Why are sedimentation pond useful for reducing the affects of soil erosion?

- They provide a water source that can be used for irrigation of crops?
-They help transport soil sediments to rivers, ponds and lake.
-They provide a place to raise fish that can be use to replace fish harmed by sedimentation
-They provide a place to collect soil sediments so that it doesn't reach ponds, lakes and rivers

Answer: D (They provide a place to collect soil sediments so that it doesn't reach ponds, lakes and rivers)

Explanation: I just took the test on accelerate. :)

Answers

Answer 1

Sedimentation ponds are useful for reducing the effects of soil erosion because : ( D ) They provide a place to collect soil sediments so that it doesn't reach ponds, lakes and rivers

What are sedimentation ponds ?

Sedimentation ponds are ponds that hold sediments and suspended solids discharged by runoff waters thereby preventing the soil sediments from reaching water bodies such as ponds, lakes and rivers.

The sediment ponds hold the water while allowing the debris and solids contained in the water to settle down.

Hence we can conclude that sedimentation ponds provide a place to collect soil sediments so that it doesn't reach ponds, lakes and rivers

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Related Questions

20. What is the meaning of intuition?
A. Using facts and observations to make a conclusion
B. Quickly understanding something without needing mental reasoning
C. Praising others instead of criticizing
D. Making decisions with strict requirements

Answers

Answer:

B) Quickly understanding something without needing mental reasoning

Answer:

[tex]\huge\boxed{\sf Option \ B}[/tex]

Explanation:

Intuition means:Taking quick decisions.Understanding quickly without using the conscious mind.Instinct.

So, Intuition actually means quickly understanding something without needing mental reasoning.

[tex]\rule[225]{225}{2}[/tex]

2. A transformer has 300,000 windings in its primary coil and uses 12,000V AC input. Show your work!
A) (4 points) How many windings would be needed to produce at output of 110V AC? Is this a step down or step up transformer?


B) (3 points) Explain why a transformer only works with AC and not DC currents.

Answers

The number of windings that would be needed to produce an output of 110V AC will be 2750.

What is induced voltage?

Electromagnetic induction is what causes the induced voltage. Electromagnetic induction is the process of generating emf (induced voltage) by subjecting a conductor to a magnetic field.

Typically, a transformer's primary winding is attached to the input voltage source and changes electrical power into a magnetic field.

The secondary winding's role is to turn this alternating magnetic field into electricity, generating the necessary output voltage.

The relation between the primary and the secondary winding is;

[tex]\rm \frac{V_s}{V_p}= \frac{N_s}{N_p} \\\\ \frac{110}{12000}= \frac{N_S}{300000} \\\\ N_s = 2750 \[/tex]

Transformers can only operate on AC current, since a flux shift is required for the induction process.

Additionally, since there won't be any flux change phenomena in the DC supply, the induction process can't take place. Transformers are utilized in AC supplies because of this.

Hence, the number of windings that would be needed to produce an output of 110V AC will be, 2750 and a transformer only works with AC.

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Part A
How did Einstein’s and Newton’s theories differ in terms of explaining the cause of gravity?

Answers

Newton thinks that object falls due to gravity whereas Einstein thinks gravity is not the reason behind it.

How did Einstein’s and Newton’s theories differ in terms of explaining the cause of gravity?

Newton concluded that objects fall because they are pulled by Earth's gravity. Einstein's thinks that these objects do not fall due to gravity. According to Einstein, these objects and Earth just freely move in a curved spacetime

So we can conclude that Newton thinks that object falls due to gravity whereas Einstein thinks gravity is not the reason behind it.

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A crate with a mass of 175.5 kg is suspended from the end of a uniform boom with a mass of 94.7 kg. The upper end of the boom is supported by a cable attached to the wall and the lower end by a pivot (marked X) on the same wall.
Calculate the tension in the cable.

Answers

The tension in the cable is mathematically given as

T =266.659 N

What is the tension in the cable.?

Generally, the equation for the angle of the boom with horizontal is  mathematically given as

A = tan-1(5 /10)

[tex]A= 26.57 \textdegree[/tex]

The angle of cable with horizontal

B = tan-1(4 / 10)

B= 21.80 degrees

Hence

175.5 * cos26.57 + 94.7 *cos26.57 * 1/2 = T (sin(26.57+21.80)) * 1

T =266.659 N

In conclusion, the tension in the cable.

T =266.659 N

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Which of the following most directly shows how society affects physics? A. Elected officials make decisions about what research is funded. B. Physicists work on projects that will get them nominated for Nobel prize. C. Citizens panel provide input on most research projects. D. Governments budget money for national science- funding agencies

Answers

The option above which most directly shows how society affects physics is that physicists work on projects that will get them nominated for Nobel prize.

Who is a physicist?

A physicist is a person who who studies physics.

Physics is one of the branches of science which involves the study of matter, light, mechanics...

In conclusion: the option below which most directly shows how society affects physics is that physicists work on projects that will get them nominated for Nobel prize.

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A long wire carries a current of 3.0 A along the axis of a long solenoid (radius = 3.0 cm, n = 900 turns/m, current = 30 mA). What is the magnitude of the magnetic field at a point 2.0 cm from the axis of the solenoid? Neglect any end effects.
Answer is 45uT, but how do you get this?

Answers

Hi there!

Let's break this problem up into two parts.

Part A: Solenoid

The magnetic field everywhere inside a solenoid is constant, and can be found using the equation:


[tex]B = \mu_0 nI[/tex]

B = Magnetic field strength (? T)
μ₀ = Permeability of Free Space (4π × 10⁻⁷ Tm/A)
n = number of turns/meter (900)

I = current (0.03 A)

We are given all of these values, so let's solve.

[tex]B = (4\pi \times 10^{-7})(900)(0.03) = 34\mu T[/tex]

However, we also have a long wire that produces a magnetic field perpendicular to that produced by the solenoid.

Part B: Long wire

The equation for the magnetic field produced by a long wire is found by:

[tex]B = \frac{\mu_0 I}{2\pi r}[/tex]

Where 'r' is the distance from the wire.

Plug in what we know:

[tex]B = \frac{(4\pi \times 10^{-7})(3)}{2\pi (0.02)} = \mu 30 T[/tex]

Now, we must do the vector sum of these two fields to find the total magnetic field. Since they are perpendicular (solenoid field points to the side, wire fire points in or out), we can use the Pythagorean Theorem.

[tex]B_T = \sqrt{B_s^2 + B_w^2}\\\\B_T = \sqrt{(34\mu T)^2 + (30\mu T)^2} \approx \boxed{45\mu T}[/tex]

And here's our answer!

A car moves at a speed of 45 km/h, when traveling 1500 meters, how long did it take to go that distance?

Answers

Thus, the car would travel a distance of 50 metres in 4 seconds.

What do we call fixed point around which a lever pivots?
A. A fulcrum
B. A whell and axle
c. A wedge
D. A cylinder
Answer asap for beainlist

Answers

Answer is A) Fulcrum

The fixed point that a lever rotates around is called the fulcrum.

Answer:

A

Explanation:

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For a vector with origin at coordinate (0, 0) (horizontal, vertical) and end at (6, 8) northeast of the origin,
what is the horizontal component of the vector?

Answers

The horizontal component of the vector is determined as 6i.

Horizontal component of the vector

The horizontal component of the vector is calculated as follows;

V = (0 i, 0 j) + (6i, 8j)

V = (6i, 8j)

where;

6i is the horizontal component of the vector8j is the vertical component of the vector

Thus, the horizontal component of the vector is determined as 6i.

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An archer shoots an arrow at a 74.0 m distant target, the bull's-eye of which is at same height as the release height of the arrow.
(a) At what angle must the arrow be released to hit the bull's-eye if its initial speed is 33.0 m/s? (Although neglected here, the atmosphere provides significant lift to real arrows.)
°
(b) There is a large tree halfway between the archer and the target with an overhanging branch 3.50 m above the release height of the arrow. Will the arrow go over or under the branch?
under
over

Answers

A. The angle at which the arrow must be released to hit the bull's-eye is 20.7 °

B. The arrow will go over the branch.

A. How to determine the angleRange (R) = 74 mInitial velocity (u) = 33 m/sAcceleration due to gravity (g) = 9.8 m/s²Angle (θ) = ?

R = u²Sine(2θ) / g

74 = 33² × Sine (2θ) / 9.8

Cross multiply

74 × 9.8 = 33² × Sine (2θ)

725.2 = 1098 × Sine (2θ)

Divide both sides by 1098

Sine (2θ) = 725.2 / 1098

Sine (2θ) = 0.6605

Take the inverse of sine

2θ = Sine⁻¹ 0.6605

2θ = 41.3

Divide both sides by 2

θ = 41.3 / 2

θ = 20.7 °

B. How to determine if the arrow will go over or under the branch

To determine if the arrow will go over or under the branch situated mid way, we shall determine the maximum height attained by the arrow. This can be obtained as follow:

Initial velocity (u) = 33 m/sAcceleration due to gravity (g) = 9.8 m/s²Angle (θ) = 20.7 °Maximum height (H) = ?

H = u²Sine²θ / 2g

H = [33² × (Sine 20.7)²] / (2 ×9.8)

H = 6.94 m

Thus, the maximum height attained by the arrow is 6.94 m which is greater than the height of the branch (i.e 3.50 m).

Therefore, we can conclude that the arrow will go over the branch

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a bus strats from from rest. if the accleration is 2m/s,find the distance travelled and the velocity after 2 seconds​

Answers

Answer:

Velocity: 4 m/s

Distance: 4 m

Explanation:

initial velocity: u = 0 m/s

Acceleration: a = 2 m/s²

Time taken: t = 2 seconds

Distance traveled: d = (what we need to find)

Final velocity: v = (what we need to find)

---------------------------------------

v = u + at

v = 0 + 2 × 2

v = 4 m/s

---------------------------------------

d = 0 × 2 + 1/2 × 2 × (2)²

d = 1/2 × 2 × 4

d = 4 m

3. a) (4 points) Compare and contrast magnetic and electric fields. Your answer should include at least 2 ways they are similar and 2 ways that they differ.


b) (4 points) Include a diagram of an electric field for a positive test charge and a diagram for a typical bar magnet. Make sure you show the field lines (including direction) and label the charges and poles.

Answers

A magnetic field is a field explaining the magnetic influence on an object in space.

A electric field is a field defined by the magnitude of the electric force at any given point in space.

What are magnetic field and electric fields?

A magnetic field is a field explaining the magnetic influence on an object in space.

A electric field is a field defined by the magnitude of the electric force at any given point in space.

The difference between magnetic fields and electric filed are:

Electric Filed

Magnetic fields creates an electric charge in surrounding.It is measured as newton per coulomb, volt per meter.An electric field is measured using an electrometer.It is proportional for the electric charge.

Magnetic Filed:

Magnetic filed creates an electric charge around moving magnets.It is measured as gauss or tesla.The magnetic field is measured using the magnetometer.It is proportional to the speed of electric charge

Similarities between Electric and Magnetic Field

Both are vector quantitiesBoth are measurableBoth produce attraction and repulsion forcesBoth are proportional to electrical charge

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Need help in showing how to get the final velocity​

Answers

I don't think the provided solution is correct because it's not dimensionally consistent. The quantity [tex]8h-1[/tex] in particular doesn't make sense since it's mixing a distance with a dimensionless constant.

Here's how I think the proper answer should look:

The net force on the box acting perpendicular to the ramp is

[tex]\sum F_\perp = F_{\rm normal} - mg \cos(\theta) = 0[/tex]

where [tex]F_{\rm normal}[/tex] is the magnitude of the normal force due to contact with the ramp and [tex]mg\cos(\theta)[/tex] is the magnitude of the box's weight acting in this direction. The net force is zero since the box doesn't move up or down relative to the plane of motion.

The net force acting parallel the ramp is

[tex]\sum F_\| = mg\sin(\theta) - F_{\rm friction} = ma[/tex]

where [tex]mg\sin(\theta)[/tex] is the magnitude of the parallel component of the box's weight, [tex]F_{\rm friction}[/tex] is the magnitude of kinetic friction, and [tex]a[/tex] is the acceleration of the box.

From the first equation, we find

[tex]F_{\rm normal} = mg \cos(\theta)[/tex]

and since [tex]F_{\rm friction} = \mu F_{\rm normal}[/tex], we get from the second equation

[tex]mg\sin(\theta) - \mu mg\cos(\theta) = ma[/tex]

and with [tex]\mu = 0.25[/tex] and [tex]\theta=60^\circ[/tex], we get

[tex]a = g\sin(60^\circ) - 0.25g \cos(60^\circ) = \left(\dfrac{\sqrt3}2 - \dfrac18\right) g[/tex]

Let [tex]x[/tex] be the length of the ramp, i.e. the distance that the box covers as it slides down it. Then the box attains a final velocity [tex]v[/tex] such that

[tex]v^2 = 2ax[/tex]

From the diagram, we see that

[tex]\sin(\theta) = \dfrac hx \implies x = \dfrac h{\sin(60^\circ)} = \dfrac{2h}{\sqrt3}[/tex]

and so

[tex]v^2 = \dfrac{4ah}{\sqrt3} = \left(2 - \dfrac1{2\sqrt3}\right) hg = \dfrac14 \left(8 - \dfrac2{\sqrt3}\right) hg[/tex]

[tex]\implies v = \dfrac12 \sqrt{\left(8 - \dfrac2{\sqrt3}\right) hg}[/tex]

A proton has a positive electric charge of q = 1.6 × 10–19 coulombs. what is the electric potential at a point 5.3 × 10–11 m from the proton? 4.4 × 10–18 volts 2.7 × 101 volts 3.0 × 10–9 volts 5.1 × 101 volts

Answers

B. The electric potential at the given point from the proton is 2.7 x 10¹ volts

Electric potential of the proton

The electric potential of the proton is calculated as follows;

V = kq/r

where;

k is Coulomb's constantq is charger is distance

V = (9 x 10⁹ x 1.6 x 10⁻¹⁹)/(5.3 x 10⁻¹¹)

V = 27.2 volts

V = 2.7 x 10¹ volts

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Latency refers to the 27 seconds of time it takes for someone to refocus on driving after they finish texting or talking on the phone. true false

Answers

The term "latency" describes the 27 seconds that pass after someone has finished texting or conversing on the phone before they can concentrate again on driving. The given statement is true.

What is latency?

A measure of delay is latency. The amount of time it takes for some data to travel across a network is known as latency.

The amount of time it takes for information to travel from its source to its destination and back is often quantified as a round trip delay.

The 27 seconds that pass after someone has done texting or talking on the phone before they can focus on driving again are referred to as "latency." The assertion is accurate.

Hence, the given statement is true.

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A solid, homogeneous sphere with of mass of M = 2.35 kg and a radius of R = 12.9 cm is resting at the top of an incline as shown in the figure.
The height of the incline is h = 1.29 m, and the angle of the incline is θ = 20.1°. The sphere is rolled over the edge very slowly. Then it rolls down to the bottom of the incline without slipping.
What is the total kinetic energy (translational plus rotational kinetic energy) of the sphere when it reaches the bottom of the incline?

Answers

The total kinetic energy  of the sphere when it reaches the bottom of the incline is  44.57 J.

Total kinetic energy of the sphere

The total kinetic energy of the sphere = translational + rotational kinetic energy.

Translational kinetic energy

K.E = ¹/₂mv²

K.E(bottom) = P.E(top) = mgh

K.E = (2.35)(9.8)(1.29)

K.E = 29.71 J

Rotational kinetic energy

K.E(rot) = ¹/₂Iω²

K.E(rot) = ¹/₂I(v²/R²)

where;

I is rotational kinetic energy

I = ¹/₂MR²

K.E(rot) = ¹/₂( ¹/₂MR²)(v²/R²)

K.E(rot) = ¹/₄Mv²

K.E(rot) = ¹/₄M(2gh)

K.E(rot) = ¹/₂Mgh

K.E(rot) = ¹/₂(29.71) = 14.855 J

Total kinetic energy = 29.71 + 14.855 = 44.57 J

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The rms voltage is given by the following.
ΔVrms = ΔVmax/[tex]\sqrt{2}[/tex] = 0.707ΔVmax

Substituting the maximum voltage, we obtain
ΔVrms = ΔVmax/[tex]\sqrt{2}[/tex]

= 0.707ΔVmax = 0.707(165 V) = 117 V.
An rms voltage of 117 V corresponds to a maximum voltage of 165 V.


What is the maximum current Imax in the resistor?

Answers

The maximum current in the resistor is determined by dividing root mean square current by 0.7071.

Maximum current in the resistor

The maximum current in the resistor is calculated as follows;

I₀ = I(rms)/0.7071

where;

I₀ is the peak current or maximum current in the resistorI(rms) is the root mean - square current

Thus, the maximum current in the resistor is determined by dividing root mean square current by 0.7071.

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A barber Wants to set up a salon in a measuring Length of 3m by 3m. He has a simple Woden Chair, 3 large mirror and one bulb. a) using the knowledge of shadows and reflection, advice the barber on how to arrange a good salon using the unly items he has. b) without acking more sources of light, how can he enhance the lighting System in his salon? S A barber Wants to set up a salon in a measuring Length of 3m by 3m . He has a simple Woden Chair , 3 large mirror and one bulb . a ) using the knowledge of shadows and reflection , advice the barber on how to arrange a good salon using the unly items he has . b ) without acking more sources of light , how can he enhance the lighting System in his salon ? ​

Answers

Two mirrors are arranged such that they are parallel to each and perpendicular to the third mirror.

Also, the light is placed at the center of the three mirrors to produce multiple images by reflection.

What is reflection of light?

Reflection is the bouncing back of light waves of a reflective surface when light shines on that surface.

The knowledge of reflection of light can be used by the Barber to set up a good salon.

The mirrors are arranged in the salon such that two of the mirrors are parallel to each and perpendicular to the third mirror. Also, the light is placed at the center of the three mirrors.

The parallel arrangement of the mirror will ensure that the clients will be able to have a full frontal and back view of themselves.

The parallel and perpendicular arrangement of the mirrors will also ensure that the light placed at the center will produce reflected to produce infinite images thus lighting up the salon.

In conclusion, the reflective properties of the mirrors as well as the angle between mirrors is used to create a well-lit salon by the barber.

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A 0.10 kg mass is oscillating at a small angle from a light string of length 0.10 m.
What is the period of the pendulum?

Answers

The time  period of the pendulum is  0.65 second.

What is time period?

The time period is a period of time during which a behavior takes place or a condition persists. Depending on the type of activity or condition under consideration, it may be expressed either in seconds or in millions of years.

The mass of the object is = 0.10 kg

Length of the string is = 0.10 m.

Acceleration due to gravity is = 9.8 m/s²

Hence,  the time  period of the pendulum is = 2π√(0.10/9.8) sec

= 0.65 second.

Hence, the time period of the pendulum is  0.65 second.

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6. A student travels 4.0 m east, 8.0 m south, 4.0 m west, and finally 8.0 m north. What is her
displacement?
What distance did she travel?

Answers

The student's path traces out a rectangle and she ends up at the same spot, so her displacement is 0 m.

On the other hand, she travels a total distance equal to the perimeter of that rectangle,

4.0 m + 8.0 m + 4.0 m + 8.0 m = 24 m

Two straight long parallel wires, separated by a distance of 1.0 m, carry a current of 4.00
each. A third wire is arranged perpendicular to the two parallel wires. If the magnetic field at a point equidistant from all the wires is zero, find the current in the third wire.

Answers

The magnitude of the current in the third wire is 8 A.

Total magnetic field

E₁ + E₂ + E₃ = 0

Equidistance from the two wires = 0.5 m

Apply Biot Savart rule to determine the magnitude of the magnetic field.

μI/2πr₁ + μI/2πr₂ + μI/2πr₃ = 0

(4π x 10⁻⁷ x 4)/(2π x 0.5) + (4π x 10⁻⁷ x 4)/(2π x 0.5) + (4π x 10⁻⁷ x I₃)/(2π x 0.5) = 0

4 x 10⁻⁷ I₃ = -3.2 x 10⁻⁶

I₃  = (-3.2 x 10⁻⁶)/(4 x 10⁻⁷)

I₃ = - 8 A

Thus, the magnitude of the current in the third wire is 8 A.

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Three ropes A, B and C are tied together in one single knot K. (See figure.)
If the tension in rope A is 65.3 N, then what is the tension in rope B?

Answers

The tension in the rope B is determined as 10.9 N.

Vertical angle of cable B

tanθ = (6 - 4)/(5 - 0)

tan θ = (2)/(5)

tan θ = 0.4

θ = arc tan(0.4) = 21.8 ⁰

Angle between B and C

θ = 21.8 ⁰ + 21.8 ⁰ = 43.6⁰

Apply cosine rule to determine the tension in rope B;

A² = B² + C² - 2BC(cos A)

B = C

A² = B² + B² - (2B²)(cos A)

A² = 2B² - 2B²(cos 43.6)

A² = 0.55B²

B² = A²/0.55

B² = 65.3/0.55

B² = 118.73

B = √(118.73)

B = 10.9 N

Thus, the tension in the rope B is determined as 10.9 N.

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A mass of 2kg is attached to the end of a vertical wire of length 2m and diameter 2mm extend the wire by 1mm. Calculate the young modulus of the wire

Answers

The applied load =F=mg=2×9.8=19.6N
diameter =1mm=1×10
−3
m
=> radius=0.5×10
−7
m
Area , A=3.14r
2
=3.14×0.25×10
−6

=0.785×10
−6

We know that,
stress=Force/area
=19.6/0.785×10
−6

24.96×10
−6

change in length,ΔL=1mm=10
−3
m
Length,L=3m
hencestrain=ΔL/L
=10
−3
/3
we know that young's modulus is given by the ratio of stress and strain,
Hence,
E=24.96×10
−6
/10
−3
/3
=74.8×10
9

=7.48×10
10
Nm
−2

Lindsay is planning a flight from St. Catherines to Hamilton, which lies due west of St. Catharines.
Her aircraft flies at a speed of 200 km/h in still air. A wind of 50.0 km/h is blowing from [W 60.0° N].
In what direction must she aim the aeroplane to fly directly to Hamilton? (KU, TI)

Answers

Lindsay should fly the plane in the direction [W 12.5° S] to get Hamilton.

Using Sine rule to solve this question

Sine rule => SinA/a = SinB/b = SinC/c = constant

The magnitude of wind is 50 with an angle of 60 degrees.

The magnitude of plane is 200 and the angle at which it should fly is unknown and should be θ.

One side is 50 km/hr at an angle of 60 degrees.

sin 60°/200 = sin θ / 50

50 × sin 60° = 200 × sin θ

√3/2 = 4 × sin θ

√3/8 = sin θ

sin θ = 0.2165

θ = sin⁻¹(0.2165)

θ = 12.5°

So Lindsay have to fly the plane in the direction of [W 12.5° S].

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A slinky spring 3m long rests on a horizontal bench with one end fixed. When the free end is suddenly pushed forward, the compression pulse travels to the fixed end and back in 2 secs. What is the speed of the longitudinal waves along the spring? What is the wavelength of the longitudinal waves produced when the free end is moved to and fro with a frequency of 2.5Hz? A slinky spring 3m long rests on a horizontal bench with one end fixed . When the free end is suddenly pushed forward , the compression pulse travels to the fixed end and back in 2 secs . What is the speed of the longitudinal waves along the spring ? What is the wavelength of the longitudinal waves produced when the free end is moved to and fro with a frequency of 2.5Hz ?​

Answers

The speed of the longitudinal waves along the spring is 1.5 m/s.

The wavelength of the longitudinal waves produced when the free end is moved to and fro is 0.6 m.

What is wavelength?

The wavelength is the distance between the adjacent crest or trough of the sinusoidal wave. The wavelength is the reciprocal of the frequency of the wave.

Wavelength λ = c/f

where c is the speed of light in vacuum = 3*10⁸ m/s

A slinky spring 3m long rests on a horizontal bench with one end fixed. When the free end is suddenly pushed forward, the compression pulse travels to the fixed end and back in 2 secs.

λ = v/f

v =fλ =λ /T where T is the time period = 2sec

Put the values we get

v = 3/2 =1.5 m/s

Thus, the speed of wave is 1.5 m/s.

Using the same expression for frequency 2.5Hz, wavelength is

λ = v/f

λ = 1.5 /2.5 = 0.6 m

Thus,  the wavelength is 0.6m.

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A force F1 of magnitude 5.90 units acts on an object at the origin in a direction = 36.0° above the positive x-axis. A second force F2 of magnitude 5.00 units acts on the object in the direction of the positive y-axis. Find graphically the magnitude and direction of the resultant force F1 + F2.

Answers

The magnitude and direction of the resultant force will be 7.65 units and 40.2°.

What is force?

Force is explained as the multiplication of mass and acceleration. Its unit is N. It is the external agent which helps to change the shape and size of an object.

Force is used to push and pull the object and sometimes changes the direction of motion. The net force acting on an object is equal to the sum of all forces acting upon it.

F = F1 + F2 + F3

Given data;

Megnitude of force 1, F₁ =  5.90 units

Megnitude of force 2, F₂ = 5.00 units

α is the angle between the two forces=36.0°

Θ is the angle of the resultant force

The megnitude of the resultant force is;

[tex]\rm F =\sqrt{ F_{1}+F_{2}+2F_{1}F_{2}cos \alpha }\\\\ F = \sqrt{5.90 + 5.00 +2 \times 5.90 \times 5 \times cos 36^0 } \\\\ F = 7.65 \ units[/tex]

The direction of the resultant force is;

[tex]\rm \theta = tan^{-1}(\frac{F_{2}}{F_{1}} )[/tex]

[tex]\rm \theta = tan^{-1}(\frac{5.00}{5.90})\\\\ \theta = 40.2 ^0[/tex]

Hence the magnitude and direction of the resultant force will be 7.65 units and 40.2°.

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A treasure chest full of silver and gold coins is being lifted from a pirate ship to the shore using two ropes as shown in the figure. The mass of the treasure chest is 75.6 kg.
What is the tension in rope A?
How much tension does rope B carry?
And what is the tension in rope C?

Answers

The tension in rope A is 740.88 N, the tension carried by rope B is 751.4 N and the tension carried by rope C is -124 N.

Angle made by B with respect to horizontal

tan θ = Δy/Δx

tan θ = (10 - 4)/(5 - 4)

tan θ = 6

θ = arc tan (6) = 80.53

Net force in vertical direction

C sin(0) + B sin(80.53)  = A sin(90)

C sin(0) + B sin(80.53)  = (75.6 x 9.8)

0 + 0.986 B = 740.88

0.986 B = 740.88

B = 740.88/0.986

B = 751.4 N

Net force in horizontal direction

C cos(0) + B cos(80.53) = (75.6 x 9.8) cos(90)

C + 0.165 B = 0

C + 0.165(751.4) = 0

C + 124 = 0

C = - 124 N

Thus, the tension in rope A is 740.88 N, the tension carried by rope B is 751.4 N and the tension carried by rope C is -124 N.

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A thin flexible gold chain of uniform linear density has a mass of 17.1 g. It hangs between two 30.0 cm long vertical sticks (vertical axes) which are a distance of 30.0 cm apart horizontally (x-axis), as shown in the figure below which is drawn to scale.
Evaluate the magnitude of the force on the left hand pole.

Answers

The magnitude of the force on the left-hand pole is mathematically given as

f'=0.167N

[tex]Q=45 \textdegree[/tex]

What is the magnitude of the force on the left-hand pole.?

Generally, the equation for Force is  mathematically given as

[tex]F=\frac{mg}{sin\theta}[/tex]

Therefore

[tex]F=\frac{17.1*10^{-3}*9.8}{sin45}[/tex]

F=0.237N

Considering horizontal

f'-fcos=0

Therefore

f'=0.237*cos45

f'=0.167N

In conclusion, the slope

[tex]tan\theta=lv/ln\\\\tan\theta=30/30\\\\\theta=tan^{-1}\\\\[/tex]

[tex]Q=45 \textdegree[/tex]

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. A wheel of diameter 0.2 m starts from rest and accelerated with constant angular acceleration to an angular velocity of 900 rev min¹ in 5 s. (a) Find the position at the end of 1 s of a point originally at the top of the wheel. (b) Compute and show in a diagram the magnitude and the direction of the acceleration at the end of 1 s.​

Answers

(a)The position at the end of 1 s of a point originally at the top of the wheel will be 9.425 radians.

(b)The magnitude and the direction of the acceleration at the end of 1 s will be 1.885 m/sec² clockwise.

What is angular acceleration?

Angular acceleration is defined as the pace of change of angular velocity concerning time.

Given data;

Diameter of the wheel,d = 0.2 m

Initial velocity,ω₀ = 0

Angular acceleration,α = c

n = 900 rev min¹

ω = 94.2478 rad /sec

Time of rolling,t = 5 s

From Newton's first equation of motion;

ω = ω₀ + αt

94.2478 rad /sec  = 0 + α(5 sec)

α  = 18.85 rad/sec²

The position at the end of 1 s of a point is found as;

Θ = ω₀t+1/2(αt²)

Θ = 0+1/2[(18.85 rad/sec²) × (1 sec)²]

Θ = 9.425 radian

The magnitude and the direction of the acceleration at the end of 1 s are found as;

a = αr

a= 18.85 rad/sec² × 0.1 m

a = 1.885 m/sec²

Hence the position at the end of 1 s and magnitude and the direction of the acceleration at the end of 1 s will be  18.85 rad/sec²and the magnitude and the direction of the acceleration at the end of 1 s will be 1.885 m/sec² clockwise.

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A pan-galactic gargle (an alien) whose mass is 85 kg exploring a large asteroid. What is the force of
gravity holding it down?

Answers

The acceleration due to gravity of the asteroid is 833.85 N.

Force of gravity holding the the alien down

F = mg

where;

m is mass of the alieng is acceleration due to gravity

Assuming the acceleration due to gravity of the asteroid = 9.81 m/s²

F = 85 x 9.81

F = 833.85 N

Thus, the acceleration due to gravity of the asteroid is 833.85 N.

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