To determine the particle's position, velocity, and acceleration as a function of time, we can use the equations of motion.
a) Position (s):
The particle's position can be found by integrating its velocity with respect to time. Since the acceleration is given by a = -2v, we can rewrite it as dv/dt = -2v. Separating variables and integrating, we have ∫(1/v) dv = -2∫dt, which gives ln(v) = -2t + C1, where C1 is the constant of integration. Exponentiating both sides, we get v = \(e^{(-2t + C1)\). Since the initial velocity v(0) = 20 m/s, we can solve for C1 and obtain v = 20e^(-2t).
Now, to find the position, we integrate the velocity with respect to time: ∫v dt = ∫20e^(-2t) dt. Integrating this expression gives us the position equation: s = \(-10e^{(-2t)} + C2\), where C2 is the constant of integration. Since the initial position s(0) = 0, we can solve for C2 and obtain the position equation: s =\(-10e^{(-2t)} + 10.\)
b) Velocity (v):
We have already determined the velocity as a function of time: v = \(20e^{(-2t).\)
c) Acceleration (a):
The acceleration is given as a = -2v. Substituting the expression for velocity, we have a = -2(20e^(-2t)), which simplifies to a =\(-40e^{(-2t)\).
Therefore, the particle's position is given by s = -10e^(-2t) + 10, velocity by v = \(20e^{(-2t)}\), and acceleration by a = \(-40e^{(-2t).\)
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Force is measured in what unit? What is this unit equal to in other units?
Answer:
Explanation:
Nnewton=kgm/s²
Four 15 o resistors are connected in a series to a 45-v battery. Draw the circuit (include an ammeter and voltmeter)
To draw the circuit diagram with four 15 ohm resistors connected in a series to a 45-v battery, along with an ammeter and voltmeter, follow the steps below:Step 1: Place the batteryTo begin with, draw the 45 V battery at the top of the page, as shown in the figure below. Step 2: Add resistorsNext, add the four 15 ohm resistors in a series circuit after the battery, as shown in the figure below.
Step 3: Add the ammeterIn the circuit, an ammeter is placed in series with the resistors to calculate the total current in the circuit. Connect the ammeter between the last resistor and the negative terminal of the battery, as shown in the figure below.Step 4: Add the voltmeter. Finally, a voltmeter is placed in parallel with the resistors to determine the voltage across them.
Connect the voltmeter in parallel with each resistor, as shown in the figure below. [Figure]Hence, this is how the circuit diagram with four 15 ohm resistors connected in a series to a 45-v battery looks like, along with an ammeter and voltmeter.
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4. What is the difference between an object's DISTANCE and its DISPLACEMENT?
Please help me with this!!!
The correct order is Option B
What is a dwarf planet?A dwarf planet is a celestial body that orbits the sun and has enough mass to assume a roughly spherical shape under its own gravity, but is not large enough to have cleared its orbit of other debris. In other words, a dwarf planet shares some of the characteristics of a planet, but is not considered a full-fledged planet because it has not cleared its orbit of other objects.
Dwarf planets are considered part of a larger class of objects known as small solar system bodies, which also includes comets, asteroids, and other objects. They are important objects to study because they can provide insights into the formation and evolution of our solar system, as well as the broader universe.
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Then, without changing speed, you round a curve and drive east. (a) Does your velocity change? (b) Do you accelerate? (a) Your velocity changes because the direction is changing. (b) Yes, because acceleration is how fast velocity changes and the velocity changed.
(a) Yes, our velocity changes because the direction is changing. (b) No, we do not accelerate.
(a) Velocity is a vector quantity that includes both magnitude (speed) and direction. When we round a curve and drive east, the direction of our motion changes.
Therefore, even if our speed remains constant, the velocity vector changes because it now points in the eastward direction instead of the previous direction.
(b) When the magnitude of the direction of the velocity is changed, we say that acceleration has occurred. In this scenario, although the direction of your velocity changes, your speed remains constant.
Since the rate at which velocity changes determines acceleration, there cannot be acceleration without a change in velocity.
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Thirteen resistors are connected across points A and B as shown in the figure. If all the resistors are
accurate to 2 significant figures, what is the equivalent resistance between points A and B?
The equivalent resistance between points A and B in the diagram is 22 Ω
How do I determine the equivalent resistance?We shall begin by obtaining the equivalent resistance in parallel (i,e the three 6 Ω resistor). Details below:
Resistor 1 (R₁) = 6 ΩResistor 2 (R₂) = 6 ΩResistor 3 (R₃) = 6 ΩEquivalent resistance (Rₜ) = ?1/Rₜ = 1/R₁ + 1/R₂ + 1/R₃
1/Rₜ = 1/6 + 1/6 + 1/6
1/Rₜ = 3/6
1/Rₜ = 1/2
Rₜ = 2 Ω
Finally, we shall determine the equivalent resistance between A and B (i.e series arrangement). Details below:
Resistor 1 (R₁) = Resistor 2 (R₂) = ... = Resistor (R₁₁) = 2 ΩEquivalent resistance (R) =?R = R₁ + R₂ + R₃ + R₄ + R₅ + R₆ + R₇ + R₈ + R₉ + R₁₀ + R₁₁
R = 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2
R = 22Ω
Thus, we can conclude that the equivalent resistance is 22 Ω
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The drone can fly for 25 minutes before the battery needs recharging.
The power output of the battery is 65.0 W
Calculate the maximum energy stored by the battery.
Answer:
105.6 KJ
Answer
3.7/5
4
hope this will help you friend.
an electric dipole swings from an initial orientation i to a final orientation f in a uniform external electric field e. the electric ddipole moment is 1.60 x 10 c m; the field magnitude is 3.00 x 10 n/c. what is the change in the dipole's potential energy?
It is not possible to determine if one needs to increase the pull on the string when increasing the speed of the stopper without additional information about the apparatus and the forces involved.
Factors such as the mass of the stopper, the tension in the string, and the radius of the circle being traversed by the stopper will all affect the necessary force to keep the stopper moving in a circular path.
It is recommended to take measurements and analyze the data to understand the relationship between the speed of the stopper and the force required to keep it moving in a circle.
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according to a fire test by the national institute for standards and technology, how quickly can flashovers occur after flames are ignited?
According to a fire test by the National Institute for Standards and Technology (NIST), flashovers can occur within as little as 3 to 4 minutes after flames are ignited in a room or enclosed space.
A flashover is a rapid and extreme escalation of a fire, where all the combustible materials in a room simultaneously ignite and cause the entire space to become engulfed in flames. Flashovers are one of the most dangerous and deadly aspects of a fire, and they can be triggered by a variety of factors such as high temperatures, lack of ventilation, and the presence of flammable materials. Understanding the conditions that can lead to a flashover is important for fire safety planning and prevention.
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Which is an action that can cause an object to move or change its state of motion?
A. Energy
B. Force
C. Equilibrium
D. Inertia
Answer: B. Force
yes the answer is force
Explanation:
Force is a push or pull which can change the state of body whether it is rest or in motion or tries to change the state of body.
I’m offering 15 points for this 1 multiple choice question. The answer is not D. Pls answer, though I think I know the the answer, but I just want to make sure.
Answer:
I wanna say C
Explanation:
because A would be getting it nowhere and B would just take more time but when you use C it would be the greatest force.
What is the speed of sound in metro city if the temperature is 26 degree celsius ?
Given equal time periods, which statement about radioactive waste is correct?
A. Radioactive decay and nuclear fission always generate the same amount of waste.
B. Nuclear fusion generates less radioactive waste than radioactive decay does.
C. Nuclear fusion generates less radioactive waste than nuclear fission does.
D. Nuclear fission generates less radioactive waste than radioactive decay does.
Box is kicked (given an initial speed), causing it to slide along a level floor. There is friction acting between the box and floor surfaces. What is true about this motion
Answer:
I would assume that the box slows down due to the frictional force between the floor and the box. In addition, the frictional force points opposite of the boxes motion. As we know, the box was given an initial speed, therefore, having an applied force. Hence, we can conclude that the frictional force opposing the motion of the crate is equal to the applied force but acting in the opposite direction. This frictional force is called static friction. When we increase the applied force (push harder), the frictional force will also increase until it reaches a maximum value.
Hope that helps!
How do you calculate substrate concentration in Km?
Michaelis-Menten equation assumes that enzyme-substrate complex forms and breaks down rapidly compared to the overall reaction rate and that reaction occurs under steady-state conditions.
What is Michaelis constant Km?Michaelis constant Km is a measure of affinity of enzyme for its substrate and is defined as the substrate concentration at which reaction rate is half its maximum value.
Michaelis-Menten equation is used to model rate of enzyme-catalyzed reaction as a function of substrate concentration : v = (Vmax [S]) ÷ (Km + [S])
v : reaction rate
[S] : substrate concentration
Vmax : maximum reaction rate
Km : Michaelis constant
To calculate the substrate concentration at Km, we can rearrange the Michaelis-Menten equation as follows: Km = {[S] * Vmax} ÷ {(v - [S])}
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Determine the fans airflow in m^3/s.Fan has an airflow of about 1.55x10^3 ft^3/minMeaning that about 1.55x10^3 cubic feet of air move over the fan blades each minute
ANSWER:
0.732 m^3/s
STEP-BY-STEP EXPLANATION:
We must convert from ft^3/min to m^3/s.
To do this, we must take into account the following conversion factors:
1 meter is equal to 3.28 feet
1 minute is equal to 60 seconds
Knowing this, we do the conversion just like this:
\(1.55*10^3\frac{ft^3}{min}\cdot\left(\frac{1\text{ m}}{3.28\text{ ft}}\right)^3\cdot\frac{1\text{ min}}{60\text{ s}}=0.732\text{ m}^3\text{/s}\)The fans airflow in m^3/s is 0.732
If the voltage waveform in fig. 2 is applied across the terminals of a 5-h inductor, calculate the current through the inductor.
The current through the inductor is 0.0764 A. To calculate the current through the 5-H inductor, use the following steps:
Step 1: Calculate the peak voltage.The peak voltage is the highest voltage of the waveform. In this case, the peak voltage is 120 volts.
Step 2: Calculate the angular frequency. The angular frequency is calculated using the formula,ω = 2πf
where f is the frequency of the waveform.
In this case, f = 50 Hz.ω
= 2π × 50
= 314.16 rad/s
Step 3: Calculate the reactance of the inductor. The reactance of the inductor is given by the formula,
XL = ωL where L is the inductance of the inductor.
In this case, L = 5 H.XL
= ωL
= 314.16 × 5
= 1570.8 Ω
Step 4: Calculate the current. The current through the inductor is given by the formula,
I = V/XL where V is the voltage across the inductor.
I = V/XL
= 120/1570.8
= 0.0764 A
Therefore, the current through the inductor is 0.0764 A.
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How much force is required to stretch a spring 12 cm, if the spring constant is 55 N/m?
Answer:
Explanation:
F = -kΔx
Since the spring constant is given in N/m, we need to convert the stretch to meters as well.
12 cm = .12 m
Now we can solve the problem:]
F = -55(-.12) so
F = 6.6N
The force required to stretch the spring is 6.6 N
Data obtained from the question Extention (e) = 12 cm = 12 / 100 = 0.12 mSpring constant (K) = 55 N/mForce (F) =? How to determine the forceThe force acting on a spring is given by:
Force (F) = spring constant (K) × Extention (e)
F = Ke
With the above formula, we can obtain the force required to stretch the spring as follow:
F = Ke
F = 55 × 0.12
F = 6.6 N
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Trong thí nghiệm giao thoa trên mặt nước, hai nguồn kết hợp A và B cách nhau 32 cm dao động cùng
pha với tần số f = 16 Hz. Biết tốc độ truyền sóng trên mặt nước là 48 cm/s. Một đường tròn có tâm tại trung
điểm O của AB, nằm trong mặt phẳng chứa các vân giao thoa, bán kính 20 cm. Số điểm dao động cực tiểu
thuộc đường tròn là
Answer:
48cm by the minus of difference of 32 CM length 20 CM because of the length of the building
A plane is traveling at Mach 0.950 through air at a temperature of 0ºC. What is the plane's speed? (Speed of sound at 0ºC is 331 m/s.)
1) 314 m/s
2) 331 m/s
3) 348 m/s
4) 353 m/s
5) Mach number is undefined at 0ºC.
Answer:
The plane's speed is approximately 900 km/h or 559 mph.
Explanation:
An airplane travels for 2.5 hours at an average rate
of 130 miles per hour. Use the distance formula, d=rt, to find how
far the plane travels.
The plane travels a distance of 325 miles if the airplane travels for 2.5 hours at an average speed of 130 miles per hour. Using the distance formula (d = rt), we can calculate the distance.
To find the distance traveled by the airplane, we can use the distance formula, which is represented as d = rt. In this formula, "d" represents the distance, "r" represents the rate or speed at which the object is traveling, and "t" represents the time taken for the travel.
Given that the airplane travels for 2.5 hours at an average rate of 130 miles per hour, we can substitute these values into the formula. The rate of the airplane is 130 miles per hour, and the time taken is 2.5 hours.
Using the formula, we can calculate the distance traveled as follows:
d = rt
d = 130 mph × 2.5 hours
Multiplying the rate (130 mph) by the time (2.5 hours) gives us:
d = 325 miles
Therefore, the airplane travels a distance of 325 miles during the 2.5 hours of travel at an average rate of 130 miles per hour.
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hello I need help with this question. I started it but am confused
Given:
The mass on the table is,
\(m=1.0\text{ kg}\)The hanging mass is,
\(M=1.5\text{ kg}\)THe coefficient of friction is,
\(\mu=0.20\)let the acceleration of the whole system is a (for the hanging mass it is downward and for the mass on the table it is rightward). the tension towards The fixed point of the pulley is T.
we can write,
\(Mg-T=Ma\ldots.\ldots..\ldots\ldots.(1)\)\(ma=T-\mu mg\ldots.\ldots.\ldots..\ldots..(2)\)Adding these equations we get,
\(\begin{gathered} (M+\mu m)g=(M+m)a \\ a=\frac{(M+\mu m)g}{M+m} \end{gathered}\)Substituting the values we get,
\(\begin{gathered} a=\frac{(1.5+0.20\times1.0)9.8}{1.5+1.0} \\ =6.67m/s^2 \end{gathered}\)Hence the acceleration is 6.66 m/s^2.
I WILL GIVE BRAINLIEST TO WHOEVER GETS THIS QUESTION CORRECT!!!
Which statement is true of a distance-time graph?
A.) A line with a curve indicates that the object has a constant speed.
B.) The line in the graph points downward if the object is speeding up.
C.) The line shows a change in speed if its angle changes.
D.) The line shows the path of the object that is moving.
Answer: c) The line shows a change in speed if its angle changes.
I'm not sure
Explanation:
Everything around us emits, reflects and absorbs EM radiation differently based
Depending on their material, temperature, and other characteristics, objects in our environment emit, reflect, and absorb electromagnetic radiation in different ways, producing a wide variety of spectral fingerprints.
We are surrounded by electromagnetic radiation from both natural sources like the sun and man-made devices like cell phones and microwaves. Based on its composition and physical characteristics, every item reacts to this radiation differently. Some materials, such as metals, are great EM radiation conductors and reflect the majority of them, giving them a bright look. Some things, such things with dark surfaces or things made of carbon, absorb most of the radiation and seem black. Radiation may flow through transparent materials like glass and water because they transfer the radiation. Objects can also generate electromagnetic radiation (EM radiation), either naturally, like heat from our bodies, or artificially, like light bulbs. It's crucial to understand how objects interact with EM radiation in a variety of disciplines, including astronomy, engineering, and medicine.
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A steam power plant operates between the pressure limit of 3.0 Mpa for the boiler and 75 kPa for the condenser. The plant operates in an ideal Rankine cycle with reheater with superheated vapor enters the high pressure turbine at 3 Mpa and 300 oC, and leaves at 1 MPa. Steam is then reheated at constant pressure to 300 oC before it is expanded to 75 kPa in a low pressure turbine. Determine:
a. the moisture content at the inlet of the condanger.
b. the met works per unit mare of steam tomane In Site.
c. the heat transter to the steam in the boter in lal per ke of steam.
d. the thermal efficiency
e. the heat transfer to cooling water passing through the condenser, in kJ per kg of steam flowing.
The dryness fraction is 0.96. Using steam tables the enthalpies at points 2, 3, and 4 can be calculated as 2936.4 kJ/kg, 2892.3 kJ/kg, and 1039.2 kJ/kg, respectively. The value of q is found to be 1438.3 kJ/kg.
a) 0.2, b) 2687 kJ/kg, c) 0.16 kJ/kg.K, d) 32%, e) 2549.52 kJ/kgPart (a): The steam is superheated at 300°C and 3 MPa, using steam tables it can be seen that the dryness fraction is 0.96.Part (b): This can be calculated using the formula shown below. The net work done by the turbine is given as follows: Net work = m (h1 - h2) + m (h3 - h4) Where m is the mass of the steam entering the turbine and h1, h2, h3, and h4 are the enthalpies at the different points in the cycle.h1 is given as 3478 kJ/kg, and using steam tables the enthalpies at points 2, 3, and 4 can be calculated as 2936.4 kJ/kg, 2892.3 kJ/kg, and 1039.2 kJ/kg, respectively.
Substituting the values in the formula gives the answer as 2687 kJ/kg.Part (c): Heat transfer per unit mass of steam to the boiler can be calculated using the formula shown below:q = h1 - h4 The value of q is found to be 1438.3 kJ/kg. Part (d): The thermal efficiency of the cycle can be calculated using the formula shown below: Efficiency = Net work output/ Heat inputHeat input can be calculated as follows: Heat input = m (h1 - h4) + m (h3 - h2) The value of heat input is calculated to be 4485.4 kJ/kg Substituting the values in the formula gives the answer as 32%.Part (e): The heat transfer to cooling water passing through the condenser is given as follows:q = m (h4 - h5)Where h4 is 1039.2 kJ/kg and h5 is 48.72 kJ/kg. The value of q is calculated to be 2549.52 kJ/kg.
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A specified volume of space contains an electric field for which the magnitude is given by E=E0cos(ωt). Suppose that E0 = 20 V/m and ω = 1.0 × 107 s−1. What is the maximum displacement current through a 0.40 m2 cross-sectional area of this volume?
Answer: \(0.708\ mA\)
Explanation:
Given
\(E_o=20\ V/m\)
\(\omega =10^7\ s^{-1}\)
Cross-sectional area \(A=0.40\ m^2\)
Current density is given by
\(J=\epsilon_o \dfrac{dE}{dt}\)
Displacement current
\(\Rightarrow I=JA\\\Rightarrow I=8.854\times 10^{-12}\times 20\times 10^7\times 0.4\\\Rightarrow I=0.708\times 10^{-3}\ A\)
The required value of the maximum displacement current of the given space is \(7.08 \times 10^{-4} \;\rm A\).
Given data:
The intensity of electric field is, \(E_{0}=20 \;\rm V/m\).
The angular frequency of electric field is, \(\omega=1.0 \times 10^{7} \;\rm s^{-1}\).
The cross-sectional area of space is, \(A =0.40 \;\rm m^{2}\).
In the given problem, the instantaneous electric field is given by \(E = E_{0} \times cos(\omega t)\)
So, the expression for the current density is,
\(J= \epsilon_{0} \times \dfrac{dE}{dt}\)
Here, \(\epsilon_{0}\) is the permittivity of free space. Solving as,
\(J= \epsilon_{0} \times \dfrac{d(E_{0} \times cos(\omega t))}{dt}\\\\J= -\epsilon_{0} \times E_{0} \times \omega \times sin(\omega t)\)
And the expression for the maximum displacement current is,
\(I = J \times A\)
And the maximum displacement current is possible only when, J is positive and J will be positive for \(sin(\omega t)=-1\).
Then solving as,
\(I = (-\epsilon_{0} \times E_{0} \times \omega \times sin(\omega t)) \times A\\\\I = (-8.85 \times 10^{-12} \times 20 \times (1.0 \times 10^{7}) \times (-1)) \times 0.40\\\\I = 7.08 \times 10^{-4} \;\rm A\)
Thus, we can conclude that the required value of the maximum displacement current of the given space is \(7.08 \times 10^{-4} \;\rm A\).
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What colors of light does an object absorb and reflect if it appears red when a white light shines on it?.
The reason the object seems red is that it absorbs all other colours and only reflects red waves.
What colors are absorbed and what colors are reflected?Reflected light is what gives coloured objects their distinctive appearance. Violet, red, and orange wavelengths are absorbed when sunlight is shone on a green leaf. Green wavelengths are seen in the reflections. In each instance, we are observing the colours that contrast with the ones being absorbed.
Red is reflected when white light strikes a red object because all other hues that make up white light are absorbed. The item appears red because of this. A filter is a translucent substance that lets some colours flow through while absorbing others.
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Mary and Carl drove to the store to shop. Their trip to the store, time at the store, and the trip home are graphed here. What was their average speed for the entire trip? A) 15 km/h B) 30 km/h C) 60 km/h D) Cannot tell from this data.
Answer: is C
Explanation: i hope it helps :)
Answer:b) 30km/h
Explanation: I just had this answer on a test got it right!!thit
suppose that each component of a vector is doubled, does the magnitude of the vector increase, decrease, or stay the same
The magnitude of a vector does not change if each of its components is doubled. Therefore, the answer is, "stay the same". This is due to the Pythagorean Theorem, which states that the magnitude of a vector is determined by the square root of the sum of the squares of its components.
Because the square of a number is greater than the number itself, squaring each component and then taking the square root of the sum results in the same magnitude as before.
Let's suppose that the vector is defined as follows: a = (a₁, a₂, a₃)
The magnitude of this vector is given by the following formula:|a| = √(a₁² + a₂² + a₃²)
Now suppose that each component is doubled. Then the new vector b is defined as follows: b = (2a₁, 2a₂, 2a₃)
The magnitude of this vector is given by the following formula: |b| = √(4a₁² + 4a₂² + 4a₃²)
Notice that each term under the square root has been multiplied by 4. However, this is balanced out by the fact that we are taking the square root of the sum. Thus, we can factor out the 4 and simplify as follows:|b| = 2√(a₁² + a₂² + a₃²)
This expression is twice the magnitude of the original vector a.
Therefore, we conclude that doubling each component of a vector doubles its magnitude. Therefore, the answer is, "stay the same".
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The figure shows a uniform, horizontal beam of length = 7 m and mass = 50 kg that ishanging by two cables as shown. If a person of mass = 60 kg stands at 3.6 m from the leftend, what are the tensions (T1 and T2) in the cables? Write only the answer to T2 incanvas (in newtons).T1T2
Given:
• Length of beam = 7 m
,• Mass of beam = 50 kg
,• Mass of person = 60 kg
,• Distance of the person from the left = 3.6 m
Let's find the tensions, T1 and T2.
First make a free body sketch:
Here, the net torque = 0.
To find the tension, T1, we have:
\(T_1*l-m_Pg*(l-l_1)-m_bg*\frac{l}{2}=0\)Where:
l = 7 m
mp = 60 kg
g is acceleration due to gravity = 9.8 m/s²
l1 = 3.6 m
mb = 50 kg
Thus, we have:
\(\begin{gathered} T_1*7-60*9.8*(7-3.6)-50*9.8*\frac{7}{2}=0 \\ \\ T_1*7-1999.2-1715=0 \\ \\ T_1=\frac{3714.2}{7} \\ \\ T_1=530.6\text{ N} \\ \end{gathered}\)Therefore, the tension T1 = 530.6 N.
To find the tension T2, we have:
\(\begin{gathered} T_2*7-60*9.8*3.6-50*9.8*3.5=0 \\ \\ T_2*7-2116.8-1715=0 \\ \\ T_2*7=2116.8+1715 \\ \\ T_2=\frac{2116.8+1715}{7} \\ T_2=547.4\text{ N} \\ \end{gathered}\)Thererfore the tension T2 = 547.5 N
• ANSWER:
T1 = 530.6 N
T2 = 547.4 N