Answer:
The answer is 48.0 NExplanation:
To find the force acting on an object given it's mass and acceleration we use the formula
Force = mass × accelerationFrom the question
mass = 0.314 kg
acceleration = 153 m/s²
We have
force = 0.314 × 153 = 48.042
We have the final answer as
48.0 NHope this helps you
When the sideways force is 100 Newtons on Skelly who has a mass of 25kg, but there is a constant 50 N drag force, then Skelly's acceleration will bem/s,
In order to determine the force on Skelly, use the following formula:
\(F=m\cdot a\)where:
m: mass = 25 kg
a: acceleration = 10m/s^2
Replace the previous values of the parameters into the formula for F:
\(F=(25kg)(10\frac{m}{s^2})=250N\)Hence, the force on Skelly is 250N
Answer:
0.33 0.17
Explanation:
What is the velocity of a dropped object after it has fallen for 12 s?
Hellow!
For this use the next formula:
Vf = Vo + gt
Initial velocity is zero, so the formula simplificate:
Vf = gt
Data:
Vf = Final velocity = ?
g = Gravity = 9.8 m/s²
t = Time = 12 s
Replacing according our data:
Vf = 9.8 m/s² * 12 s
Vf = 117.8 m/s
The final velocity will be 117.8 meters per second.
(a)Suppose during 2020due to relief in Taxation Marginal Propensity to Consume (MPC) will increase from 0.65 to 0.75then calculate Tax multiplier (KT). (b)By using the Tax multiplier value calculated in part (a), find the change in national income if Tax amount is increased from 4500billion rupees to 5100billion rupees. (c)How Subsidies and Ehsas program amount will affect the Aggregate Demand (AD)?
Answer:
abcd
Explanation:
Answer:
where is the answer pls send me answer on my what.s up number
Explanation:
what is the physics behind why electric parallel plates move from positive to negative
The physics behind the movement of electric charges between parallel plates is based on the principles of electrostatics. Electric charges are either positive or negative, and they are affected by electric fields.
Electric fields are created by a difference in electric potential, which is measured in volts. When a voltage is applied to a set of parallel plates, the charges within the plates will be affected by the electric field, and will move in response to it.
What are electric parallel plates?When a voltage is applied to a set of parallel plates, the positive charges in the plate connected to the positive voltage will be attracted to the negative voltage, while the negative charges in the plate connected to the negative voltage will be attracted to the positive voltage.
The movement of charges between the plates is also affected by the presence of any obstacles or resistances in the electric field, such as resistance in the wire. This can slow down the movement of charges and result in a decrease in the current flowing through the circuit.
In all, the movement of charges between electric parallel plates is the result of the electric field created by a difference in electric potential, and the movement of charges is called drift velocity. The movement is also affected by the presence of resistance.
Learn more about electric parallel plates from
https://brainly.com/question/28529259
#SPJ1
A breadfruit falls from a tree and hits the ground in 2 seconds. How tall is the tree and what is the velocity with which the coconut hits the ground?
Answer:
i don'tkniw
Explanation: ido not know
based on what you know about light and matter interactions, select all of the correct statements from the following list. emission spectra have dark lines. electrons will move to higher orbits when an atom absorbs enough energy. the size of an electron's orbit depends on its energy. atoms absorb energy by emitting photons. absorption spectra have bright lines. low-density hot gases produce emission spectra. hot solids emit continuous spectra.
The correct statements are: Emission spectra have dark lines, Electrons will move to higher orbits when an atom absorbs enough energy, The size of an electron's orbit depends on its energy, Low-density hot gases produce emission spectra, and Hot solids emit continuous spectra.
Why do emission spectra have dark lines?An emission spectrum is produced when atoms in a sample emit light of certain wavelengths as they return from excited states to lower energy states. These spectra show bright lines corresponding to the emitted wavelengths but also have dark lines or gaps where no light is emitted.
Why do hot solids emit continuous spectra?When a solid object is heated, it emits light at all wavelengths, resulting in a continuous spectrum. This is because the solid contains many atoms or molecules that are vibrating and moving, and their energies and motions result in a continuous range of emitted wavelengths.
To learn more about wavelength, visit here:
https://brainly.com/question/13533093
#SPJ1
If a marathon runner runs 9.5 miles in one direction, 8.89 miles in another direction, and 2.333 miles in a third direction, how much distance did the runner run?
We have that the total distance covered by the runner is
\(d_t=20.723miles\)
The total distance covered by the runner is a sum of all miles covered by the runner
Therefore
With
\(d_t\)=Total distance
\(d_t=d_1+d_2+d_3\\\\d_t=9.5+8.89+2.333\)
\(d_t=20.723miles\)
in conclusion
The total distance covered by the runner is
\(d_t=20.723miles\)
For more information on this visit
https://brainly.com/question/12319416
What is the magnetic force on a 2.0-m length of (straight) wire carrying a current of 30 A in a region where a uniform magnetic field has a magnitude of 55 mT and is directed at an angle of 20° away from the wire?
To determine the magnetic force on a straight wire carrying a current in a uniform magnetic field, we can use the formula for the magnetic force:
F = I * L * B * sin(θ)
where:
F is the magnetic force,
I is the current in the wire,
L is the length of the wire,
B is the magnitude of the magnetic field, and
θ is the angle between the wire and the magnetic field.
In this case, the values are:
I = 30 A (current in the wire)
L = 2.0 m (length of the wire)
B = 55 mT = 0.055 T (magnitude of the magnetic field)
θ = 20° (angle between the wire and the magnetic field)
Substituting the values into the formula:
F = 30 A * 2.0 m * 0.055 T * sin(20°)
Calculating sin(20°):
F = 30 A * 2.0 m * 0.055 T * 0.3420
F ≈ 1.5714 N
Therefore, the magnetic force on the 2.0-meter length of wire carrying a current of 30 A in a region with a uniform magnetic field of magnitude 55 mT and at an angle of 20° away from the wire is approximately 1.5714 N.
To know more about magnetic force:
https://brainly.com/question/10353944
#SPJ1
Two identical loudspeakers 2.00 m apart are emitting sound waves into a room where the speed of sound is 340 m/s. Abby is standing 5.00 m in front of one of the speakers, perpendicular to the line joining the speakers, and hears a maximum in the intensity of the sound.
Required:
What is the lowest possible frequency of sound for which this is possible?
Answer:
The lowest possible frequency of sound for which this is possible is 1307.69 Hz
Explanation:
From the question, Abby is standing 5.00m in front of one of the speakers, perpendicular to the line joining the speakers.
First, we will determine his distance from the second speaker using the Pythagorean theorem
l₂ = √(2.00²+5.00²)
l₂ = √4+25
l₂ = √29
l₂ = 5.39 m
Hence, the path difference is
ΔL = l₂ - l₁
ΔL = 5.39 m - 5.00 m
ΔL = 0.39 m
From the formula for destructive interference
ΔL = (n+1/2)λ
where n is any integer and λ is the wavelength
n = 1 in this case, the lowest possible frequency corresponds to the largest wavelength, which corresponds to the smallest value of n.
Then,
0.39 = (1+ 1/2)λ
0.39 = (3/2)λ
0.39 = 1.5λ
∴ λ = 0.39/1.5
λ = 0.26 m
From
v = fλ
f = v/λ
f = 340 / 0.26
f = 1307.69 Hz
Hence, the lowest possible frequency of sound for which this is possible is 1307.69 Hz.
An oral solution has a dosage of 500 mg in 5 mL. If a 0.7 g dosage is required, how many mL must be given?
Answer:
7 mL
Explanation:
Given that:
mass of an oral solution = 500 mg
solution in mL = 5mL
Thus, the ratio = 5 mL/500 mg
= 0.01 mL/mg
since 1000 mg = 1g
∴
= 0.01 mL/mg × 1000 mg/1g
= 10 mL/g
Now, suppose the amount of 0.7 g dosage is required:
∴
the needed amount of mL will be:
= 10 mL/g × 0.7 g
= 7 mL
1. What outdoor activities do you prefer? Why? 2. What outdoor activities are you interested in, but have never tried?
The outdoor activities u prefers most is swimming because I feel relaxed after that.
The outdoor activities I am more interested in but I have not tried is mountain climbing.
What is outdoor activities?Outdoor activities refers to exercises or activities that is carried out outside an enclosed areas. These include swimming, mountain climbing, running and the rest.
Therefore, The outdoor activities u prefers most is swimming because I feel relaxed after that.
The outdoor activities I am more interested in but I have not tried is mountain climbing.
Learn more about outdoor activities below.
https://brainly.com/question/19310247
#SPJ1
19. According to the U.S. Census, how many people were living without healthcare in 2017?
A. 48 million
B. 28 million
C. 20 million
D. 30 million
A space vehicle is coasting at a constant velocity of 22.3 m/s in the y direction relative to a space station. The pilot of the vehicle fires a RCS (reaction control system) thruster, which causes it to accelerate at 0.203 m/s2 in the x direction. After 56.7 s, the pilot shuts off the RCS thruster. After the RCS thruster is turned off, find (a) the magnitude and (b) the direction of the vehicle's velocity relative to the space station. Express the direction as an angle (in degrees) measured from the y direction.
Answer:
Explanation:
Initial velocity in y direction Vy = 22.3 m /s
initial acceleration in x direction ax = .203 m /s ²
time of acceleration t = 56.7 s
final velocity in x direction
v = u + a t
Vx = 0 + .203 x 56.7 = 11.51 m /s
Final velocity in y direction will remain same as initial velocity in y direction = 22.3 m /s because there is no acceleration in y direction .
Magnitude of final velocity
= √ ( Vx² + Vy²)
= √ (22.3² + 11.51² )
= √ ( 497.29 + 132.48)
= 25.1 m /s
Direction of final velocity from y direction be Ф
TanФ = Vx / Vy = 11.51 / 22.3 = .516
Ф = 27.3° .
A 1000 kg car and a 2000 kg car are lifted the same distance in a
mechanic's shop. Neglecting friction, raising the more massive car
requires
Answer:
Twice as much work
Explanation:
What is SeaWorld?
What is this
What is that
SeaWorld is a chain of theme parks and oceanariums that showcase marine life through educational exhibits, live shows, and thrilling rides. While it has faced criticism for its treatment of animals, SeaWorld has made changes to prioritize conservation and phased out its orca breeding program.
SeaWorld is a chain of theme parks and oceanariums that primarily focuses on marine life and entertainment. The company operates various parks across the United States, including SeaWorld parks in Orlando, San Diego, and San Antonio, as well as Busch Gardens parks in Tampa and Williamsburg. SeaWorld offers a combination of educational exhibits, live shows, and thrilling rides, with a special emphasis on marine animals such as dolphins, whales, sea lions, penguins, and sharks.
SeaWorld parks provide visitors with opportunities to observe and interact with marine creatures up close, while also offering educational programs that aim to raise awareness about marine conservation and preservation. The parks feature captivating shows featuring trained animals, where they perform impressive behaviors and stunts, showcasing their intelligence and natural abilities.
Over the years, SeaWorld has faced criticism from animal rights activists and environmentalists, who argue that the captivity and use of marine animals for entertainment purposes is unethical and harmful to the animals' well-being. These concerns have led to significant changes in the company's practices, including the phasing out of its orca breeding program and the introduction of more educational and conservation-focused initiatives.
To learn more about SeaWorld
https://brainly.com/question/13298282
#SPJ8
A car is traveling at 100 km/hr. How many hours will it take to travel a distance of
650 km?
Answer:6.5
Explanation: take 650 and divide it by 100
\(x = 100 + 650 \\ \sqrt22y1x \leqslant y3.y1y \geqslant y = - y..x1431} \)
Squid use jet propulsion for rapid escapes. A squid pulls water into its body and then rapidly ejects the water backward to propel itself forward. A 1.5 kg squid (not including water mass) can accelerate at 20 m/s2 by ejecting 0.15 kg of water. Part A What is the magnitude of the thrust force on the squid
Answer: see attachment
Explanation:
A rocket moves straight upward, starting from rest with an acceleration of +29.4 m/s2 . It runs out of fuel at the end of 4.00s and continues to coast upward, reaching a maximum height before falling back to earth. (a) Find the rocket’s velocity and position at the end of 4.00s. (b) Find the maximum
Answer:
a) The velocity and position of the rocket at the end of 4 seconds are 117.6 meters per second and 235.2 meters, respectively, b) The maximum height reached by the rocket is 940.296 meters, c) The rocket crashes on the ground at a velocity of -96.030 meters per second.
Explanation:
The complete statement is:
A rocket moves straight upward , starting from rest with an acceleration of 29.4 m/s2. it runs out of fuel at the end of 4.00 s and countinues to coast upward , reaching a maximum height before falling back to earth . a) find the rocket's velocity and position at the end of 4.00 s . b) Find the maximum height the rocket reaches. c) find the velocity on the instant before the rocket crashes on the ground.
a) The rocket accelerates uniformly, whose equations of motion are:
\(y = y_{o} + v_{o}\cdot t + \frac{1}{2}\cdot a \cdot t^{2}\)
\(v = v_{o} + a\cdot t\)
Where:
\(y\) - Final position, measured in meters.
\(y_{o}\) - Initial position, measured in meters.
\(v_{o}\) - Initial velocity, measured in meters per second.
\(t\) - Time, measured in second.
\(a\) - Acceleration, measured in meters per square second.
\(v\) - Final velocity, measured in meters per second.
If we know that \(y_{o} = 0\,m\), \(v_{o} = 0\,\frac{m}{s}\), \(t = 4\,s\) and \(a = 29.4\,\frac{m}{s^{2}}\), the velocity and position of the rocket are, respectively:
\(y = 0\,m+\left(0\,\frac{m}{s} \right)\cdot (4\,s)+\frac{1}{2}\cdot \left(29.4\,\frac{m}{s^{2}} \right) \cdot (4\,s)^{2}\)
\(y = 235.2\,m\)
\(v = 0\,\frac{m}{s} + \left(29.4\,\frac{m}{s^{2}}\right)\cdot (4\,s)\)
\(v = 117.6\,\frac{m}{s}\)
The velocity and position of the rocket at the end of 4 seconds are 117.6 meters per second and 235.2 meters, respectively.
b) Now, the rocket experiments a free-fall motion. The maximum height of the rocket is obtained by equalizing the equation of velocity to zero and evaluating the equation of position later. That is:
\(y = 235.2\,m+\left(117.6\,\frac{m}{s} \right)\cdot t+\frac{1}{2}\cdot \left(-9.807\,\frac{m}{s^{2}} \right) \cdot t^{2}\)
\(v = 117.6\,\frac{m}{s}+\left(-9.807\,\frac{m}{s^{2}} \right)\cdot t\)
Then,
\(0 = 117.6 -9.807\cdot t\)
\(t = 11.991\,s\)
The maximum height reached by the rocket is:
\(y = 235.2+117.6\cdot (11.991)+\frac{1}{2}\cdot (-9.807)\cdot (11.991)^{2}\)
\(y = 940.296\,m\)
The maximum height reached by the rocket is 940.296 meters.
c) The rocket experiments a free-fall motion and is accelerated by gravity until collision happens. The equations of motion below are presented:
\(0\,m = 940.296\,m+\left(0\,\frac{m}{s} \right)\cdot t+\frac{1}{2}\cdot \left(-9.807\,\frac{m}{s^{2}} \right) \cdot t^{2}\)
\(v = 0\,\frac{m}{s}+\left(-9.807\,\frac{m}{s^{2}} \right)\cdot t\)
From the equation of position we get the instant when rocket hits the ground, whose roots are found by Quadratic Formula:
\(t_{1} \approx 9.792\,s\) and \(t_{2} \approx -9.792\,s\)
Only the first root is physically reasonable.
By the second equation we calculate the final velocity:
\(v = 0-9.807\cdot (9.792)\)
\(v = -96.030\,\frac{m}{s}\)
The rocket crashes on the ground at a velocity of -96.030 meters per second.
A vehicle, starting from rest, accelerates on a circular track with a 335m diameter.
The distance travelled by the vehicle around the circular track is 1,052.4 m.
What is the distance travelled by the vehicle in one complete cycle?
The distance travelled by the vehicle in one complete cycle is calculated by using the following equation as show below.
d = 2πr
d = πd
Where;
r is the radius of the circular trackd is the diameter of the circular trackIn one complete cycle, the vehicle will travel the circular track only once.
d = π(335 m)
d = 1,052.4 m
Thus, the distance travelled by the vehicle around the circular track is a function of the diameter of the circular track.
Learn more about distance round a circle here: https://brainly.com/question/3100527
#SPJ1
The complete question is below:
A vehicle, starting from rest, accelerates on a circular track with a 335m diameter. What is the distance travelled by the vehicle when it makes one complete cycle?
Most violent storms form in _____.
A. continental tropical air masses
B. continental polar air masses
C. maritime polar air masses
D. maritime tropical air masses
the most violent storms are hurricanes so it would be a I think
Answer:
maritime tropical air masses
Explanation:
so d would be your answer
what is the general importance of water?
Cheetahs can accelerate to a speed of 20.0 m/s s and can continue to accelerate to reach a top speed of 29.8 m/s. Assume the acceleration is constant until the top speed is reached and is zero thereafter. Let the +x-direction point in the direction the cheetah runs.
Express the cheetah's top speed in miles per hour
The final speed of the Cheetah is 66.6607 miles per hour.
What is acceleration?Acceleration is rate of change of velocity with time. Due to having both direction and magnitude, it is a vector quantity. Si unit of acceleration is meter/second² (m/s²).
If a body changes its velocity or direction of velocity, the physical quantity "acceleration" comes into play.
Initial speed of the Cheetah is = 20.0 m/s
Final speed of the Cheetah is = 29.8 m/s
Now 1 meter per second = 2.237 miles per hour
Hence, Final speed of the Cheetah is = 29.8 × 2.237 miles per hour
= 66.6607 miles per hour.
Learn more about acceleration here:
brainly.com/question/12550364
#SPJ1
An insect lands 0.1m from the centre of a turn table while the record is turning at 55 rev/min at what linear speed will the insect be carried
collision with the near stationary photograph
The linear speed will be the insect be 0.5759 meter/second carried collision with the near stationary photograph.
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.
Given that an insect lands 0.1m from the center of the turn table.
Rotational speed of the turn table = 55 rev/min
= (55×2π/60) rad/second
= 5.759 rad/second.
Hence, the speed of the insect be = Rotational speed × length
= 5.759 rad/second × 0.1 M.
= 0.5759 meter/second.
Therefore, the speed of the insect be 0.5759 meter/second.
Learn more about speed here:
https://brainly.com/question/28224010
#SPJ1
PLS HELP!!
The speed of light is 300,000,000 m/s. What is the frequency of microwaves with a wavelength of 0.01 meter?
Answer:
c = 3.00E8 m/s speed of light
c = f * λ frequency ^ wavelength
f = c / λ = 3.00E8 m/s / .01 m = 3.00E10 / sec
f = 30,000,000,000 /sec
2. What is the resistance expected on a heater that is feed by 480V AC and the Electric Power is 4.6kW?
The resistance expected of the heater is 50.1 ohms.
What is resistance?Resistance can be defined as the opposition to the flow of electric current in an electric circuit. The S.I unit of resistance is Ohms (Ω).
To calculate the resistance of the heater, we use the formula below.
Formula:R = V²/P............. Equation 1Where:
R = Resistance of the heaterP = Power of the heaterV = Voltage supplied to the heaterFrom the question,
Given:
V = 480 VP = 4.6 kW = 4600 WSubstitute these values into equation 1
R = (480²)/4600R = 50.1 ohms.Hence, the resistance expected of the heater is 50.1 ohms.
Learn more about resistance here: https://brainly.com/question/17563681
Please list in detail a community service you wish to develop. Your writings must include (1) The name of your community service (2) How are you funding your community service (3) Where is your community service taken place (4) Who is your community service wishing to assist (5) The purpose of your community service (6) In conclusion how do you overall feel about assiting you community
The name of my community service is “Feed the Homeless”. The aim of this program is to provide nutritious food and basic necessities to the homeless community in my city. The homeless community faces various challenges and difficulties in their everyday life.
One of the major challenges they face is the availability of food and basic necessities. The primary purpose of this community service is to alleviate the burden of the homeless population by providing them with healthy and fresh food.To fund this community service, we will be reaching out to various local businesses, donors, and fundraising events. We will also partner with food banks and other charitable organizations to support our program.Our community service will take place in various areas in the city, where we see a high population of homeless people. We will set up tents and food stations in these areas to distribute food and basic necessities.We are wishing to assist the homeless community who are deprived of food and basic necessities. Our program targets all ages and genders of homeless people and focuses on providing them with healthy and fresh food.The purpose of our community service is to help the homeless community in our city. We believe that providing healthy and fresh food to the homeless will not only alleviate their hunger but also their overall health. This service will also help to reduce food waste and promote a healthier lifestyle in the community.In conclusion, I am excited to assist the homeless community in my city through this community service program.It is essential to help and support people who are in need, and I believe that our small contribution can make a big impact. I hope that our program can inspire other individuals and organizations to get involved and help make a difference in our community.For such more question on charitable
https://brainly.com/question/27627435
#SPJ8
What is true of the bottom layer of the ocean
Answer:
well i tough it was infinte but its not an the layer is a d i c k
Explanation:
assignment questions
Answer:
which on a is the question
The archerfish uses a remarkable method for catching insects sitting on branches or leaves above the waterline. The fish rises to the surface and then shoots out a stream of water precisely aimed to knock the insect off its perch into the water, where the archerfish gobbles it up. Scientists have measured the speed of the water stream exiting the fish's mouth to be 3.7 m/s. An archerfish spots an insect sitting 18 cm above the waterline and a horizontal distance of 28 cm away. The fish aims its stream at an angle of 39° from the waterline.
Required:
Determine the height above the waterline that the stream reaches at the horizontal position of the insect.
Answer:
The fish gobbles the mosquito at height 18 cm.
Explanation:
Initial velocity, u = 3.7 m/s
horizontal distance, d = 28 cm
Angle, A = 39 degree
Let the time is t.
Horizontal distance = horizontal velocity x time
d = u cos A x t
0.28 = 3.7 cos 39 x t
t = 0.097 s
Let the height is h.
Use the second equation of motion
\(h =u t-0.5 gt^2\\\\h= u sin A t - 0.5 gt^2\\\\h= 3.7 sin 39 \times 0.097 - 0.5\times 9.8\times 0.097\times0.097\\\\h =0.226 -0.046 \\\\h=0.18 m=18 cm\)
An 8.0 Kg mass is placed at = 3 where should a 10 Kg mass be placed along the − so that the center of mass will be located ay = 4.5?
Answer:
Therefore, the 10 kg mass should be placed at x = 5.7 m along the x-axis to achieve a center of mass located at y = 4.5 m.
Explanation:
To find the position along the x-axis where a 10 kg mass should be placed such that the center of mass is located at y = 4.5, we can use the formula for the center of mass:
x_cm = (m1 * x1 + m2 * x2) / (m1 + m2)
Here, m1 and x1 represent the mass and position of the 8 kg mass, respectively. m2 is the mass of the 10 kg mass, and we need to find x2, its position.
Given:
m1 = 8 kg
x1 = 3 m
x_cm = unknown (to be found)
m2 = 10 kg
y_cm = 4.5 m
Since the center of mass is at y = 4.5, we only need to consider the y-coordinate when calculating the center of mass position along the x-axis.
To solve for x2, we can rearrange the formula as follows:
x2 = (x_cm * (m1 + m2) - m1 * x1) / m2
Substituting the given values:
x2 = (x_cm * (8 kg + 10 kg) - 8 kg * 3 m) / 10 kg
Simplifying:
x2 = (x_cm * 18 kg - 24 kg*m) / 10 kg
Now, we can set the y-coordinate of the center of mass equal to 4.5 m and solve for x_cm:
4.5 m = (8 kg * 3 m + 10 kg * x2) / (8 kg + 10 kg)
Simplifying:
4.5 m = (24 kg + 10 kg * x2) / 18 kg
Multiplying both sides by 18 kg:
81 kg*m = 24 kg + 10 kg * x2
Subtracting 24 kg from both sides:
10 kg * x2 = 81 kg*m - 24 kg
Dividing both sides by 10 kg:
x2 = (81 kg*m - 24 kg) / 10 kg
Simplifying:
x2 = 8.1 m - 2.4 m
x2 = 5.7 m
(brainlest?) ples:(
Answer:
the 10 kg mass should be placed at x = -2.4 m to achieve a center of mass at y = 4.5 m.
Explanation:
To find the position along the x-axis where the 10 kg mass should be placed so that the center of mass is located at y = 4.5, we can use the principle of the center of mass.
The center of mass of a system is given by the equation:
x_cm = (m1x1 + m2x2) / (m1 + m2),
where x_cm is the x-coordinate of the center of mass, m1 and m2 are the masses, and x1 and x2 are the positions along the x-axis.
Given:
m1 = 8 kg,
x1 = 3 m,
m2 = 10 kg,
y_cm = 4.5 m.
To solve for x2, we need to find the x-coordinate of the center of mass (x_cm) by using the y-coordinate:
y_cm = (m1y1 + m2y2) / (m1 + m2),
where y1 and y2 are the positions along the y-axis.
Rearranging the equation and substituting the given values:
4.5 = (83 + 10y2) / (8 + 10).
Simplifying the equation:
4.5 = (24 + 10*y2) / 18.
Multiplying both sides by 18:
81 = 24 + 10*y2.
Rearranging the equation:
10*y2 = 81 - 24,
10*y2 = 57.
Dividing both sides by 10:
y2 = 5.7.
Therefore, the y-coordinate of the 10 kg mass should be 5.7 m.
To find the x-coordinate of the 10 kg mass, we can use the equation for the center of mass:
x_cm = (m1x1 + m2x2) / (m1 + m2).
Substituting the given values:
x_cm = (83 + 10x2) / (8 + 10).
Since the center of mass is at x_cm = 0 (the origin), we can solve for x2:
0 = (83 + 10x2) / (8 + 10).
Rearranging the equation:
83 + 10x2 = 0.
24 + 10*x2 = 0.
10*x2 = -24.
Dividing both sides by 10:
x2 = -2.4.