If a stone has 390 J of energy and is moving with a speed of 12m/s, what is the mass of the stone?
Answers
Answer: 5.42 kg
Explanation:
The formula for kinetic energy is:
KE = 1/2 * m * v^2
where KE is the kinetic energy, m is the mass of the object, and v is the velocity of the object.
We are given the kinetic energy (KE) and velocity (v), so we can rearrange the formula to solve for the mass (m):
m = 2 * KE / v^2
Substituting the given values, we get:
m = 2 * 390 J / (12 m/s)^2
m = 2 * 390 J / 144 m^2/s^2
m = 5.42 kg (rounded to two decimal places)
Therefore, the mass of the stone is approximately 5.42 kg.
Related Questions
Which is easier for a beginner? (This is for archery)
O long bow
O recurve bow
Answers
Answer:
The recurve bows
Explanation:Vote brainliest plz
Write a short scene or describe a situation where at least two phase changes take place.
Be sure to include the names (2 points) and descriptions (4 points) of the phase changes
as well as how/why they occur (4 points). In your descriptions, be sure to explain what
the particles (atoms or molecules) are doing. Also be sure to explain what is happening
with energy. Please write in complete sentences.
Answers
A phase change occurs when a substance changes from one state of matter to another.
A scene in which at least two phase changes take place is when ice is converted to vapor.
To convert ice to vapor, we need to supply energy to the ice in form of heat. The molecules in the ice begin to move faster as they acquire more energy and eventually the lattice falls apart and ice is converted to liquid.
As more energy is supplied, the molecules acquire even greater energy and move at higher speeds, all the intermolecular bonds between the molecules are severed as the liquid turns into vapor.
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what does a paleontologist study?
Answers
Answer:
Paleontology is the study of the history of life on Earth as based on fossils. Fossils are the remains of plants, animals, fungi, bacteria, and single-celled living things that have been replaced by rock material or impressions of organisms preserved in rock.
Which statement is correct about waves?
A. All waves move at the same speed in any
medium.
B. Waves carry the energy but do not carry the matter.
C. Waves must always move from one place to another.
D. Sound waves have more energy than light waves.
Answers
Answer:
b is the correct answer
Explanation:
QUESTION 14
The sides of a small rectangular box are measured to be 1.75 +/- 0.01 cm, 7.25 +/- 0.02 cm, and 8.5 +/- 0.1 cm long. Calculate the uncertainty in its volume in cubic centimeters
A) 1.2x10^-3 cm^3
B) 0.13 cm^3
C) 2 cm^3
D)0.02 cm^3
Answers
Answer:
firts divide then multiply divide again and your and your answer should d
which type of image is formed by convex lens on a screen?
Answers
Answer:
The type of image formed on a screen by a convex lens is real, enlarged and inverted.
Explanation:
A lens can be defined as a transparent optical instrument that refracts rays of light to produce a real image.
Basically, there are two (2) main types of lens and these includes;
I. Diverging (concave) lens.
II. Converging (convex) lens.
A converging lens refers to a type of lens that typically causes parallel rays of light with respect to its principal axis to come to a focus (converge) and form a real image.
Basically, the type of image formed on a screen by a converging (convex) lens is real, enlarged and inverted because it is usually thick across the middle (causing rays of light to converge) but thin at the lower and upper edges.
James defines a circle as "the set of all the points equidistant from a given point." His statement is not precise enough because he should specify that
Answers
(b) the set of points is in a plane
A circle has points in a plane, a center, a radius, and a diameter. Depending on the situation, at least one of the following words must be included in the definition of a circle:
Points in a planeRadiusCenterDiameterBased on James' definition of a circle, he needed to specify that the points are in a plane (option b).
The phrase "the set of all the points," as he defines it, has a variety of meanings. among them are:
the set of points on a line.
a plane's set of points.
the region's collection of points
James should have made it clear that the collection of points is in a plane.
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The complete question is mentioned below:
James defines a circle as "the set of all the points equidistant from a given point." His statement is not precise enough
because he should specify that
(a) a circle includes its diameter
(b) the set of points is in a plane
(c) a circle includes its radius
(d) the set of points are collinear
An object rotates describing a horizontal circumference when subjected to a centripetal force F. What centripetal force will act on the object if the radius of the circle is doubled and the kinetic energy of the object is halved? A) F/4 B) F/2 C) F D) 4F please explain this to me : (
Answers
Answer:
Option A: F/4
Explanation:
Centripetal force, \(F = \frac{mv^{2} }{r}\)
Where v = speed
r = radius
Since Kinetic Energy, \(E_{k} = 0.5 mv^{2}\)
Writing centripetal force in terms of kinetic energy, \(F = \frac{2 E_k}{r}\)
If the initial radius of the circle, r₁ =r
The doubled radius, r₂ = 2r
If the initial kinetic energy, \(KE_1 = E_{k}\)
The halved kinetic energy, \(KE_2 = 0.5E_{k}\)
Therefore, the new Centripetal force becomes:
\(F_{2} = \frac{2(0.5 E_k)}{2r} \\F_{2} = \frac{0.5 E_k}{r}\\F_{2} =\frac{1}{4} * \frac{2 E_k}{r}\\Since, F = \frac{2 E_k}{r} \\F_{2} =\frac{1}{4} * F\\F_{2} =\frac{F}{4}\)
an electromagnet's coil has 50 loops. what will happen to the strength of the electromagnet if another 50 loops are added?
Answers
We can conclude that the electromagnet's strength is inversely correlated with the coil's number of turns. The electromagnet's strength doubles when the number of turns is doubled, every coil of wire increases the "magnetic flux density" of your magnet.
What is energy ?
Energy is a quality of matter and radiation that is the capacity to perform work. It can appear in a variety of forms, such as thermal energy, light energy, mechanical energy, electrical energy, and chemical energy. According to the law of conservation of energy, energy can be changed from one form to another but cannot be produced or destroyed.
Numerous natural processes and activities, such as photosynthesis in plants, the flow of ocean currents, and the production of electricity in power plants, depend on energy. Energy is frequently referred to as a scalar quantity in physics and is typically measured in units of joules (J) or electron volts (eV).
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Two thin hollow plastic spheres, about the size of a ping-pong ball with masses ( m1=m2=0.002 kg) have been rubbed with wool. Sphere 1 has a charge q1=-8 × 10e-9 C and is at location < 0.37, -0.26, 0 > m. Sphere 2 has a charge q2= -6 × 10e-9 C and is at location < -0.31, 0.45, 0> m. It will be useful to draw a diagram of the situation, including the relevant vectors.
(a) What is the relative position vector pointing from q1 to q2 ? < , , > m
(b) What is the distance between q1 and q2 ? m
(c) What is the unit vector in the direction of r ? < , , >
(d) What is the magnitude of the gravitational force exerted on q2 by q1? N
(e) What is the gravitational force (vector) exerted on q2 by q1 ? < , , > N
(f) What is the value of ? N
(g) What is the electric force (vector) exerted on by ? < , , > N
(h) What is the ratio of the magnitude of the electric force to the magnitude of the gravitational force?
(You see that electric forces between two small charged objects are typically very much larger than gravitational forces between those same small objects. It takes the entire mass of the Earth to exert a sizable gravitational force on a small object.)
(i) If the two masses were 6 times farther away (that is, if the distance between the masses were 6 ), what would be the ratio of the magnitude of the electric force to the magnitude of the gravitational force now?
Answers
The relative position vector pointing from q₁ to q₂ (-0.68 î + 0.71 ) and the distance between q₁ and q₂ (0.983 m)
What is gravitational force?According to Newton's universal law of gravitation, there is a direct relationship between the sum of the masses of the two bodies and an inverse relationship between the square of the distance between them.
Given m₁=m₂
=0.002kg
q₁= -8×10⁻⁹ C at (0.37, -0.26, 0) m
q₂= -6×10⁻⁹ C at ( -0.31, 0.45, 0)m
a) Position vector from q₁ to q₂ is :
ř = Position vector of q₂ - Position vector of q₁
ř = ř₂ - ř₁
ř₂ = -0.31 î + 0.45 ĵ
ř₁ = 0.37 î + -(0.26) ĵ
ř = ř₂ - ř₁
= (-0.31 î + 0.45 ĵ ) - (0.37 î - 0.26 ĵ )
=( -0.31 - 0.37)î + (0.45+0.21)ĵ
= -0.68 î + 0.71 ĵ
b) distance between q₁ and q₂ is |ř| :
= √-0.68² + 0.71²
= √ 0.4624 +0.504
= 0.983 m
c) unit vector in direction of r is ř/|r| :
= -0.68 î + 0.71 ĵ / 0.983
= -0.6916 î + 0.7223 ĵ
d) the strength of the gravitational pull that q₁ has on q₂ :
Fg = G×m₁×m₂/|r²
= 6.67× 10⁻¹¹ ×0.002×0.002/ 0.983²
= 2.76×10⁻¹⁶ N
e) the gravitational force is always attracted so it will be toward q₁
so the vector is ř₃ = ř₁ - ř₂
= ( 0.37 î + 0.26 ĵ ) - ( -0.31 î + 0.45 ĵ )
= ( 0.68 î - 0.71 ĵ )
ř₃ = √0.68² + 0.71²
= √0.4624 + 0.504
= 0.983
f) infact ř₃ = -ř & |ř₃| = |ř|
so unit vector in direction of r₃ is
ř₃/ |r₃|
( 0.69 î - 0.71 ĵ ) / 0.983
ř₃ = 0.6916 î - 0.7223 ĵ
in vector form force bye q₁ on q₂ is
Fg = 2.76×10⁻¹⁶ × (0.6916 î - 0.7223 ĵ)
= 1.908×10⁻¹⁶ î - 1.9935× 10⁻¹⁶ ĵ
g) the electric force on q₂ by q₁ :
(Fe) = k×q₁×q₂/r²
= 9 × 10⁹ × (-8 ×10⁻⁹ ) × (-6 ×10⁻⁹ ) / 0.983²
= 4.47× 10⁻⁷ N
in vector form, since the force is repulsive so it is away from the charge
Fe = 4.47×10⁻⁷ × ( -0.6916 î + 0.7223 ĵ)
= -3.0914× 10⁻⁷ î + 3.22868× 10⁻⁷ ĵ
h) ratio |Fe| / |Fg|
= 4.47× 10⁻⁷ / 2.76× 10⁻¹⁶
= 1.61 × 10⁹ N
i) The new distance between the particle is now 6(ř) :
On applying formula
F'e = k×q₁×q₂ / (6|r|)²
= k×q₁×q₂ / 36 (r)²
= 1 / 36( k×q₁×q₂ / r ) = Fe/36
F'g = G ×m₁ ₓm₂ / (6|r|)²
= G× m₁ × m₂ / 36 (r)²
= 1 / 36(G×m₁×m₂ / r²) Fg/36
Ratio Fe/36/Fg/36
= Fe/Fg = 1.61 ×10⁹ N
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Two disks, A and B, are initially at rest at the left end of a track, as shown above. Disk B is more massive than disk A. The track has a horizontal section and then curves upward at the right end. The disks are each pushed to the right over a distance x0
by identical constant horizontal forces of magnitude F
. There is negligible friction between the track and the disks.
The figure presents two graphs, both in the first quadrant. For both graphs, the horizontal axis is labeled Position, the vertical axis is labeled Velocity, and the origin is labeled O. The graph on the left is labeled Graph 1. The graph is a curve that begins at the origin and extends upward and to the right, with a slope that is steeper near the origin and less steep at the upper right end of the curve. The second graph is labeled Graph 2. The graph is a straight line that begins at the origin and extends upward and to the right.
(a) Which of the graphs shown above correctly models the velocity of disk A as a function of position as it is being pushed by the force? Justify your answer.
(b) After sliding across the horizontal portion of the track, both disks slide partway up the curved section of the track. Identify which disk, if either, reaches a greater maximum height. If both disks reach the same maximum height, state this explicitly.
(c) In a clear, coherent paragraph-length response, justify your answer to part (b).
(d) Consider the case where friction is not negligible and the coefficient of kinetic friction between each disk and the track is the same. The disks are again pushed by the same force over the same distance, and each disk slides partway up the ramp. Identify which disk, if either, would reach a greater maximum height than the other in this case. If both disks reach the same maximum height in this case, state this explicitly. Briefly justify your answer.
Answers
The velocity vs displacement curve will be a parabolic graph and the height attained by object B will be lesser than object A.
What is Velocity?Velocity is the change in displacement of an object with the change in time. It is a vector quantity because it has both magnitude and direction. The SI unit of velocity is meter per second (m/s).
u = 0
x₀ = Distance travessed by both the discs
F= constant
f = 0
a) (F-f) = ma
a = F/ m
v² = u² + 20x
v² = 0 + (2F/m)x
v = \(\sqrt{(2f/m)x}\)
v v/s x curve will be similar to parabolic graph of v² = (2f/ m)x
b) Energy would be conserved for both.
Since, velocity gained by both is same as Vi = \(\sqrt{(F/m)Xo}\)
-mgh = 1/2mvf² - 1 mvi² = - 1 mvi²
mgh = 1/2mvi² = FXo/2m (Since, vf = 0)
So, h = (FXo/ 2mg)
Since, mb > ma
Hb < Ha
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a projectile is launched at an angle of 600 with respect to the horizontal and with initial speed of 30 m/s. what is the horizontal range of the projectile?
Answers
The horizontal range of the projectile is 91.7 meters in the given case.
The horizontal range of a projectile can be found using the formula:
A projectile is any object that is thrown, launched, or otherwise propelled through the air and subject to the force of gravity. Examples of projectiles include a baseball being thrown by a pitcher, a rocket being launched into space, or a cannonball fired from a cannon.
\(R = (v0^2/g) * sin(2θ)\)
where R is the horizontal range, v0 is the initial speed, θ is the launch angle, and g is the acceleration due to gravity (9.81 m/s^2).
Plugging in the given values, we get:
\(R = (30^2/9.81) * sin(2*60)\\R = (900/9.81) * sin(120)\\R = 91.7 meters\)
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If ocean water did not move it would be hot in the _ region and frigid in the _ region
Answers
If ocean water did not move, it would be hot in the equatorial region and frigid in the polar regions.
Ocean currents are responsible for redistributing heat around the planet. Without these currents, the equatorial region would receive more sunlight and heat than it loses, resulting in an accumulation of heat in the water. On the other hand, the polar regions would lose more heat than they receive, resulting in frigid temperatures.
The rotation of the Earth also influences the movement of ocean water through the Coriolis effect. Without this effect, ocean currents would be less predictable, and their impact on climate and temperature distribution would be more severe. Therefore, ocean currents play a crucial role in regulating Earth's climate, and their disruption could have significant consequences for both marine life and global weather patterns.
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overall force acting on an object.
Answers
Answer:
Gravity
Explanation:
Gravity is a force that acts upon every single object on Earth.
Question (4) - (10%) : Choose the right answer. The in-situ density of a soil is determined using the sand bottle. The weight of the excavated soil is 1210gm. The weight of the sand bottle before and after pouring sand into the hole is 7800gm and 6587gm, respectively. The weight of sand filling the cone is 300gm, and its density is 1.47gm/cm
3
. If the water montent is 11.7%. calculate the in-situ drv density? (gm/cm
3
)
Answers
Given data:Weight of excavated soil, W = 1210 g Weight of sand bottle before pouring sand, W1 = 7800 g Weight of sand bottle after pouring sand.
W2 = 6587 g Weight of sand filling the cone, Ws = 300 g Density of sand filling the cone, ρs = 1.47 g/cm³Water content, w = 11.7% = 0.117 Bulk density.
\(ρb = W/Vvwhere,Vv = [(W1 - W2) / Ws] × Vcis\)
the volume of soil displaced by the sand bottle, where Vc is the volume of the sand cone.In-situ dry density, ρd = ρb / (1 + w)We know that,Volume of sand cone.
\(Vc = [(Ws - W2 + W1) / ρs] cm³\)
Substitute the given values in the above equation,
Hence, the in-situ dry density is 0.0449 g/cm³.
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A car traveled 60km in 45 min.What is the cars average speed in km/hr
Answers
Given that,
Distance = 60 km
Time = 45 min
To find,
The average speed of the car.
Solution,
Average speed of an object is equal to the total distance divided by total time taken.
45 min = 0.75 hour
It can be given as :
\(V=\dfrac{60\ km}{0.75\ h}\\\\=80\ km/h\)
Therefore, the average speed of the car is 80 km/hr.
3. What is the best way to help with
mining problem in the future?
Answers
Answer:
1) Mining companies have an impressive track record for delivering continuous improvements in safety and risk governance standards. We have no doubt that the professionalism and expertise present within the industry will ensure that any new and emerging risk challenges are dealt with in an equally determined fashion.
2) Insurers have recognized the approach and achievements of mining companies in identifying, mitigating and retaining their risks. Many mining companies have close and longstanding relationships with their insurers built through regular dialogue with mining company executives and visits to mining sites and processing facilities.
3) This document should be of value to any organization involved in this ever-evolving industry.
4) The very nature of mining natural resources means that many businesses will have operations in some of the most remote and inhospitable areas in the world and very often coupled with a high susceptibility to natural catastrophe.
5) In addition to the traditional risk factors, the mining industry now faces an even wider range of challenges. Factors such as climate change, new technologies, economic uncertainties and secure supply of key consumables like electricity, water, gas and other fuels are all difficult to predict and bring additional complications to securing appropriate balance sheet protection.
An electron is confined to a region of space of length 0.300 nm. what is the value of e2, the second allowed energy of the electron?
Answers
The second allowed energy of an electron is 4 times the first allowed energy.
The first allowed energy can be calculated using the following equation:
En = n²h² / 8mL²where n is the principal quantum number, h is Planck's constant, m is the mass of the electron, and L is the length of the region of space to which the electron is confined.
The value of the first allowed energy is given by;E1 = h² / 8mL²
The value of h = 6.626 x 10^-34 J·s, and the value of m = 9.11 x 10^-31 kg.
Therefore, we have:E1 = (6.626 x 10^-34 J·s)² / 8(9.11 x 10^-31 kg)(0.300 x 10^-9 m)² = 3.69 x 10^-19 J
The second allowed energy of the electron, E2, is given by:E2 = 4E1= 4 × 3.69 x 10^-19 J= 1.48 x 10^-18 J
The answer is 1.48 x 10^-18 J.
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what is the speed of a wave a wavelength of 2.3 meters and a frequency of 5 Hz
Answers
Explanation:
The speed of a wave can be calculated using wavelength, Frequency.speed = wavelength x frequency.The wavelength of the wave is 2.3 meters.The frequency of the wave is 5 Hz.So,
speed = wavelength x frequency
speed = 2.3 meters x 5 Hz => 11.5 meters per second
Therefore, the speed of the wave is 11.5 meters per second.
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A spring with spring constant 58N/cm is stretched 4cm. How much force is it applying
Answers
Answer:
232 N
Explanation:
By Hooke's law, the force applied to a spring is proportional to the stretch of the spring, so
F = kx
Where F is the force, k is the spring constant and x is how much it is stretched.
So, replacing k by 58N/cm and x by 4 cm, we get
F = (58 N/cm)(4 cm)
F = 232 N
Therefore, the force applied is 232 N
A ship
a sound
wave
sends
straight
to the sea bed and receves the echo
1.5 seconds later. The speed of sound in
water
How deep is the
at that place?
collin
is 1500 m/s.
Sea
sea
Answers
Answer:
The sea bed is 1125 m deep.
Explanation:
Speed
It's the rate of change of the distance (d) traveled by an object over time (t).
The speed can be calculated by the formula:
\(\displaystyle v=\frac{d}{t}\)
It's known the speed of sound in water is v=1500 m/s. A sound wave is sent to the sea bed and bounces back to the ship 1.5 seconds later.
That is the time the wave takes to travel twice the distance from the ship to the sea bed, thus the required distance uses half of that time or t=1.5/2 = 0.75 seconds.
Solving the equation for d:
d = v.t
d = 1500 m/s * 0.75 s
d = 1125 m
The sea bed is 1125 m deep.
the electrical operating conditions are typically measured with a(n):
Answers
The electrical operating conditions are typically measured with Multimeter, Oscilloscope, and Clamp Meter. Thus, option D is the accurate answer.
A multimeter is the most common and versatile instrument which is used to measure the voltage, resistance, and current passing through the conductors. IT can able to provide continuous frequency. An Oscilloscope is also a device used to measure electrical waveforms
A clamp Meter is a small handheld device that can able to measure both AC and DC currents in the circuit in digital format. It uses a small induction coil to measure the amount of current passing through the conductor.
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The complete question is:
the electrical operating conditions are typically measured with a(n):
a. Multimeter
b. Oscilloscope
c. Clamp Meter
d. All the above
A body moves in a straight line. At time, it's acceleration is given by a = 12t + 1. When t =0, the velocity of the body v is 2 metres per second and its displacement from the origin s is 0.
1. Express v and s in terms of t.
2. Determine velocity and displacement of the body after 3 seconds.
Answers
Answer:
v = 6t² + t + 2, s = 2t³ + ½ t² + 2t
59 m/s, 64.5 m
Explanation:
a = 12t + 1
v = ∫ a dt
v = 6t² + t + C
At t = 0, v = 2.
2 = 6(0)² + (0) + C
2 = C
Therefore, v = 6t² + t + 2.
s = ∫ v dt
s = 2t³ + ½ t² + 2t + C
At t = 0, s = 0.
0 = 2(0)³ + ½ (0)² + 2(0) + C
0 = C
Therefore, s = 2t³ + ½ t² + 2t.
At t = 3:
v = 6(3)² + (3) + 2 = 59
s = 2(3)³ + ½ (3)² + 2(3) = 64.5
You pull a sled with a package on it across a snow-covered flat lawn. If you
apply a force of 65.1 N to the sled, it accelerates at 1.24 m/s2. What is the
combined mass of the package and the sled? (Assume there is no friction.)
Answers
Answer:52.5
Explanation:
You pull a sled with a package on it across a snow-covered flat lawn. If you apply a force of 65.1 N to the sled, it accelerates at 1.24 m/s2. The combined mass of the package and the sled m = 52.50 kg
The given data to find Mass,
The force applied to the sled, F = 65.1 N
Acceleration of the sled, a = 1.24 m/s²
What is force?Forces are defined by both strength and direction.
Force is a vector quantity. It is a quantity that is described by Magnitude and Direction. The strength of a force is its magnitude and the direction, well it is the direction the magnitude is applied on the object.
We need to find the combined mass of the package and the sled. Let it is m. Using definition of force as follows :
F = ma
m = F/a
m = 65.1 /1.24
Mass, m = 52.5 Kg.
If you apply a force of 65.1 N to the sled, it accelerates at 1.24 m/s2. The combined mass of the package and the sled m = 52.50 kg
Hence, Option C is the correct answer.
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three pendulums all have the same arm length, and they all start their downward swings from the same height. the first pendulum has a mass of 67 g. the second pendulum has a mass of 1.5 kg. the final pendulum has a mass of 3.3 kg. assuming that the effects of air drag are negligible, which pendulum attains the highest speed?
Answers
All three pendulums will reach the same maximum velocity, according to the question.
What is pendulum energy?The pendulum will start swinging as the weighted end is removed since gravity will drag it downward. Kinetic energy, the force a moving item exerts, is created from potential energy. At its lowest, so when mass is traveling the quickest, an active pendulum possesses the highest kinetic energy.
Briefing:From conservation of energy;
Energy at A = Energy at B
\(\frac{1}{2} mv^{2}\) = mg\(H_{max}\)
\(H_{max}\) = \(\frac{v^{2} }{2g}\)
\(H_{max}\) = Independent of mass
So, all pendulum will attain the highest speed.
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Consider an object launched upward against the force of
gravity. What is the velocity of the object at the moment it
reaches its the maximum height?
Answers
Answer:
Zero
Explanation:
When it reaches max height, it stops and begins to fall back down....at this point the velocity = 0
A 5 kg object is moving downward at a velocity of 12 m/s and is
currently 2.6 meters above the ground.
calculate its kinetic energy
calculate its potential energy
calculate its mechanical energy
Answers
Answer:
the first one i think
Explanation:
Charges of 7.2nC and 6.7nC are 32 cm apart. Find the equilibrium position for a -3.0nC charge.
Answers
Answer:
I don't know I'm sorry I will tell you another answer asks me
Two point charges are separated by a certain distance. How does the strength of the electric field produced by the first charge, at the position of the second charge, change if the second charge is doubled?
Answers
Answer:
The field will remain the same
Explanation:
This is because electric field given as
E1= kq1/r²
And that of second charge
E² = kq2/r²
Is not affected by the size of the second charge q2
Un niño de masa m se mece en un columpio sostenido por dos cadenas, cada una de longitud R. Si la tensión en cada cadena en el punto más bajo es T. Encuentre:
La fuerza que ejerce el asiento sobre el niño en el punto más bajo. (Ignore la masa del asiento.)
Answers
The force exerted by the seat on the child at the lowest point is (-m × g + 2T).
At the lowest point, the child is in equilibrium, with the gravitational force pulling down on the child balanced by the tension force in the chains pulling up. The force exerted by the seat on the child is equal in magnitude and opposite in direction to the gravitational force acting on the child.
The gravitational force on the child is given by:
F_gravity = m × g
where m is the mass of the child and g is the acceleration due to gravity (g = 9.81 m/s^2).
The tension force in each chain at the lowest point is T. Since there are two chains, the total upward force is 2T.
Therefore, the force exerted by the seat on the child is:
F_seat = -F_gravity + 2T
where the negative sign indicates that the force is in the opposite direction to the gravitational force.
Substituting the expressions for F_gravity and T, we get:
F_seat = -m × g + 2T
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