilibrium position, where T is the period of oscillation, m is the mass of the object attached to the spring, and k is the spring constant.
T = 2π √(1.65 kg / 74.65 kg/s^2) = 0.15 sec
So the time it takes for the mass to reach the new equilibrium position is approximately 0.15 seconds.
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If a building is 44 m tall, how long would it take to fall off it?
Answer:
2.995 seconds
Explanation:
We can use this kinematics equation to evaluate time.
[tex]y=v_0t-\frac{1}{2}gt^2[/tex]
Lets solve for [tex]t.[/tex]
Combine [tex]\frac{1}{2}[/tex] and [tex]gt^2[/tex].
[tex]y=v_0t-\frac{gt^2}{2}[/tex]
Subtract [tex]y[/tex] from both sides.
[tex]0=v_0t-\frac{gt^2}{2}-y[/tex]
[tex]0=-\frac{gt^2}{2} -v_0t-y[/tex]
Multiply both sides of the equation by -1.
[tex]0=\frac{gt^2}{2} -v_0t+y[/tex]
Multiply both sides of the equation by 2.
[tex]0=gt^2 -2v_0t+2y[/tex]
Use the quadratic formula to solve for t.
[tex]\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex]
[tex]\frac{-b-\sqrt{b^2-4ac} }{2a}[/tex]
[tex]a=-g\\b=2v_0\\c=-2y[/tex]
Solution 1 Steps
[tex]t=\frac{-2v_0+\sqrt{(2v_0)^{2} -4*-g*-2y} }{2*-g}[/tex]
[tex]t=\frac{-2v_0+\sqrt{4v_0^2 -4*-g*-2y} }{2*-g}[/tex]
[tex]t=\frac{-2v_0+\sqrt{4v_0^2 -8gy} }{-2g}[/tex]
Solution 2 Steps
[tex]t=\frac{-2v_0-\sqrt{(2v_0)^{2} -4*-g*-2y} }{2*-g}[/tex]
[tex]t=\frac{-2v_0-\sqrt{4v_0^2 -4*-g*-2y} }{2*-g}[/tex]
[tex]t=\frac{-2v_0-\sqrt{4v_0^2 -8gy} }{-2g}[/tex]
One of these solution will most likely lead to a negative answer. The solution that gives a positive answer is correct. Lets enter our values into both equations to see which one is correct.
We can assume the initial velocity is 0.
We are given
[tex]v_0=0\\g=-9.81\\y=44[/tex]
Lets try the first solution.
[tex]t=\frac{-2*0+\sqrt{(4*0^2) -(8*-9.81*44)} }{-2*-9.81}[/tex]
[tex]t=\frac{0+\sqrt{0 -(8*-9.81*44)} }{-2*-9.81}[/tex]
[tex]t=\frac{0+\sqrt{0 --3453.12} }{-2*-9.81}[/tex]
[tex]t=\frac{\sqrt{3453.12} }{19.62}[/tex]
[tex]t=2.995[/tex]
Our first solution was positive so there is no need to check the second solution.
Two expressions were used for the drag force experienced by a moving object in a liquid. One depended upon the speed, while the other was proportional to the square of the speed. In which types of motion would each of these expressions be more applicable than the other one
The expression for drag force that is proportional to the speed of the object is known as linear drag, while the expression that is proportional to the square of the speed is known as quadratic drag.
What is linear drag?Linear drag is generally more applicable to objects moving at low speeds, such as a swimmer moving through water. In this case, the drag force is directly proportional to the speed of the object, and the drag coefficient is constant.Quadratic drag is generally more applicable to objects moving at high speeds, such as a bullet moving through air. In this case, the drag force is proportional to the square of the speed of the object, and the drag coefficient increases as the speed of the object increases. This type of drag is caused by the formation of a turbulent boundary layer around the object, which results in a significant increase in drag force at high speeds.So linear drag is more applicable to low speed and quadratic drag is more applicable to high speed.
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A block of substance has a width of 4.9 cm, a length of 5.1 cm, and height of 1.9 cm . Its mass is 0.54 kg. Calculate the density of the substance.
The 4.7 g/cm3 is the density of the substance.
What is density ?
How tightly something is packed can be used to gauge a material's density. Formally, it is defined as the mass per unit of volume. Formula for Density or Density Symbol: D D = m/V, where m is mass and V is volume, stands for density.
What is mass ?
The most basic characteristic of matter, it is one of the fundamental quantities in physics. As a way to gauge how much matter is there in a body, we might use the term mass. Kilograms are the SI unit of mass (kg).
density = mass of sample/ volume of sample
mass = 1.5 kg = 1500 g
volume = W*L*H
Vol = 3.2*17.1*5.8 cm3 = 317.376 cm3
Now,
D = mass/V = 1500/317.376
D = 4.726255 g/cm3
=4.7 g/cm3
Therefore, 4.7 g/cm3 is the density of the substance.
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light waves with a frequency of 7.26 x 10^14 HZ lies in the violet region of the visible spectrum. what is the wavelength of this frequency of light?
Answer:
4.13×10⁻⁷ m
Explanation:
Applying
v = λf................... Equation 1
Wherfe v = speed of light, λ = wavelength of light, f = frequency of light.
make λ the subject of the equation
λ = v/f....................... Equation 2
Note: Light is an electromagnetic wave, and all electromagnetic wave moves with thesame speed which is 3×10⁸ m/s.
From the question,
Given: f = 7.26×10¹⁴ Hz
Constant: v = 3×10⁸ m/s
Substitute these values into equation 2
λ = (3×10⁸)/(7.26×10¹⁴)
λ = 4.13×10⁻⁷ m
How does a simmering pot of spaghetti sauce illustrate convection currents
Answer:
1: As the substance’s thermal energy increases, the kinetic energy of its particles increases, and vice versa.
2: Its molecules move around more quickly, so there is more space between them, making it less dense than the air above it.
3: Warmer sauce at the bottom of the pot is less dense, so it rises, forcing cooler sauce down, where it is warmed.
4: Hot soup warms the bowl where it sits.
5: transfer of thermal energy through infrared waves
Explanation:
This is correct for the Thermal Energy Transfer Quick Check
A simmering pot of spaghetti sauce provides an excellent illustration of convection currents because the process of heating the sauce causes hot molecules to rise and cool molecules to sink. This creates a circular motion known as a convection current.
When the pot is placed on a hot stove, the heat from the burner is transferred to the bottom of the pot, which in turn heats the sauce. As the sauce heats up, the molecules nearest to the heat source become hotter and lighter. These hot, lighter molecules rise to the top of the pot, creating a convection current. As they reach the surface, they cool down, become heavier, and then sink back down to the bottom of the pot.
This process of hot molecules rising and cool molecules sinking creates a circular motion that evenly distributes the heat throughout the sauce, ensuring that it cooks evenly. The convection currents in the pot are also responsible for the bubbles that rise to the surface of the sauce, releasing trapped steam and preventing the pot from boiling over.
In conclusion, a simmering pot of spaghetti sauce illustrates convection currents because it shows how hot molecules rise and cool molecules sink, creating a circular motion that evenly distributes heat and ensures that the sauce cooks evenly.
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2.) What would the force of friction be between the surface and wood block if there was no
gravity?
Answer:
The coefficient of friction between the surface of the block is 1/4
You are on roller blades on top of a small hill. Your potential energy is equal to 1000 joules. The last time you checked your mass was 60.0 kilograms. What is the height of the hill
The height of the hill can be calculated using the formula PE = mgh, where m is the mass, g is the acceleration due to gravity (9.8 m/s2), and h is the height of the hill. So, solving for h, we get h = PE/mg = 1000 J/ (60.0 kg*9.8 m/s2) = 10.2 m.
Therefore, the height of the hill is 10.2 m. The potential energy of an object is the energy it possesses due to its position or state. As the object moves, its potential energy can be converted into kinetic energy, or the energy it has due to its motion. In this case, the rollerblader is on top of the hill, so it has potential energy due to the height of the hill.
The formula for potential energy is PE = mgh, which means that the potential energy is equal to the mass multiplied by the acceleration due to gravity multiplied by the height. In this case, the mass is known to be 60.0 kg, and the potential energy is known to be 1000 J. By using the formula and substituting in the known values, the height of the hill can be calculated.
The height of the hill is determined to be 10.2 m, which is relatively small. This means that the hill is not too steep, and the rollerblader would not have to use a lot of energy to go down it.
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1. An unknown sample has a mass of 49. 2 g. The original volume of water in a graduated
cylinder is 47. 0 mL. When the unknown sample is placed into the graduated cylinder, the
water level rises to 52. 5 mL. What is the identity of this substance?
According to given data the volume of the unknown sample is 52. 5 mL - 47. 0 mL = 5.5 ml.
Why is a graded cylinder referred to as such?One typical style of lab glassware is graduated cylinders. They are a long, cylindrical vase with graduations marking the volume of liquid they can hold. Spouts are frequently included to make pouring easier.
Why is graduation significant?Your graduation will go down in history as a significant event; it will stand for development, change, and embarking on new experiences. Celebrate your accomplishments thus far and be grateful for the memories this phase of your schooling has provided you.
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Which causes the biggest problem in detecting infrared photons from an astronomical object?
a. smog
b. carbon dioxide
c. water vapor
d. light pollution
The correct option is C ; Water vapor , Water vapour is water that is gaseous rather than liquid. It can be generated by either evaporation or sublimation.
Water vapour, unlike clouds, fog, or mist, which are just suspended particles of liquid water in the air, cannot be seen since it is in gaseous form.
Water vapor has the same chemical formula as regular water - H2O - but the water molecules in vapor interact with each other less and are not as organized as they are in water and ice. Pressure, temperature, and relative humidity all influence whether water is liquid or gas.
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What is the major difference between static and dynamic stretching ?
Explanation:
This intense stretching method uses bouncing movements to push your body beyond its normal range of motion. Whereas static stretches are performed slowly and gradually, the ballistic method stretches muscles much farther and faster. You can do many of the same stretches as ballistic or static stretches.
9. Calculate the kinetic or potential energy in joules for each of the following situations: a. A 2.5 kg book is held 2.0 m above the ground. b Anabolieman
Explanation:
[tex]kinetic \: energy = \frac{1}{2} m {v}^{2} \\ but \: {v}^{2} = {u}^{2} + 2gh \\ {v}^{2} = 0 + (2 \times 10 \times 2) \\ v = 6.32 \: m {s}^{ - 1} \\ k.e = \frac{1}{2} \times 2.5 \times 6.32 {}^{2} \\ = 50 \: joules[/tex]
[tex]potential \: energy = mgh \\ = 2.5 \times 2 \times 10 \\ = 50 \: joules[/tex]
A wheel rotates at 2 rad/s. What is its period and frequency?
(1) The frequency of the oscillation is 0.32 Hz.
(2) The period of the oscillation is 3.13 seconds.
What is the period of the wheel's oscillation?
The period of the wheel's oscillation is the time taken for the wheel to make one complete oscillation.
The period of an oscillatory motion is the reciprocal of the frequency of the oscillation.
The frequency of the oscillation is the number of cycles completed by the oscillatory object in a given second.
The frequency of the wheel undergoing oscillatory motion is calculated by using the following formula.
f = ω / 2π
where;
ω is the angular speed of the wheelf is the frequencyf = ( 2 rad/s ) / 2π
f = 0.32 Hz
The period of the oscillation is calculated as follows;
T = 1 / f
T = 1 / 0.32 s
T = 3.13 seconds
Thus, the period of oscillation and frequency of the oscillation are inversely proportional.
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When a satellite is a distance d from the center of Earth, the magnitude of the gravitational force that the satellite exerts on Earth is F. What is the magnitude of the gravitational force that the satellite exerts on Earth when the satellite's distance from the center of Earth is 3d?
plsss help
According to Newton's law of gravitation, the new gravitational force will be F/9
Newton's Law of GravitationIt states that, the force of attraction between two masses is directly proportional to the product of the masses and inversely proportional to the square of the distance between them.
When a satellite is a distance d from the center of Earth, the magnitude of the gravitational force that the satellite exerts on Earth is F. That is,
F = GMm/d²
Where
M = mass of the earthm = mass of the satelliteG = universal gravitational constantThe magnitude of the gravitational force that the satellite exerts on Earth when the satellite's distance from the center of Earth is 3d can be expresses as follow
f = GMm/(3d)²
f = GMm/9d²
f = GMm/d² × 1/9
Since GMm/d² = F
f = F × 1/9
f = F/9
Therefore, the magnitude of the gravitational force that the satellite exerts on Earth when the satellite's distance from the center of Earth is 3d is F/9 Newton
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A certain satellite orbiting Earth has a speed of about 17,000 miles/hour. What is its approximate speed expressed to the correct number of significant figures in kilometers/second
The speed of the satellite in terms of kilometers per second is 455.89 km/sec
The speed of the satellite = 17,000 miles/hour
The speed of the satellite can be converted into kilometers/second by converting the miles into kilometers and then the hour into seconds
1 miles = 1.609 km
Thus, the speed of the satellite,
= 17,000 x 1.609 km/hour
= 27,353 km/hr
Then, the speed of the satellite in one second is
1 hour = 60 seconds
Thus, the speed of the satellite,
= 27,353 x 1/60 km/sec
= 455.89 km/sec
Thus, the speed of the satellite is 455.89 km/sec
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Why is i0 10 12 W m2 used as a reference intensity for intensity level?
Since I0 is the lowest sound intensity that a person with normal hearing can detect, it is chosen as the reference point. Given that log10 1 = 0, the decibel level of a sound with an intensity of 10–12 W/m2 is = 0 dB. In other words, the human hearing threshold is zero decibels.
The reference value I0 is 10–12 W/m2, which corresponds to the threshold of hearing intensity at 1000 Hz. The Sound Intensity Level, or SIL for short, is the intensity decibel scale. The related sign, like in our text, is LI.
Much more frequently than sound intensities in watts per square meter, sound intensity levels are expressed in decibels (dB). Both the scientific literature and the public media use decibels as their preferred measurement unit. The rationale behind this decision of units has to do with how we hear. There is a reference intensity, I0 = 1012 W/m2. The lowest or threshold intensity of sound that a person with normal hearing can perceive at a frequency of 1000 Hz is specifically known as I0. The degree of sound intensity is not the same as the intensity. is a unitless quantity that informs you of the sound level in relation to a predefined standard (1012 W/m2, in this case), as it is defined in terms of a ratio.
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A 1. 25 in. By 3 in. Rectangular steel bar is used as a diagonal tension member in a bridge truss. The diagonal member is 20 ft long, and its modulus of elasticity is 30,000,000 psi. If the strain in the diagonal member is measured as 0. 001200 in. /in. , determine:
The length of the diagonal member is 20 ft, and if its modulus of elasticity is 30,000,000 psi. If the strain in the diagonal member is measured as 0. 001200 in, the elongation of the member is 29 inches.
What is a truss?A truss is constructed of a number of components, such as beams, connected at nodes to create a rigid framework. According to engineering definition, a truss is a structure that "consists of merely two-force members, where the members are placed so that the assembly as a whole behaves as a single entity."
A truss is a piece of furniture comprised of components arranged into linked triangles that function as a single unit. Trusses are most typically used in towers, roofs, and bridges. If a truss' members essentially lie on a single plane, it is referred to as a plane truss.
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Suppose a cart is being moved by a force. If suddenly a load is dumped into the cart so that the cart's mass is doubled, what happens to the cart's acceleration
According to the given statement If suddenly a load is dumped into the cart so that the cart's mass is doubled The acceleration slows.
Give an explanation of acceleration.which speaks of the rate of change in time of the speed and direction of motion. Something is said to be accelerating when it starts to move faster or slower. Even if the speed slows down, motion on a circle accelerates because the direction is constantly changing.
Does accelerating mean going faster?Any process in which the velocity changes is referred to as acceleration. There are only two ways to speed up because velocity consists of both a speed and a direction.
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How much weight is generated by an 80 kg person on planet earth? On the moon?
Which of the following statements regarding heat is accurate? NEED ASAP
Question 10 of 10
A 200 N force is applied to an object, which then accelerates at 2 m/s2 What
is the mass of the object?
A. 100 kg
B. 400 kg
C. 25 kg
O D. 50 kg
Answer:
a
Explanation:
f=ma
200=2*m
divide both sides by 2
m=100
If the Barbie had a mass of 0.23kg and the Barbie was dropped 11ft 11inches (assuming there was no rubber bands) how fast would the Barbie be moving at the bottom of the path?
The Barbie would be moving with speed 27.69 ft/s at the bottom of the path.
What is speed?Speed is distance travelled by the object per unit time. Due to having no direction and only having magnitude, speed is a scalar quantity With SI unit meter/second.
Mass of the Barbie = 0.23 kg.
Initial height of the Barbie: h= 11 ft 11 inches = ( 11 + 11/12) feet = 11.92 feet.
Acceleration due to gravity: g = 32.17 ft/s²
Hence, the speed of the Barbie at the bottom of the path = √(2gh)
= √( 2 × 32.17 ×11.92) ft/s
= 27.69 ft/s.
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helppp pls you have to label a-d
Answer:
A
C
D
B
Explanation.
At point A The body is at rest so k.E is zero but the height is maximum so that p.E is max.
From the viewpoint of an alien astronomer, how does Jupiter affect observations of our Sun?
a) It causes the Sun to move in a small ellipse with an orbital period of about 12 years.
b) It makes the Sun periodically get somewhat brighter.
c) It makes the Sun appear dimmer when viewed with infrared light.
d) It causes the Sun to move in a small ellipse in the sky, with the same ellipse repeated every night.
Jupiter affect observations of the Sun, from the viewpoint of an alien astronomer, by causing the Sun to move in a small ellipse with an orbital period of about twelve years. The correct option is option a.
Being the fifth closer planet to our Sun, Jupiter is the biggest planet in our Solar System. Jupiter is one of the gas giants in the Solar System.
From the Sun, Jupiter's average distance is about 480 million miles, and it takes nearly twelve years for Jupiter to make one revolution. Jupiter has a ring, albeit flat and small, like the rest of the gas giants. Jupiter's rotation is the fastest of all planets in the Solar System, rotating once on its axis every ten hours.
From the viewpoint of an alien astronomer outside our Solar System, the Sun will look as if it orbits Jupiter and takes 12 years to complete a revolution. Planets in general have orbits that are elliptical.
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In the definition of weight, W = mg, the mass m refers to an inertial mass.
True or false
Answer:
True
Explanation:
In the definition of weight, W = mg, the mass m refers to an inertial mass.
The aorta is a major artery, rising upward from the left ventricle of the heart and curving down to carry blood to the abdomen and lower half of the body. The curved artery can be approximated as a semicircular arch whose diameter is 4.1 cm. If blood flows through the aortic arch at a speed of 0.30 m/s, what is the magnitude (in m/s2) of the blood's centripetal acceleration
The centripetal acceleration of the aorta in which the blood travels with the speed of 0.30 m/s is 2.2 m/s²
The diameter of the aorta = 4.1 cm
= 4.1 x 10⁻² m
The speed of the blood through the aorta = 0.3 m/s
The centripetal acceleration of the blood passing through the aorta can be found using the formula,
a = v²/r
where a is the centripetal acceleration
v is the speed of the blood passing through the aorta
r is the diameter of the aorta
Let us substitute the known values in the above equation, we get
a = 0.30² / (4.1 x 10⁻²)
= 0.09 / (4.1 x 10⁻²)
= 0.022 x 10²
= 2.2 m/s²
Therefore, the centripetal acceleration of the aorta is 2.2 m/s²
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The piton in fig 2. 1. 15 i pulled out of the cylinder from piton x to piton y without changing the temperature of the air encloed if the original preure in the cylinder wa 1. 0 multiply by 10 calculate the air preure when the piton i at poition y
The pressure at position y to be 10.0, which is the air pressure when the piston is at position y.
If the original pressure in the cylinder was 1.0, and the piston is pulled out from position x to position y without changing the temperature of the enclosed air, the air pressure at position y will be increased. This is due to the change in volume of the cylinder as the piston is pulled out. As the volume increases, the number of air molecules inside the cylinder also increases, which causes an increase in the air pressure.
To calculate the air pressure when the piston is at position y, we can use the gas law known as Boyles' Law, which states that the pressure and volume of a gas are inversely proportional. Therefore, if the volume increases, the pressure will decrease, and if the volume decreases, the pressure will increase.
P₁V₁=P₂V₂Where P₁ is the initial pressure, V₁ is the initial volume, P₂ is the final pressure, and V₂ is the final volume.
By substituting the given values, we have:
1.0V₁ = P₂(V₁+V)Where V is the change in volume due to the movement of the piston.
Solving for P₂:
P₂= 1.0*V₁/(V₁+V)P₂= 1.0*1.0/(1.0+V)As we know, the original pressure is 1.0, and if we multiply it by 10, we will get the final pressure at position y to be 10.0, which is the air pressure when the piston is at position y.
This question is not written in a proper manner. The corrections are:
The piston in fig. 2. 1.15 is pulled out of the cylinder from piston x to piston y without changing the temperature of the air enclosed. If the original pressure in the cylinder was 1.0, multiply by 10 to calculate the air pressure when the piston is at position y.Learn more about piston–cylinder here: brainly.com/question/24884868
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Re word this paragraph; so Its 'put in my own words' try to mix up the places of each sentences too please!
-
The sun creates three different types of electromagnetic radiation, which is considered harmful to humans. The light created includes X-rays, gamma rays, and ultraviolet light. These rays are harmful because of their high energy values, which are caused by their large frequencies. The gases of Earth's atmosphere absorb the high energy radiation, causing their molecules to move faster, but none of the light radiation reaches Earth's surface. Luckily for us, the high frequency of gamma rays and X-rays, as well as most ultraviolet light, cannot penetrate Earth's atmosphere and does not reach Earth's surface. If those harmful rays did reach Earth's surface it would make the planet plain to earth's
-
Answer:
here you go -
Explanation:
try using the paraphrasing tool website!
The sun makes three unique sorts of electromagnetic radiation, which is considered hurtful to people. The light made incorporates X-beams, gamma beams, and bright light. These beams are unsafe as a result of their high energy esteems, which are brought about by their enormous frequencies. The gases of Earth's air assimilate the high energy radiation, making their atoms move quicker, yet none of the light radiation arrives at Earth's surface. Fortunately for us, the high recurrence of gamma beams and X-beams, also as most bright light, can't enter Earth's environment and doesn't arrive at Earth's surface. In the event that those hurtful beams arrived at Earth's surface it would make the planet plain to earth's
Help! again lol
Answer:
The weather is just the state of the atmosphere at any time, including things such as temperature, precipitation, air pressure and cloud cover.
Explanation:
Daily changes in the weather are due to winds and storms. Seasonal changes are due to the Earth revolving around the sun.
atmosphere:The atmosphere covers the Earth. It is a thin layer of mixed gases which make up the air we breathe. This thin layer also helps the Earth from becoming too hot or too cold
Ocean:Oceans cover about 70 percent of Earth's surface. Their large size and thermal properties allow them to store a lot of heat.
ice: Ice is the world's largest supply of freshwater. It covers the remaining 3 percent of Earth's surface including most of Antarctica and Greenland. Ice plays an important role in regulating climate, because it is highly reflective.
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A 50.0-kg child stands at the rim of a merry-go-round of radius 2.70 m, rotating with an angular speed of 3.95 rad/s. What minimum coefficient of static friction is required
A 50.0-kg child stands at the rim of a merry-go-round of radius 2.70 m, rotating with an angular speed of 3.95 rad/s. Minimum coefficient of static friction is required 13.56.
To find the minimum coefficient of static friction required, we need to calculate the centrifugal force acting on the child and compare it to the force of friction.
The centrifugal force acting on the child is given by:
= Fc
= m * r * w^2
where
= m
= 50.0 kg (mass of child)
= r
= 2.70 m (radius of the merry-go-round)
= w
= 3.95 rad/s (angular velocity)
So, Fc = 50.0 kg * 2.70 m * (3.95 rad/s)^2
= 6629.775 N
The force of friction acting on the child is given by:
= Ff
= friction coefficient * normal force
where
friction coefficient = minimum coefficient of static friction required (unknown)
= normal force
= m * g
The normal force is equal to the weight of the child, which is
= m * g
= 50.0 kg * 9.8 m/s^2
= 490 N
So, Ff = friction coefficient * 490 N
To find the minimum coefficient of static friction, we need to set Ff equal to Fc and solve for the friction coefficient:
friction coefficient = Ff / N
friction coefficient = 6629.775 N / 490 N
= 13.56
So the minimum coefficient of static friction required is 13.56.
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What is the radius of the event horizon of this 10-Solar-mass black hole, in units of kilometers (km)
The radius of the event horizon of a 10-Solar-mass black hole is 2950 kilometers.
How do you calculate the radius of the event horizon?The radius of the event horizon of a black hole is known as the Schwarzschild radius and it is a function of the mass of the black hole. The Schwarzschild radius is given by the formula:
r = 2GM/c^2
where
r = radius of the event horizon (in meters)
G = gravitational constant (6.674 x 10^-11 N*(m/kg)^2)
M = mass of the black hole (in kg)
c = speed of light in a vacuum (2.998 x 10^8 m/s)
For a 10-Solar-mass black hole, we can use the mass conversion factor 1 Solar mass = 1.989 x 10^30 kg.
M = 10 x 1.989 x 10^30 kg
Now, we can substitute the values into the formula
r = 2 x 6.674 x 10^-11 x M/ (2.998 x 10^8)^2
r = 2GM/c^2 = 2 x 6.674 x 10^-11 x (10 x 1.989 x 10^30) / (2.998 x 10^8)^2
r = 2.95 x 10^3 m = 2950 kilometers
So, the radius of the event horizon of a 10-Solar-mass black hole is 2950 kilometers.
To know more about the Schwarzschild radius:
brainly.com/question/12647190
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