When a mass of m = 29 kg is hung from the middle of a fixed straight aluminum wire, the wire sags to make an angle of 12∘ with the horizontal as shown in (Figure 1) . The elastic modulus for aluminum is 7.0×1010N/m2. Determine the radius of the wire

The velocity of the boat after the package is thrown is 0.36 m/s.

Apply the principle of conservation of linear momentum;

Pi = Pf

where;

v(74 + 135) = 15 x 5

v(209) = 75

v = 75/209

v = 0.36 m/s

Thus, the velocity of the boat after the package is thrown is 0.36 m/s.

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The fundamental forces in nature are strong force, weak force, electromagnetic force, and the gravitational force.

There are four fundamental forces at work in the universe. These fundamental forces include;

Thus, the fundamental forces in nature are strong force, weak force, electromagnetic force, and the gravitational force.

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The approximate magnitude of the force between them is [tex]-4.032*10^-^6 N[/tex]

According to Coulomb, the electric force for charges at rest has the following properties:

Like charges repel each other; unlike charges attract.

Thus, two negative charges repel one another, while a positive charge attracts a negative charge.

The equation in Coulomb's law is :

[tex]F =\frac{{kq_1q_2}}{r^2}[/tex]

Where F is the force between charges, k is a constant, q₁ is the charge of the first particle, q₂ is the charge of the second particle and r is the distance between the two particle charges.

According to the question,

The given values are:-

q₁ =  +8.0 × 10⁻⁹

q₂ = –1.4 × 10⁻⁸

Substituting to the equation:

[tex]F =\frac{{kq_1q_2}}{r^2}[/tex]

=[tex]\frac{ { 9*10^{9} * 8* 10^{-9} *-1.4*10^{-8} }}{(5x10^-1)^2}[/tex]

= -4.032 x 10⁻⁶ N

Therefore,

-4.032 x 10⁻⁶ N is the approximate magnitude of the force between them.

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The total resistance of the resistors is R=44Ω. And the current will be I= 0.27 A.

Resistors are electronic components whose main function is to limit the flow of electrical charges by converting electrical energy into thermal energy.

A)The resistances connected in series in an arm of a circuit, total resistance of that arm of is given by algebric sum individual resistances.

R = R1 + R2 + R3 = 12 + 8 + 24 = 44Ω

B) Ohm's law gives that:

V = IR

Where,

(I) = V/R = 12 / 44 = 3/11 = 0.27 A

C) In series combination, all the resistances are connected one after other in a linear fashion. So, current flowing through first resistor passes to second, and then third and so on. Hence, the current flowing through all the resistance in series combination is same as the current flowing through that arm of circuit.

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The notation that is commonly used on force diagrams to show forces acting on an object is FD.

A free body diagram is a diagram that contains all the forces acting on an object.

These forces acting on an object include the following :

Thus, the notation that is commonly used on force diagrams to show forces acting on an object is FD.

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Answer:

The focal length is R/2 = 25 cm / 2 = 12.5 cm

A ray from the center of curvature is focused back on itself (R cm)

As the angle of the ray is changed to being parallel to the axis the ray from the mirror will be brought closer to the mirror      

f(parallel) < focus (back upon itself)

compare  angles of  incidence and reflection

The statement that best explains the movement of electric current is that the ground is positively charged and the clouds are negatively charged.

Lightning storm can be defined as the electrical outlet that occurs due to unsteadiness of the storm clouds and the ground.

Lightning storm occurs when opposite charges build up enough in the air leading to rapid discharge of electricity.

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Answer:

86.47 V

Explanation:

It will be multiplied by the ratio of the windings

980/340 * 30 = 86.47 v

Answer:

Probs paper cuz the rest are metals

We can get water from the sweat and exhaled breath of the people present in the space station.

We can get water from the sweat and exhaled breath. The water we drink is recycled from the sweat and exhaled breath of the people present in the space station which was collected through  condensation on the Space Station's walls.

So we can conclude we can get water from the sweat and exhaled breath of the people present in the space station.

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The speeds and velcity will be 0.020 m/sec and 0.0149 m/sec.

Speed is defined as the rate of change of the distance or the height attained. it is a time-based quantity. it is denoted by u for the initial speed while V for the final speed. its si unit is m/sec.

Given data;

d1=50 m E

d2=95 m N
Time period,t = 12 min = 12 × 60 sec = 7200 sec

The displacement is the shortest distance found from the pythogorous theorem as;

Displacement = √[(50 )²+(95)²]

Displacement = 107.35 m

a)The speed is found as;

Speed = distance / time

Speed = 50 +95 / 7200

Speed = 0.020 m/sec

b)The velocity is found as;

Velocity = Displacement / time

Velocity = 107.35 / 7200

Velocity = 0.0149 m/sec

Hence the speed and the velcity will be 0.020 m/sec and 0.0149 m/sec.

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Answer:

Probably competition with television news-

by 1953 television was becoming common in many houses and people could obtain news from television newscasts

1. The amount of work done during the lifting process is 8426.824 J

2. The average power used in the process is 80.26 Watts

Wd = mgh

Wd = 33. 2 × 9.8 × 25.9

Wd = 8426.824 J

P = Wd / t

P = 8426.824 / 105

P = 80.26 Watts

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Answer:

i don't know if this helps but The refractive index of the material of the prism of an angle 60 degree is 1.62 for sodium light. there you go hope it helps

Explanation:

Answer:motion

Explanation:

kinetic energy of an object that it possess due to its motion.

The net force on particle q3 is 112.11 N

The electrostatic force F between two charged objects placed distance apart is directly proportional to the product of the magnitude of charges and inversely proportional to the square of the distance between them.

F = kq₁q₂/r²

where k = 9 x 10⁹ N.m²/C²

The Particles q1 = -53.0 uc, q2 = +105 uc, and q3 = -88.0 uc are in a line. Particles qı and q2 are separated by 0.50 m and particles q2 and q3 are separated by 0.95 m.

The net force F3 = F13 + F23

Substitute the values, we get the force F on q3 as

F3 = 9 x 10⁹x53.0 x 10⁻⁶x 88.0 x 10⁻⁶ / (0.5+0.95)² + 9 x 10⁹x105.0 x 10⁻⁶x 88.0 x 10⁻⁶ / (0.95)²

F3 = 112.11 N

Thus, the magnitude of the force on charge q3 is 112.11 N.

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Answer: See below

Explanation:

Given:

Mass of the Mercedes-Benz (m) = 1700 kg

Inclination of the road (θ) = 15.0

The free body diagram is shown in figure attached below

a) The normal force is equal to the cos component of the weight of the car.

[tex]\begin{aligned}&f=m g \cos \theta \\&f=1700 \times 9.81 \times \cos 15 \\&f=16108.74 \mathrm{~N}\end{aligned}[/tex]

b) The static force will be equal to the weight's sin component.

[tex]\begin{aligned}&f=m g \sin \theta \\&f=1700 \times 9.81 \times \sin 15 \\&f=4316.32 \mathrm{~N}\end{aligned}[/tex]

Answer:

My Answer is Answer

Explanation:

We can use Coulomb's equation, which states that the force between two point charges is imparted: due to the other two charges ([tex]\rm Q_1[/tex] and [tex]\rm Q_2[/tex]) to obtain a net force on the +5.0 nC charge ([tex]\rm Q_3[/tex]).

[tex]\rm F = k * |Q_1 * Q_2| / r^2[/tex]

where:

F = force between the charges

k = Coulomb's constant ≈ 9.0 x [tex]\rm 10^9 N.m^2/C^2[/tex]

[tex]\rm Q_1[/tex] and [tex]\rm Q_2[/tex] = magnitudes of the charges

r = distance between the charges

Calculating the forces separately for each pair of charges and then find the net force:

Force between [tex]\rm Q_3[/tex] and [tex]\rm Q_1[/tex]:

[tex]\rm Q_3[/tex] = +5.0 nC = +5.0 x [tex]10^-^9[/tex] C

[tex]\rm Q_1[/tex] = +6.0 nC = +6.0 x [tex]10^-^9[/tex] C

[tex]\rm r_1[/tex] = distance between [tex]\rm Q_3[/tex] and [tex]\rm Q_1[/tex] = √[(0.00 m - 0.30 m[tex])^2[/tex] + (0.00 m - 0.00 m[tex])^2[/tex]] ≈ 0.30 m

[tex]\rm F_1[/tex]= k * |[tex]\rm Q_3[/tex] * [tex]\rm Q_1[/tex]| / [tex]\rm r_1^2[/tex]

[tex]\rm F_1[/tex] = (9.0 x [tex]10^9[/tex] N·[tex]\rm m^2/C^2[/tex]) * |(5.0 x [tex]10^-^9[/tex] C) * (6.0 x [tex]10^-^9[/tex] C)| / (0.30 [tex]\rm m)^2[/tex]

[tex]\rm F_1[/tex]≈ 6.0 N (towards the left)

Force between [tex]\rm Q_3[/tex] and [tex]\rm Q_2[/tex]:

[tex]\rm Q_3[/tex] = +5.0 nC = +5.0 x [tex]10^-^9[/tex] C

[tex]\rm Q_2[/tex] = -1.0 nC = -1.0 x [tex]10^-^9[/tex] C

r2 = distance between Q3 and Q2 = √[(0.00 m - 0.00 m)^2 + (0.00 m - 0.10 m)^2] ≈ 0.10 m

[tex]\rm F_2[/tex] =[tex]\rm k * |Q_3 * Q_2| / r2^2[/tex]

[tex]\rm F_2[/tex] = (9.0 x [tex]\rm 10^9 N.m^2/C^2[/tex]) * |(5.0 x [tex]10^-^9[/tex] C) * (-1.0 x [tex]10^-^9[/tex] C)| / (0.10 [tex]\rm m)^2[/tex]

[tex]\rm F_2[/tex] ≈ 45.0 N (towards the top)

Now we can sum the forces in the x and y directions to determine the net force:

Net force in the x-direction = [tex]\rm F_1[/tex] = 6.0 N (to the left)

Net force in the y-direction = [tex]\rm F_2[/tex] = 45.0 N (upwards)

The Pythagorean theorem can be used to determine the magnitude and direction of the net force.

Magnitude of net force = √(Net force in the x-direction[tex])^2[/tex]+ (Net force in the y-direction[tex])^2[/tex]

Magnitude of net force ≈ √(6.0 N[tex])^2[/tex] + (45.0 N[tex])^2[/tex]≈ √(36 [tex]\rm N^2[/tex] + 2025 [tex]\rm N^2[/tex]) ≈ √(2061 [tex]\rm N^2[/tex]) ≈ 45.4 N

The direction of the net force is the angle θ:

θ = arctan(Net force in the y-direction / Net force in the x-direction)

θ = arctan(45.0 N / 6.0 N) ≈ arctan(7.5) ≈ 82.9°

As a result, the net force exerted by the other two charges on the +5.0 nC charge has a strength of about 45.4 N and is directed about 82.9° above the negative x-axis (in the upper left direction).

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The Velocit,y Height and flow rate is is mathematically given as

Generally, the equation for the Continuity equation is  mathematically given as

A1v1=A2v2

Therefore

[tex]v2=\frac{r1^2}{r2^2}v1[/tex]

v2= 1.92m/s

Generally, the equation for Pressure  is  mathematically given as

the difference is related by

[tex]P=\rho g h[/tex]

Therefore

[tex]h=P / \rho g[/tex]

(1000)(9.81)(h)=2*10100

h=2.06m

Generally, the equation for Flow rate is  mathematically given as

[tex]F=\rho Av[/tex]

Therefore

[tex]F=(1000)\pi (0.45)^2 1.1[/tex]

F= 700kg/s

In conclusion, The resulting solutions are

v2= 1.92m/s

h=2.06m

F= 700kg/s

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Answer:

A principle stating that energy cannot be created or destroyed, but can be altered from one form to another.

Explanation:

Manufacturers of pails prefer a cone shape because it has a suitable base as well as more space for its contents.

The most common shape of pails is the shape of the frustum of a cone.

Pails are useful to contain liquids as well as some grainy solids like sand.

Because of their unique shapes, pails are able to rest on their bases and also has enough space to contain enough liquid as their top part spreads outwards.

In conclusion, the choice of shape of pails is to ensure they rest on the base and also have enough space for their contents.

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Answer:

b

Explanation:

c is a velocity time graph, showing how a body moves with constant velocity with change in time

The boom makes an angle of θ = 60.2° with the vertical wall and the tension in the horizontal rope is mathematically given as

[tex]T_1=730.85 \mathrm{~N}[/tex]

[tex]T_1'=\frac{1980.51 \mathrm{~N}}{}[/tex]

Generally, the equation for is  mathematically given as

1) Tension in vertical rope,

[tex]T_{1}=74.5 \times 9.81\\T_1=730.85 \mathrm{~N}[/tex]

2) Tension in horizontal rope,

[tex]\sum{Mg} =0\\Mg\frac{l}{2} \sin \theta+T_{1} \frac{l}{2} \sin \theta &=T_{2} l \cos \theta \\[/tex]

[tex]T_{2} &=\frac{M g(l / 2) \sin \theta+T_{1}(l / 2) \sin \theta}{l \cos \theta} \\\\&=\frac{M g \tan \theta}{2}+\frac{T_{1} \tan \theta}{2} \\\\T_{2} &=\frac{142 \times 9.81 \tan 61.8}{2}+\frac{730.85 \times \tan 61.8}{2} \\\\=& 1299+681.51[/tex]

[tex]T_1=\frac{1980.51 \mathrm{~N}}{}[/tex]

In conclusion, the tension in the horizontal rope is

[tex]T_1=\frac{1980.51 \mathrm{~N}}{}[/tex]

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1)The centripetal acceleration will be 84622.360 km/h².

2)The time the turn take is 0.19 hour.

3)The distance the airplane cover during the turn is 505.54 km.

The acceleration needed to move a body in a curved way is understood as centripetal acceleration.

The direction of centripetal acceleration is always in the path of the center of the course. The total acceleration is the result of tangential and centripetal acceleration.

The given data in the problem;

R is the radius= 80.5 m

v is the linear speed = 2610 km/h

a is the total acceleration.

1)

The centripetal acceleration is found by

[tex]\rm a_c = \frac{v^2}{R} \\\\ a_c = \frac{(2610 \ km/h)^2}{80.5} \\\\ a_c = 84622.360 \ km/h^2[/tex]

2)

The time the turn take is;

[tex]\rm a= \frac{4 \pi^2R}{T^2} \\\\\ 84622.360 = \frac{4 \times (3.14)^2 \times 80.5}{T^2} \\\\\ T = 0.19 \ hr[/tex]

3)

The distance the airplane cover during the turn is;

C= 2πR

C=2 × 3.14 × 80.5 km

C= 505.54 km

Hence centripetal acceleration, time the turn take, and distance the airplane cover during the turn will be 84622.360 km/h²,0.19 sec, and 505.54 km respectively.

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(a) The magnitude of acceleration in a vertical takeoff from the Moon will be 0.73 m/s².

(b)Option d is correct.

Force is defined as the push or pulls applied to the body. Sometimes it is used to change the shape, size, and direction of the body.

Force is defined as the product of mass and acceleration. Its unit is Newton.

Given data;

Force, F =?

Mass of a fully loaded module,m = 10,600 kg

Acceleration due to gravity on moon,g = 1.67 m/s²

Thrust of its engines is,F= 25,500 N.

The net force is found as follows;

[tex]\rm F_{net} = F -W[/tex]

ma = F-W

(10,600) kg × a = 25,500 N - (10,600 kg )(1.67)

a = 0.73 m/s²

b)

Yes, it lifts off from Earth. Because the thrust of the module's engines is greater than its weight on Earth.

F>W

Hence option d is correct.

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Answer:

m=image distance÷object distance

Answer:

tough

ques

Explanation:

The statement regarding work and retirement that is true is that most older Americans say they would prefer to enter retirement gradually.

Retirement is defined as the time in an individuals life that such leaves the Labour market or the workforce.

In some countries such as the United States of America, most elderly citizen prefer taking retirement process slowly.

Therefore, the statement regarding work and retirement is that retirement is a gradual process which one starts to process while actively in service

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The direction of torque τ this method is mathematically given as

D=X  

Option A is correct.

Generally, the equation for torque is  mathematically given as

τ = r X F

Since F is the force exerted on the body at r, we need to know the direction of this torque with regard to the body's center of mass.

In conclusion, the direction of this method is

D=X   Option A.

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When the fish begins to swim around, the reading of the scale won't change because mass of the fish and the bucket is constant.

The weight of the fish inside the bucket depends on the mass of the bucket and fish.

W = mg

where;

Thus, when the fish begins to swim around, the reading of the scale won't change because mass of the fish and the bucket is constant.

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