Calculate the frequency of a sound wave produced when a tennis racquet string is plucked. The tension of the string is 274 N, the mass of the string is 28 kg and the length of the string is 0.74 m.

Answer:

6.2 x 10^6

Explanation:

The 6 at the end is an exponent the carrot is the symbol

Answer:

6.2*10^7 miles

Explanation:

Answer:

A

Explanation:

m = 80 kg

a = 1.67 m/s^2

The mass is the same anywhere in the universe. So Bubba will be 80 kg anywhere. That makes A and C the only possible answers.

F = Weight = m * a

F = 80 * 1.67

F = 134 N

The answer is A

Answer:

The proper hand placement while driving is at 9 and 3 o'clock position or 10 and 2 o'clock position on the steering wheel. It is important to keep hands in the correct hand placement to ensure maximum control of the vehicle in case of sudden events or emergency situations, and to avoid fatigue or cramping in the hands and arms. Keeping hands at the proper placement allows for quick and effective responses to unexpected road conditions and enables the driver to make necessary adjustments to maintain the safety of themselves and others on the road.

The weight of the 100 kg object on the surface of the planet is approximately 8.9 × 10¹² Newtons.

To calculate the weight of a 100 kg object on the surface of a planet, we need to use the formula for gravitational force:

F = (G * M * m) / r²

Where:

F is the gravitational force (weight)

G is the gravitational constant (approximately 6.67430 × 10⁻¹¹ N m²/kg²)

M is the mass of the planet (4.8 × 10²⁴ kg)

m is the mass of the object (100 kg)

r is the radius of the planet (diameter / 2)

Given that the diameter of the planet is 12,000 km, we can find the radius by dividing it by 2:

r = 12,000 km / 2 = 6,000 km = 6,000,000 m

Now, we can substitute the values into the formula:

F = (6.67430 × 10⁻¹¹ N m²/kg² * 4.8 × 10²⁴ kg * 100 kg) / (6,000,000 m)²

Simplifying the expression:

F = (6.67430 × 10⁻¹¹ N m²/kg² * 4.8 × 10²⁶ kg) / 36,000,000,000 m²

F ≈ 8.9 × 10¹² N

Therefore, the weight of the 100 kg object on the surface of the planet is approximately 8.9 × 10¹² Newtons.

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The running speed of Jenny willl be 2.5 times the velocity she walks.

The change of distance concerning to time is defined as speed. Speed is a scalar quantity. It is a time-based component. Its unit is m/sec.

Condition 1;

She takes 25 minutes to run 1,000 m and walk 1,600 m The total time to run as well as the walk is 25 minutes.

\(\rm t = t_r +t_w \\\\ 25 = t_r +t_w\)

As we know that;

Distance = speed × time

\(\rm x_r = v_r \times t_r \\\\ t_r = \frac{x_r}{v_r}\)

For walking;

\(\rm t_w = \frac{x_w}{v_w}\)

\(\rm t = t_r +t_w \\\\ 25 = \frac{x_r}{v_r} +\frac{x_w}{v_w} \\\\ 25 = \frac{1000 \ m}{v_r} +\frac{1600 \ }{v_w} \\\\ 40 v_w +64 v_r = v_rv_w\)

Same as for condition 2;

\(\rm 100 v_w + 40 v_r = v_rv_w\)

\(\rm 40 v_w +64 v_r =\rm 100 v_w + 40 v_r \\\\ v_r = 2.5 v_w\)

Condition 3;

\(\rm d_w = 800 \ m\)

\(\rm d_w = v_w \times t_w\)

\(\rm t_w = \frac{d_w}{v_w } \\\\ \rm t_w = \frac{800}{v_w } \\\\\)

Hence their running speed of Jenny willl be 2.5 times the velocity at she walks.

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Answer:

if you make it longer it would require less force.

Explanation:

Answer:

true

Explanation:

is true because i feel that is true

Answer:

Force and acceleration are related in a linear fashion. A Newton is the amount of force applied to a 1 g object that will cause it to have an acceleration of 1 km/s^2. The net force on an object is the resultant of the force vectors. The process of breaking a vector into its components is called vector resolution.

Explanation:

Force and acceleration are related in a linear fashion. A Newton is the amount of force applied to a 1 g object that will cause it to have an acceleration of 1 km/s^2. The net force on an object is the resultant of the force vectors. The process of breaking a vector into its components is called vector resolution.

Answer:

Yea

Explanation:

Let's compare a brick to a small table, does it take more force and strength to push a car or a small table? A car, because it's heavier and has more mass.

Answer:

Heavier objects (objects with more mass) are more difficult to move and stop. Heavier objects (greater mass) resist change more than lighter objects. Example: Pushing a bicycle or a Cadillac, or stopping them once moving. The more massive the object (more inertia) the harder it is to start or stop.

Explanation:

☝️

a) The gravitational potential energy of the system of three masses at the given positions is 188.36md.

(b) The redefined reference height is h₀ = 0.55d.

(c) The new reference height measured from the base is h₀' = 0.96d.

(a) The gravitational potential energy of the system of three masses at the given positions is calculated as;

total gravitational potential energy = P.E(mass 1) + P.E(mass 2) + P.E(mass 3)

T.G.P.E = m₁gh₁ + m₂gh₂ + m₃gh₃

where;

T.G.P.E = (4.6m x 9.8 x 3d) + (2.21m x 9.8 x 2d) + (m x 9.8 x d)

T.G.P.E = 135.24md  +   43.32md  + 9.8md

T.G.P.E = 188.36md

(b) The redefined reference height is calculated as follows;

0 =  (4.6m x 9.8 x h₀) + (2.21m x 9.8 x (h₀ - d) + (m x 9.8 x (h₀ - 2d)

0 = 45.08mh₀ + 21.66mh₀ - 21.66md  +  9.8mh₀ - 19.6md

0 = 45.08h₀ + 21.66h₀ - 21.66d  +  9.8h₀ - 19.6d

0 = 76.54h₀ - 41.26d

76.54h₀ = 41.26d

h₀ = 41.26d/75.54

h₀ = 0.55d

(c) The new reference height measured from the base such that the highest two objects have the exact same gravitational potential energy is calculated as follows;

m₂gh₂ = m₁gh₁

2.21m x 9.8 x h₂ = 4.6m x 9.8 x h₁

21.66mh₂  =  45.08mh₃

21.66h₂  =  45.08h₁

h₁ = 21.66h₂/45.08

h₁ = 0.48h₂

h₀' = 0.48 x (2d)

h₀' = 0.96d

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The graph of the given values in the table is shown below:

In the previous graph, speed is represented by the vertical values (each unit represents 10.0 m/s) and time is represented by horizontal values (each unit represents 1.0s).

As you can notice on the graph, for a time of 5.0s the speed is 25.0m/s (by considering the red lines with show the values on vertical and horizontal axis)

The force is 400.2 N

The work done is 120 J

The power is 48W

Force is a physical concept that describes the influence that one object has on another object, causing it to accelerate or deform. Force can be defined as any influence that changes the motion of an object, such as a push or a pull.

How to solve:

under equilibrium condition

F * 1.45 m =68 kg * 9.81 m/s^2 *0.87 m

F =400.2 N

b)

work done = m*g*h =68 kg*9.81 m/s^2*0.180 m =120.0744 J =120 J

c)

power =120.0744 J *(24 /60 s) =48.02976 W = 48 W

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Answer:

its true!!

Explanation: have a nice day !!

Answer:

Energy of gamma ray = 506250 eV

Explanation:

We are told that the mass of an electron or positron is 9 × 10-31 kg.

This means that their energies will be the same.

Thus; E_e = E_p

Now, since electron and positron annihilate to form gamma(γ) particle, then using work energy principle, we have;

E_γ + E_γ = E_e + E_p

Thus;

2E_γ = E_e + E_p

Since E_e = E_p, we now have;

2E_γ = 2E_e

Thus;

E_γ = E_e

Since all the energy of the electron is converted, then from Einstein's relativity theory, this implies that;

E_e = mc²

c is speed of light = 3 × 10^(8) m/s

And m is given as 9 × 10^(-31) kg

Thus;

E_e = 9 × 10^(-31) × (3 × 10^(8))^(2)

E_e = 810 × 10^(-16) J

Since E_γ = E_e

Thus;

E_γ = 810 × 10^(-16) J

We are given that; 1.6 × 10^(-19) J = 1eV

Thus; 810 × 10^(-16) J gives;

(810 × 10^(-16) × 1)/(1.6 × 10^(-19)) = 506250 eV

Answer:Convex lens spectacles is required for reading purpose..

Explanation:

I don't say you have to mark my ans as brainliest but if it has really helped you please don't forget to thank me...

Answer:

The water pressure on the upper pipe is 92.5 kPa.

Explanation:

Given that,

Pressure in lower pipe= 120 kPa

Speed of water in lower pipe= 1 m/s

Acceleration due to gravity = 10 m/s²

Density of water = 1000 kg/m³

Radius of lower pipe = 12 m

Radius of uppes pipe = 6 m

Height of upper pipe = 2 m

We need to calculate the velocity in upper pipe

Using continuity equation

\(A_{1}v_{1}=A_{2}v_{1}\)

\(\pi r_{1}^2\times v_{1}=\pi r_{2}^2\times v_{2}\)

\(v_{2}=\dfrac{r_{1}^2\times v_{1}}{r_{2}^2}\)

Put the value into the formula

\(v_{2}=\dfrac{12^2\times1}{6^2}\)

\(v_{2}=4\ m/s\)

We need to calculate the water pressure on the upper pipe

Using bernoulli equation

\(P_{1}+\dfrac{1}{2}\rho v_{1}^2+\rho gh_{1}=P_{2}+\dfrac{1}{2}\rho v_{2}^2+\rho gh_{2}\)

Put the value into the formula

\(120\times10^{3}+\dfrac{1}{2}\times1000\times1^2+1000\times10\times0=P_{2}+\dfrac{1}{2}\times1000\times(4)^2+1000\times10\times2\)

\(120500=P_{2}+28000\)

\(P_{2}=120500-28000\)

\(P_{2}=92500\ Pa\)

\(P_{2}=92.5\ kPa\)

Hence, The water pressure on the upper pipe is 92.5 kPa.

Given that the mass of fridge, m = 200 kg and acceleration is, a = 5 m/s^2

Force can be calculated using, Newton's law of motion,

Substituting the values, the force will be

Thus, the force needed to apply to the fridge is 1000 N.

The bug will cross the sticky region once in each cycle of its motion, where a cycle is defined as one complete round trip from the top of the bowl to the bottom and back to the top.

To find the number of cycles the bug goes through, we can use conservation of mechanical energy. At the top of the bowl, the bug has only potential energy, which is converted to kinetic energy as it slides down the bowl. At the bottom of the bowl, all of the potential energy has been converted to kinetic energy, and as the bug slides up the other side of the bowl, the kinetic energy is converted back into potential energy. At the top of the bowl again, the bug has only potential energy, and the cycle repeats.

Because there is no friction (except for the sticky patch), the total mechanical energy of the system is conserved. Therefore, the potential energy at the top of the bowl is equal to the potential energy at the bottom of the bowl, and the kinetic energy at the bottom of the bowl is equal to the kinetic energy at the top of the bowl.

We can set the potential energy at the top of the bowl to zero, and use the conservation of energy to find the potential energy at the bottom of the bowl:

mgh = (1/2)mv^2

where m is the mass of the bug, g is the acceleration due to gravity, h is the depth of the bowl, and v is the speed of the bug at the bottom of the bowl.

Solving for v, we get:

v = sqrt(2gh)

Plugging in the numbers, we get:

v = sqrt(29.810.12) = 0.775 m/s

The time it takes for the bug to slide from the top of the bowl to the bottom and back up to the top is twice the time it takes to slide from the top to the bottom:

t = 2sqrt(2h/g) = 2sqrt(2*0.12/9.81) = 0.774 s

Therefore, the frequency of the bug's motion is:

f = 1/t = 1/0.774 = 1.29 Hz

Since the bug completes one cycle in each oscillation, the bug will cross the sticky region 1.29 times per second, or approximately once every 0.78 seconds.

Answer:

Calculate the displacement of the car during the above acceleration. { ⃑ = –130 m} c. ... A 2.0 kg brick has a sliding coefficient of friction of 0.38.

Explanation:

Elements combine to form compounds. The correct answer is A.

Elements combine with each other in chemical reactions to form compounds. A compound is a substance composed of two or more different elements chemically combined in a fixed ratio by mass. For example, water is a compound composed of hydrogen and oxygen in a fixed ratio of 2:1 by mass.

B. Molecules are formed when two or more atoms combine chemically, but these atoms can be of the same element or different elements. For example, oxygen gas (O2) is a molecule composed of two oxygen atoms.

C. Atoms are the smallest unit of matter that retains the properties of an element. Atoms do not combine to form other atoms or compounds.

D. Mixtures are composed of two or more substances physically mixed together, but the substances retain their individual properties and can be separated by physical means. Mixtures are not formed by the chemical combination of elements. Examples of mixtures include air and saltwater.

Therefore, The correct answer is option A.

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Answer:

Endurance, or aerobic

Strength, or resistance training

Balance

Flexibility

Explanation:

Answer:

Walking. Walking is simple, yet powerful. It can help you stay trim, improve cholesterol levels, strengthen bones, keep blood pressure in check, lift your mood, and lower your risk for a number of diseases (diabetes and heart disease, for example).

For the following are four electrical components:

a. For components A and B, both of which obey Ohm's law, the current-voltage characteristics would be a straight line passing through the origin. The slope of the line for component B would be steeper than that of component A, indicating higher resistance.

b. The shape of the characteristic for component C, the filament lamp, can be explained by its construction. A filament lamp consists of a filament made of a resistive material, typically tungsten, which heats up and emits light when an electric current passes through it.

c. The component chosen for D, which does not obey Ohm's law, could be a diode. A diode is a two-terminal electronic component that allows the current to flow in only one direction.

For the following are four electrical components:

a. Sketches of current-voltage characteristics:

For components A and B, both of which obey Ohm's law, the current-voltage characteristics would be a straight line passing through the origin. The slope of the line for component B would be steeper than that of component A, indicating higher resistance.

  Current (I)

     ^

     |          B

     |         /

     |        /

     |       /

     |      /

     |     /

     |    /

     |   /

     |  /

     | /

     |/

     +------------------> Voltage (V)

     Current (I)

     ^

     |          A

     |         /

     |        /

     |       /

     |      /

     |     /

     |    /

     |   /

     |  /

     | /

     |/

     +------------------> Voltage (V)

For component C, a filament lamp, the current-voltage characteristic would be a curve that is not linear. It would exhibit a non-linear increase in current with increasing voltage. At lower voltages, the lamp would have low resistance, but as the voltage increases, the resistance of the filament also increases due to the phenomenon of thermal self-regulation. This leads to a slower increase in current at higher voltages.

For component D, a component that does not obey Ohm's law, the current-voltage characteristic could be any non-linear curve depending on the specific component chosen. Examples of components that do not obey Ohm's law include diodes and transistors.

b. The shape of the characteristic for component C, the filament lamp, can be explained by its construction. A filament lamp consists of a filament made of a resistive material, typically tungsten, which heats up and emits light when an electric current passes through it. As the voltage across the filament increases, the temperature of the filament increases as well, causing its resistance to increase. This increase in resistance results in a slower increase in current with increasing voltage, leading to the characteristic non-linear curve observed.

c. The component chosen for D, which does not obey Ohm's law, could be a diode. A diode is a two-terminal electronic component that allows the current to flow in only one direction. It exhibits a non-linear current-voltage characteristic where it conducts current only when the voltage is above a certain threshold, known as the forward voltage. Below this threshold, the diode has a high resistance and blocks current flow in the reverse direction. The characteristic curve of a diode would show negligible current flow until the forward voltage is reached, after which it exhibits a rapid increase in current with a relatively constant voltage.

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Answer:

\(4.77\ \text{A}\)

Explanation:

F = Magnetic force = 4.11 N

\(I_n\) = Net current

\(I_2\) = Current in one of the wires = 7.68 A

B = Magnetic field = 0.59 T

\(\theta\) = Angle between current and magnetic field = \(65^{\circ}\)

\(l\) = Length of wires = 2.64 m

\(I\) = Current in the other wire

Magnetic force is given by

\(F=I_nlB\sin\theta\\\Rightarrow I_n=\dfrac{F}{lB\sin\theta}\\\Rightarrow I_n=\dfrac{4.11}{2.64\times 0.59 \sin65^{\circ}}\\\Rightarrow I_n=2.91\ \text{A}\)

Net current is given by

\(I_n=I_2-I\\\Rightarrow I=I_2-I_n\\\Rightarrow I=7.68-2.91\\\Rightarrow I=4.77\ \text{A}\)

The current I is \(4.77\ \text{A}\).

Answer:

We are given:

m = 1500 kg

initial velocity (u) = 35 m/s

final velocity (v) = 0 m/s

time (t) = 5 seconds

acceleration = a m/s/s

Force (f) = F  newtons

Solving for acceleration:

Using the first equation of motion:

v = u + at

replacing the variables

0 = 35 + a(5)

a = -35/5

a = -7 m/s/s

Force applied by the brakes:

From newton's second law of motion:

F = ma

replacing the variables

F = (1500)(-7)

F = -10500 N

Therefore, the force applied by the brakes is -10500 N, we have a negative sign since the force is being applied opposite to the direction of motion

Answer:

Part A

\(x = 0.33 \ m\)

Part B

\(y = 23.49 \ m/s\)

Explanation:

From the question we are told to convert

    13 inches to meters

Now

     1 in   =   0.0254 \  m

      13 \  in  =  x  m

=>  \(x = \frac{13 * 0.0254 }{1}\)

=>     \(x = 0.33 \ m\)

For  part B  we are told to covert 77ft/s  to meters /srconds

   So  

         1 ft/s  =  0.305 \ m/s  

         77 ft/s  =  y

=>      \(y = \frac{77 * 0.305 }{1}\)

=>     \(y = 23.49 \ m/s\)

If the dog walked at a constant speed the whole way, the graph of the dog's position versus time would be a straight line. This is because the dog's velocity (which is the derivative of position with respect to time) would be constant, and the acceleration (which is the derivative of velocity with respect to time) would be zero.

A straight line on a position-time graph indicates that the object is moving at a constant velocity. The slope of the line would be equal to the velocity of the dog.

If the graph is a horizontal line, it would indicate that the dog is at rest. If the line slopes upward, the dog is moving in the positive direction (for example, to the right in a position-time graph), and if the line slopes downward, the dog is moving in the negative direction.

In all, A constant speed means a constant velocity and the line is a straight line with a particular slope.

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Answer:

(a) 4.83 seconds

(b) 167.3m

(c) 40m

Explanation:

This is a two-dimensional motion. Therefore, the components of the initial velocity - \(u_X\) and \(u_Y\) - in the x and y directions are given as follows:

\(u_X\) = u cos θ                 --------------(*)

\(u_Y\) = u sin θ                -------------(**)

Where

θ = angle of projection

(a) To calculate the time taken for the apple to strike the ground.

For simplicity, let's first calculate the maximum height H reached by the apple.

Using one of the equations of motion as follows, we can find H:

v² = u² + 2as               ---------------(i)

Where;

v = velocity at maximum height = 0 [at maximum height, velocity is 0]

u = initial vertical velocity of the apple = \(u_Y\)

=> u = \(u_Y\) = u sin θ

=> \(u_Y\) = 40 sin 30°

=> \(u_Y\) = 40 x 0.5

=> \(u_Y\) = 20 m/s

a = acceleration due to gravity = -g [apple moves upwards against gravity]

a = -10m/s²

s = H = maximum height reached from the top of the building

Substitute these values into equation (i) above to have;

0² = \(u_Y\)² + 2aH

0² = (20)² + 2(-10)H

0 = 400 - 20H

20H = 400

H = 20m

The total time taken to strike the ground is the sum of the time taken to reach maximum height and the time taken to strike the ground from maximum height.

=>Calculate time t₁ to reach maximum height.

Using one of the equations of motion, we can calculate t₁ as follows;

v = \(u_Y\)  + at                ---------------(ii)

Where;

v = velocity at maximum height = 0

u = initial vertical velocity of the apple = \(u_Y\)

a = -g = -10m/s²           [acceleration due to gravity is negative since the apple is thrown upwards to reach maximum height]

t = t₁ = time taken to reach maximum height.

Equation (ii) then becomes;

0 = 20  + (-10)t₁

10t₁ = 20

t₁ = 2 seconds

=>Calculate time t₂ to strike the ground from maximum height.

Now, using one of the equations of motion, we can calculate the time taken as follows;

Δy = \(u_Y\) t + \(\frac{1}{2}\)at                ---------------(iii)

Where;

Δy = displacement from maximum height to the ground = maximum height from top of building + height of building = 20 + 20 = 40m

a = g = 10m/s²            [acceleration due to gravity is positive since the apple is now coming downwards from maximum height]

t = t₂    [time taken to strike the ground from maximum height]

\(u_Y\) = initial vertical velocity from maximum height = 0

\(u_Y\) = 0

Equation (iii) then becomes

40 = 0t + \(\frac{1}{2}\)(10)t₂²

40 = 5t₂²            [divide through by 5]

8 = t₂²

t₂ = ±\(\sqrt{8}\)

t₂ = ±\(2\sqrt{2}\)

t₂ = +2\(\sqrt{2}\) or -2\(\sqrt{2}\)

since time cannot be negative,

t₂ = 2\(\sqrt{2}\) = 2.83 seconds

Therefore, the time taken for the apple to strike the ground is;

t₁ + t₂ = 2 +  2.83 = 4.83 seconds

(b) The distance from the foot of the building where the apple will strike the ground

Since this is the horizontal distance, we use the horizontal version of equation (iii) as follows;

Δx = \(u_X\) t + \(\frac{1}{2}\)at       -----------(v)

Where

Δx = distance from the foot of the building to where the apple strikes the ground.

\(u_X\) = initial horizontal velocity of the apple as expressed in equation (*)

\(u_X\) = 40 cos 30

\(u_X\) = 34.64 m/s

t = time taken for the motion of the apple = 4.83 seconds [calculated above]

a = acceleration due to gravity in the horizontal direction = 0. [For a projectile, there is no acceleration in the horizontal direction since velocity is constant]

Substitute these values into equation (v) as follows;

Δx = \(u_X\) t + \(\frac{1}{2}\)(0)t

Δx = 34.64 x 4.83

Δx = 167.3 m

Therefore, the distance from the foot of the building is 167.3m

(c) The maximum height reached by the apple from the ground

This is the sum of the height reached from the top of the building (20m which has been calculated in (a) above) and the height of the building.

= 20m + 20m = 40m

The break shot speed of the player is determined as 96.5 ft/s.

use the following kinematic equation to determine the time of motion of the player.

h = vt + ¹/₂gt²

h = 0 + ¹/₂gt²

h = ¹/₂gt²

t = √(2h/g)

t = √(2 x 2.75/32.17)

t = 0.171 s

vx = x/t

vx = 16.5 ft / 0.171 s

vx = 96.5 ft/s

Thus, the break shot speed of the player is determined as 96.5 ft/s.

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Answer:

Hewo Otaku Kun Here! (UwU)

Explanation:

1. A rock sitting at the edge of a cliff has potential energy. If the rock falls, the potential energy will be converted to kinetic energy.

2. Tree branches high up in a tree have potential energy because they can fall to the ground.

3. A stick of dynamite has chemical potential energy that would be released when the activation energy from the fuse comes into contact with the chemicals.

4. The food we eat has chemical potential energy because as our body digests it, it provides us with energy for basic metabolism.

5. A stretched spring in a pinball machine has elastic potential energy and can move the steel ball when released.

6. When a crane swings a wrecking ball up to a certain height, it gains more potential energy and has the ability to crash through buildings.

7. A set of double "A" batteries in a remote control car possess chemical potential energy which can supply electricity to run the car.

happy to help!

from: Otaku Kun ^^

The force in the cord ab is 37.6 lb when being lifted at a constant speed, and the angle u for balance.

The rotation of the earth is an example of a body that is moving with uniform velocity when its speed is increasing throughout an interval of time.

The sum of the forces in each direction must be zero in order to lift the block at a steady speed.

XFx = 0 : F sin θ − T sin 20° = 0

XFy = 0 : T cos 20° − F cos θ − 20 = 0

The tension in cord CAD stays constant throughout because there is no friction on the pulley: F = 20 lb.

20 sin θ − T sin 20° = 0......... (1)

T cos 20° − 20 cos θ − 20 = 0 ........(2)

Solve equation (1) for T

T = 20 sin θ/sin 20

and substitute it into equation (2).

(20 sin θ/sin 20°)cos 20° − 20 cos θ − 20 = 0

cot 20°sin θ − cos θ − 1 = 0

cot 20°sin θ − 1 = cos θ

cot 20°sin θ − 1 = √1 − sin2θ

cot²20°sin²θ − 2 cot 20°sin θ + 1 = 1 − sin²θ

(cot²20° + 1) sin²θ − 2 cot 20°sin θ = 0

csc²20°sin²θ − 2 cot 20°sin θ = 0

(csc²20°sin θ − 2 cot 20°) sin θ = 0

csc²20°sin θ − 2 cot 20° = 0 or sin θ = 0

sin θ = 2 cot 20°/csc² 20°

= 2 cos 20°sin 20° = sin 40° or sin θ = 0

θ = 40° or θ ≠ 0°.

Substitute this nonzero value for θ into the formula for T.

T =20 sin θ/sin 20°

≈ 37.6 lb

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