Answer:
a) [tex]- ( g - \frac{q}{m} \frac{\sigma }{ 2 \epsilon_o} ) \frac{sin \theta}{R }[/tex] = [tex]\frac{d^2 \theta}{d t^2}[/tex]
b) f = 2π [tex]\sqrt{ \frac{R}{ g - \frac{q}{m} \frac{\sigma }{2 \epsilon_o} } }[/tex]
Explanation:
a) To have the equations of motion, let's use Newton's second law.
Let's set a reference system where the x-axis is parallel to the path and the y-axis is in the direction of tension of the rope.
For this reference system the tension is in the direction of the y axis, we must decompose the weight and the electrical force.
Let's use trigonometry for the weight that is in the vertical direction down
sin θ = Wₓ / W
cos θ = W_y / w
Wₓ = W sin θ
W_y = W cos θ
we repeat for the electric force that is vertical upwards
F_{ex} = F_e sin θ
F_{ey} = F_e cos θ
the electric force is
F_e = q E
where the field created by an infinite plate is
E = [tex]\frac{ \sigma}{2 \epsilon_o}[/tex]
let's write Newton's second law
Y axis
T - W_y = 0
T = W cos θ
X axis
F_{ex} - Wₓ = m a (1)
we use that the acceleration is related to the position
a = dv / dt
v = dx / dt
where x is the displacement in the arc of the curve
substituting
a = d² x /dt²
we substitute in 1
q E sin θ - mg sin θ = m [tex]\frac{d^2 x}{dt^2}[/tex]
we have angular (tea) and linear (x) variables, if we remember that angles must be measured in radians
θ = x / R
x = R θ
we substitute
sin θ (q E - mg) = m \frac{d^2 R \ theta}{dt^2}
[tex]- ( g - \frac{q}{m} \frac{\sigma }{ 2 \epsilon_o} ) \frac{sin \theta}{R }[/tex] = [tex]\frac{d^2 \theta}{d t^2}[/tex]
this is the equation of motion of the system
b) for small oscillations
sin θ = θ
therefore the solution is simple harmonic
θ = θ₀ cos (wt + Ф)
if derived twice, we substitute
- ( g - \frac{q}{m} \frac{\sigma }{ 2 \epsilon_o} ) \frac{\theta}{R } θ₀ cos (wt + Ф) = -w² θ₀ cos (wt + Ф)
w² = [tex]\frac{g}{R}[/tex] - [tex]\frac{q}{m} \frac{ \sigma }{2 \epsilon_o} \frac{1}{R}[/tex]
angular velocity is related to frequency
w = 2π f
f = 2π / w
f = 2π/w
f = 2π [tex]\sqrt{ \frac{R}{ g - \frac{q}{m} \frac{\sigma }{2 \epsilon_o} } }[/tex]
a system of 11 protons and 15 neutrons has a net charge of
Explain why the same side of the moon is always facing Earth.
Answer:
The moon keeps the same face pointing towards the Earth because its rate of spin is tidally locked so that it is synchronized with its rate of revolution (the time needed to complete one orbit). In other words, the moon rotates exactly once every time it circles the Earth.
You wish to make a simple amusement park ride in which a steel-wheeled roller-coaster car travels down one long slope, where rolling friction is negligible, and later slows to a stop through kinetic friction between the roller coaster's locked wheels sliding along a horizontal plastic (polystyrene) track. Assume the roller-coaster car (filled with passengers) has a mass of 743.0 kg and starts 83.4 m above the ground. (a) Calculate how fast the car is going when it reaches the bottom of the hill. m/s (b) How much does the thermal energy of the system change during the stopping motion of the car
Answer:
(a) The car is going approximately 40.43 m/s at the bottom of the hill
(b) The thermal energy will increase by 607,268.76 J
Explanation:
In the question, we have;
The height of the roller coaster above ground = 83.4 m
The mass of the roller coaster, m = 743.0 kg
(a) By the conservation of energy principle, we have;
The potential energy at the top of the hill, P.E., is equal to the kinetic energy at the bottom of the hill, K.E.
∴ P.E. = K.E.
P.E. = m·g·h
Where;
m = The mass of the roller coaster = 743.0 kg
g = The acceleration due to gravity = 9.8 m/s²
h = The height of the roller coaster = 83.4 m
Therefore, we have;
P.E. = 743.0 kg × 9.8 m/s² × 83.4 m = 607,268.76 J
P.E. = 607,268.76 J
K.E. = 1/2·m·v²
∴ K.E. = 1/2 × 743.0 kg × v²
P.E. = K.E.
∴ P.E. = K.E. = 607,268.76 J
1/2 × 743.0 kg × v² = 607,268.76 J
v² = 607,268.76 J/(1/2 × 743.0 kg) = 1,634.64 m²/s²
v = √(1,634.64 m²/s²) ≈ 40.43 m/s
(b) Given that the material wheel moves along polystyrene track, the sound released will be minimal and almost all the kinetic energy will be converted to heat energy when the train stops, therefore, the thermal energy will increase by K.E. = 607,268.76 J
The thermal energy change of the system is 624,492 J.
We know that in the roller coaster, there is an energy transformation from gravitational potential energy to kinetic energy. As such we can write;
mgh = 1/2mv^2
Where we cancel out the mass from both sides, we are left with;
gh=0.5v^2
v= √gh/0.5
v = √10 × 83.4 m/0.5
v = 41 ms-1
Now the kinetic energy is converted also into heat energy hence;
Thermal energy change of the system = 1/2 mv^2 = 0.5 × 743.0 kg × ( 41 ms-1)^2 = 624,492 J
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When two positive charges are brought close together, what happens to the
field lines of the charges?
Answer:
they will move away from each other
Which statement about homeostasis is most accurate? *
1:Homeostasis is the ability of the body to change to match the surrounding environment.
Homeostasis is the ability of the body to maintain balance inside the cells, even as the surrounding environment changes
Homeostasis is the ability to fight disease.
Answer:
Homeostasis is the ability of the body to maintain balance inside the cells, even as the surrounding environment changes
The correct option is (1)Homeostasis is the ability of the body to change to match the surrounding environment.
What is Homeostasis?
Homeostasis is the ability of an organism or system to maintain a stable internal environment, despite changes in external conditions. This is achieved through a variety of physiological and behavioral mechanisms that help regulate various bodily functions such as temperature, blood sugar levels, hydration, and oxygen levels.
The process of homeostasis involves the detection of changes in the internal or external environment, followed by a response that helps restore the optimal conditions. For example, if the body's temperature rises above normal levels, the brain triggers sweat production to cool down the body.
Homeostasis is essential for the proper functioning of cells, tissues, organs, and the entire organism. It helps maintain a balance between various bodily functions and ensures that cells have the necessary conditions to carry out their functions. Without homeostasis, cells would be unable to survive and carry out the functions required for life.
Hence the correct statement about homeostasis is, Homeostasis is the ability of the body to change to match the surrounding environment.
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A box with mass 1.10 kg is located on a horizontal tabletop with friction. The coefficient of kinetic friction is 0.500. The tabletop is square and measures 1.00 m on its side. The box starts at one corner and finishes at the diagonal edge. The path it follows is by first traveling one edge, turning and traveling to the final location. You push the box by exerting a force on it that makes an angle of 30.0o with the horizontal. How much work does the friction force do
Answer:
W = 6.5 W
Explanation:
Work is defined by
W = F . d
W = f d cos tea
where the point represents the scaled product and the bold letters indicate vectors
they ask us the work of the friction force
we write the translational equilibrium equation
y Axis
N -W = 0
N = mg
x axis
F - fr = 0
F = fr
the formula for the friction force is
fr = μ N
we substitute
fr = μ m g
we substitute in the equation of work
W = fr d cos θ
W = μ m g d cos θ
let's calculate
W = 0.500 1.10 9.8 Σ d_i cos θ_i
W = 5.39 d cos tea
we have two displacement
the first on one side of the box, suppose that side is on the y-axis, therefore the angle between the displacement and the friction force is 70º
and there is a second displacement in the x axis, in this case the angle between the friction force and the displacement is 30º
therefore the total workload is the sum of those work
W = 5.39 (1 cos 70 + 1 cos 30)
W = 5.39 (0.342 + 0.866)
W = 6.5 W
Is TV light is converging rays, divergent rays or parallel rays?
a race car goes around a circular track of radius 150 m at speed of 10.0 m/s. How long does it take to complete one lap?
Answer:
94.25 seconds
Explanation:
Solve for period (T) using: v=(2*pi*r)/T
rearrange: vT=2*pi*r
rearrange: T=(2*pi*r)/v
Plug in values.
T=(2*pi*150)/10
T=94.25 seconds
If a race car goes around a circular track of a radius of 150 m at speed of 10.0 m/s ,then the time taken to complete the one lap would be 94.25 seconds.
What is speed?The total distance covered by any object per unit of time is known as speed. It depends only on the magnitude of the moving object. The unit of speed is a meter/second. The generally considered unit for speed is a meter per second.
As given in the problem a race car goes around a circular track of radius 150 m at speed of 10.0 m/s.
vT = 2 × π × r
T = (2 × π × r)/ v
T = (2 × π× 150)/10
T = 94.25 seconds
Thus, the time taken to complete the one lap would be 94.25 seconds.
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The surface of the sun has a temperature of about 5,800 Kelvin. What is the average kinetic energy of particles on the surface of the sun? Please show your work
Answer:
273.15
Explanation:
So that's three over two times 1.38 times ten to the minus twenty-three joules per Kelvin, times 5500 degrees Celsius, the surface of the sun converted into Kelvin by adding 273.15. This works out to 1.20 times ten to the minus nineteen joules. So that's the average kinetic energy of hydrogen atoms.
What is the terminal velocity of blood? A. 8.9 feet/seconds B. 9.8 feet/seconds C. 25.1 feet/second D. 52.1 feet/seconds
Answer:
the answer is c) 25.1 feet/second
Explanation:
because the blood droplets can not increase speed past terminal velocity 100.
The terminal velocity of blood is 25.1 ft/s in air. So, option C is correct.
What is meant by terminal velocity ?Terminal velocity is defined as the maximum velocity to which a freely falling drop can accelerate.
Here,
When a drop of blood is observed, it can be found that due to the effect of gravity, the velocity of the freely falling blood drop increases. So, it moves with increasing velocity, which is due to the influence of acceleration due to gravity. During the free fall of blood drop, there are resistive forces in air that opposes the motion or tries to reduce the velocity of the blood drop. The friction in air affects the freely falling blood drop and the blood drop tends to reduce its velocity and reaches a maximum of velocity after which it cannot accelerate, which is due to the frictional force in air. This maximum velocity is called terminal velocity. The terminal velocity of blood is 25.1 feet/second.
Hence,
The terminal velocity of blood is 25.1 ft/s in air.
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A friend pushes a sled across horizontal snow and when it gets up to speed the friend jumps on. After the friend jumps on, the sled gradually slows down. Which forces act on the combined sled plus friend after the friend jumps on
Answer:
v’ =( [tex]\frac{1}{1+ \frac{M}{m} }[/tex] ) v
we see that the greater the difference, the more the sled slows down.
friction force
Explanation:
When the man pushes the sled he does work and the sled acquires a speed and as long as it is supplied with an energy equal to the work of the chipping force with the snow, the speed is maintained.
When he jumps on the sled, a collision occurs and the initial moment
p₀ = mv
is increased by the increase in mass
m_f= (m + M_{man} ) v '
In this case there is no longer any external force applied and the only external force is friction, which causes the sled to stop, even when it is small, but the significant reduction in speed is due to the increase in masses.
p₀ = p_f
mv = (m + M_{man}) v '
v ’= [tex]\frac{m}{m+M}[/tex] v
v’ =( [tex]\frac{1}{1+ \frac{M}{m} }[/tex] ) v
Therefore, we see that the greater the difference, the more the sled slows down.
The only forces that act on the sled with the man are the friction that is responsible for the decrease in speed and weight with the normal
You are an astronaut and NASA has asked you to determine how mass and weight change throughout the solar system they have provided you with a rover with a mass of 227 kg on earth what is the rovers mass on the moon if the moon's gravity is 1.60 ms²
Answer:
The mass will be 227kg.
Explanation:
Mass is a measure of how much "stuff" is in an object. It's a measure of the number and type of atoms in something, and is fixed. If you and I went to the moon right now, our bodies wouldn't change what they were made of. I would still be made up of all the same "stuff," as would you! So my mass would be the same and so would yours.
Weight would change on the moon, because weight is a measure of the local pull of gravity on an object's mass. Earth's gravitational force is about 10m/s2 and the moon's is about 1.6m/s2. So on the moon, I would have a weight of about 1/6 my weight on Earth... but I'd still wear the same size jeans!
Which of the following would require the greatest number of calories?
a. heating 1 g of water from 10°C to 80°C
b. heating 10 g of water from 10°C to 40°C
c. heating 100 g of water from 10°C to 20°C
d. heating 1000 g of water from 10°C to 12°C
Answer:
D
Explanation:
You are boiling more grams for more time because the more water the longer it takes which requires more calories to burn it.
ASAP
If a cart is released with some initial
velocity, it will slowly come to a stop.
What happens to the energy of the cart's
motion?
If the cart is pulled along at a constant velocity, no acceleration, the energy of the carts motion is constant but the force pulling it adds energy continuously. Where does the extra energy go?
Answer:
A) Energy is dissipated into heat and sound energy due to Friction
B) The energy goes into heat and sound energy due to friction again, otherwise the cart would accelerate due to an unbalanced force. Therefore, we know there's friction, and the friction causes energy loss.
4 people are playing a tug of war. Two are pulling on the right side. Two are pulling on the left side. On the right side, one is pulling with a force of 60 N and the other with a force of 70 N. On the left side, one is pulling with a force of 30 N. How much force should the second person on the left apply to keep the rope in equilibrium? HINT: The rope will be in equilibrium if the net force is 0.
Answer:
100
Explanation:
since the two at the left side is pulling with a force of 70 and 60 which equals to 130 for the rope to be in equilibrium, those at the left must also pull with same force. Which makes it 130-30=100N
Two girls are estimating each other's power. One runs up some step
ng each other's power. One runs up some steps, and the other times her. Here are their
results:
height of one step = 20 cm
number of steps = 36
mass of runner = 45 kg
time taken = 4.2 s
a .Calculate the runner's weight. (Acceleration due to gravity g=10m
b .Calculate the increase in the girl's gravitational potential energy as she runs up the steps.
c. Calculate her power. Give your answer in kilowatts (kW).
Answer:
A. 450 N
B. 3240 J
C. 0.77 KW
Explanation:
From the question given above, the following data were obtained:
Height of one step = 20 cm
Number of steps = 36
Mass of runner = 45 kg
Time taken = 4.2 s
Next, we shall convert 20 cm to metre (m). This can be obtained as follow:
100 cm = 1 m
Therefore,
20 cm = 20 cm × 1 m /100 cm
20 cm = 0.2 m
Next, we shall determine the total height. This can be obtained as follow:
Height of one step = 0.2 m
Number of steps = 36
Total height =?
Total height = 36 × 0.2
Total height = 7.2 m
A. Determination of the runner's weight.
Mass of runner (m) = 45 kg
Acceleration due to gravity (g) = 10 m/s²
Weight (W) =?
W = m × g
W = 45 × 10
W = 450 N
B. Determination of the increase in the potential energy.
At the ground level, the potential energy (PE₁) is 0 J.
Next, we shall determine the potential energy at 7.2 m. This can be obtained as follow:
Mass of runner (m) = 45 kg
Acceleration due to gravity (g) = 10 m/s²
Total height (h) = 7.2 m
Potential energy at height 7.2 m (PE₂) = ?
PE₂ = mgh
PE₂ = 45 × 10 × 7.2
PE₂ = 3240 J
Final, we shall determine the increase in potential energy. This can be obtained as follow:
Potential energy at ground (PE₁) = 0 J
Potential energy at height 7.2 m (PE₂) = 3240 J
Increase in potential energy =?
Increase in potential energy = PE₂ – PE₁
Increase in potential energy = 3240 – 0
Increase in potential energy = 3240 J
C. Determination of the power.
Energy (E) = 3240 J
Time (t) = 4.2 s
Power (P) =?
P = E/t
P = 3240 / 4.2
P = 771.43 W
Finally, we shall convert 771.43 W to kilowatt (KW). This can be obtained as follow:
1000 W = 1 KW
Therefore,
771.43 W = 771.43 W × 1 KW / 1000 W
771.43 W = 0.77 KW
Therefore, her power is 0.77 KW
He-Ne Laser device emits photons of wave length 632.8 nm by rate 4.5 x 1020 photon/s, so
the power of the laser beam =
a. 3.14 W
b. 141.3 W
c. 314.1 w
d. 431.4 W
Answer: Option b.
Explanation:
We know:
Wavelength = 632.8 nm
Fluence = 4.5*10^20 photon/s
The energy of a single photon of wavelength λ is:
E = (h*c)/λ
where:
h = 6.6*10^(-34) J*s
c = 3*10^8 m/s
And we should rewrite the wave length in meters, so:
λ = 632.8 nm = 632.8*10^(-9) m
replacing these in the energy equation, we get:
E = (6.6*10^(-34)J*s)*(3*10^8 m/s)/(632.8*10^(-9) m) = 3.13*10^(-19) J
So each one of the 4.5x10^20 photon that flow each second have this energy, then the power is:
P = (3.13*10^(-19) J)*(4.5*10^20 /s) = 140.85 J/s
and 1 W = 140.85 J/S
Then the power is:
P = 140.85 W
Then the correct answer is the option b, where the units are a little bit different than mine because I used really simplified values for c and h.
A tank is is half full of oil that has a density of 900 kg/m3. Find the work W required to pump the oil out of the spout. (Use 9.8 m/s2 for g. Assume r = 15 m and h = 5 m.) W = 1.59 J
Answer:
3.9 × 10^7 J
Explanation:
Given that a tank is is half full of oil that has a density of 900 kg/m3. Find the work W required to pump the oil out of the spout. (Use 9.8 m/s2 for g. Assume r = 15 m and h = 5 m.) W = 1.59 J
Solution
Since the tank is half full, the height = 2.5m
Pressure = density × gravity × height
Pressure = 900 × 9.8 × 2.5
Pressure = 22050 Pascal
The cross sectional area of the pump will be area of a circle.
A = πr^2
A = π × 15^2
A = 706.858 m^2
Using the formula
Density = mass/volume
Mass = density × volume
Mass = 900 × 706.86 × 2.5
Mass = 1590.435
Energy = mgh
Energy = 1590.435 × 9.8 × 2.5
Energy = 38965657.8 J
Since the work done = energy
Therefore, the work done = 3.9 × 10^7 J
1. Odysseus traveled from Troy to Ithaca. What
was the acceleration of Odysseus' ship if its mass
was 900,000 kg and it moves across the water with
a force of 300,000 N?
Answer: 0.33 m/s^2
Explanation:
The acceleration of Odysseus' ship as it moves across the water from Troy to Ithaca is 0.33m/s²
Given the data in the question;
Mass of Odysseus' ship; [tex]m= 900000kg[/tex]Force with which Odysseus' ship moves across the water; [tex]F = 300000N[/tex]Acceleration; [tex]a = ?[/tex]To determine the acceleration of the ship, We the equation from Newton's Second Law of Motion:
[tex]F = m\ *\ a[/tex]
Where F is the force, m is the mass and a is the acceleration
Lets make acceleration ''a'', the subject of the formula
[tex]a = \frac{F}{m}[/tex]
Now, we substitute our given values into the equation
[tex]a = \frac{300000N}{900000kg}[/tex]
We know that, A newton is defined as [tex]1 kg.m/s^2[/tex]
[tex]a = \frac{300000 kg.m/s^2}{900000kg} \\\\a = 0.33m/s^2[/tex]
Therefore, the acceleration of Odysseus' ship as it moves across the water from Troy to Ithaca is 0.33m/s²
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If the hoop has speed vo at the bottom of
the pipe, what is its speed when it has rolled
halfway up the side of the pipe?
The speed of the hoop when it has rolled halfway up the side of the pipe is √(v₀² - gR).
Conservation of energyThe speed of the hoop when it has rolled halfway up the side of the pipe is calculated as follows;
K.E = P.E
- ¹/₂mv₀² + ¹/₂Iω² = (mgh₀ - mghf)
- ¹/₂mv₀² + ¹/₂Iω² = (0 - 0.5mgh) (hf = 0.5h) (half way up)
¹/₂Iω² = ¹/₂mv₀² - 0.5mgh
where;
I is moment of inertia of the hoop = mr²ω is angular speed = v/r¹/₂(mr²)(vf/r)² = ¹/₂mv₀² - 0.5mgh
¹/₂vf² = ¹/₂v₀² - ¹/₂gh
vf² = v₀² - gh
vf = √(v₀² - gh)
where;
h is the distance traveled half-way up the pipe = Rvf = √(v₀² - gR)
[tex]v_f = \sqrt{v_0^2 - gR}[/tex]
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What is the hottest planet in the milky way galaxy
Answer:
Venus
Explanation:
a car moved 120km to the north. what is its displacement?
Joe has a mass of 110 kg. If Joe has to climb a 10 m ladder to get to the top of a chimney, how much work did do?
A long, straight, current-carrying wire runs from north to south.
a. A compass needle placed above the wire points with its north pole toward the east. In What direction is the current flowing
b. If a compass is put underneath the wire, in which direction will the compass needle point?
Answer:
a. The current is flowing from South to North. So, the current flows in the North direction
b. West
Explanation:
a. A compass needle placed above the wire points with its north pole toward the east. In What direction is the current flowing?
Using Maxwell's corkscrew rule, with the thumb of the right hand pointing in the direction of the current and the closed fingers pointing in the direction of the magnetic field.
Since the compass is placed above the wire and points east, the direction of the magnetic field at that point is east.
Since the magnetic field is tangential to the circular path around the wire, to produce an eastward magnetic field above the wire, the current must go from South to North. So, the current flows in the North direction.
b. If a compass is put underneath the wire, in which direction will the compass needle point?
If the compass is put underneath the wire, using Maxwell's corkscrew rule, since the current points northward, and the magnetic field is tangential to the circular path around the wire, the magnetic field below the wire points west.
So, the direction of the compass needle when the compass is put beneath the wire is west.
The part of the eye that gives its shape is the:
3)
An eagle carries a 330g snake to a height of 250 m.
What is the potential energy of the snake after the eagle carries it away?
-)))
A)
1,050,00)
B)
10,000
©
80.850)
D)
808.5)
Answer:
b
Explanation:
Answer:
The table shows the height y (in thousands of feet) of an unmanned aerial vehicle (UAV) x minutes after it begins its descent from cruising altitude. Minutes, x Height (thousands of feet), y 0,62 5,58 10,54 15,50
what factors affect potential energy
Velocity tells us not only how fast something is going, but in what direction it is traveling.
True
False
Answer:
true
Explanation:
because I tride it
A 65.0 kg skier slides down a 37.20 slope with mu = 0.107.
What is the friction force?
Answer:
54.3N
Explanation:
The normal force is perpendicular to the slope, so:
Normal Force = cos(37.2)(9.8*65).......507.39N
F(friction)=mu*F(normal)
F(friction)=(0.107)(507.39)
F(friction)=54.3N
Answer:
magnitude of friction force- 54.3
friction force- -54.2
Explanation:
An elevator filled with passengers has a mass of 1663 kg. (a) The elevator accelerates upward from rest at a rate of 1.20 m/s2 for 3.25 s. Calculate the tension in the cable (in N) supporting the elevator. 18317 Correct: Your answer is correct. N (b) The elevator continues upward at constant velocity for 8.92 s. What is the tension in the cable (in N) during this time
Answer:
(a) T = 18309.63 N = 18.31 KN
(b) T = 16314.03 N = 16.314 KN
Explanation:
(a)
The tension in an elevator while moving upward with some acceleration is given by the following formula:
[tex]T = m(g+a)\\[/tex]
where,
T = Tension = ?
m = mass = 1663 kg
g = acceleration due to gravity = 9.81 m/s²
a = acceleration of elevator = 1.2 m/s²
Therefore,
[tex]T = (1663\ kg)(9.81\ m/s^2 + 1.2\ m/s^2)\\[/tex]
T = 18309.63 N = 18.31 KN
(b)
Constant velocity means no acceleration. So, in that case, the tension will be equal to the weight of the elevator:
[tex]T = mg\\T = (1663\ kg)(9.81\ m/s^2)\\[/tex]
T = 16314.03 N = 16.314 KN