Plane Mirror Question 2 (Grade 10 Science)

Plane Mirror Question 2 (Grade 10 Science)

Answers

Answer 1

Answer:

Explanation:

The index of refraction (n) of a gem can be calculated using the formula:

n = c / v

where c is the speed of light in a vacuum (approximately 3 x 10^8 m/s) and v is the speed of light in the gem.

In this case, we know that the speed of light in the gem is l.q5 x 10^8 m/s. So, we can plug this value into the formula and calculate the index of refraction:

n = c / v = (3 x 10^8 m/s) / (l.q5 x 10^8 m/s) = 3 / l.q5

The value of n is a dimensionless number and it's usually between 1 and 2.

It's not possible to identify the gem using the index of refraction alone. There are many gems with similar indexes of refraction. Index of refraction alone is not enough to identify a gem. The gemstone's color, brilliance, and other physical and optical properties must be taken into account to identify it.

Answer 2

The index of refraction of the unknown gem is 1.54.

What is index of refraction?

The index of refraction measures how a light beam bends when it travels through different media.

The refractive index is calculated by dividing the speed of light at a given wavelength in in vacuum space by its speed of light in that medium.

The speed of light in that gem = 1.95 × 10⁸ meter/second

The index of refraction of the unknown gem is = (speed of light in vacuum/speed of light in that gem)

= (3 × 10⁸ meter/second)/(1.95 × 10⁸ meter/second)

= 1.54.

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Related Questions

I need help with my homework

Answers

C. The center of mass and center of gravity will coincide if the acceleration due to gravity is constant or uniform.

What is center of mass?

The center of mass of an object is the unique point where the weighted relative position of the distributed mass sums to zero.

What is center of gravity?

Center of gravity is the point from which the weight of a body or system may be considered to act.

Thus, the center of mass and center of gravity will coincide if the acceleration due to gravity is constant or uniform.

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By how many newtons does the weight of a 100-kg person decrease when he goes from sea level to mountain top at an altitude of 5000 m? The mean radius of the earth is 6.38 × 106 m.

Answers

The weight of a 100-kg person decreases by 4 N when he goes from sea level to mountain top at an altitude of 5000 m.

What determines the weight of a person?

The weight of a person is determined by the mass of the body and the acceleration due to gravity.

The acceleration due to gravity, g is dependent on the mass of the earth, M the radius of the earth and the gravitational force constant , G.

Mathematically, the acceleration due to gravity at the mountain top is determined using the formula:

g = GM/r²

where:

G = 6.67 × 10⁻¹¹ Nm²/kg²

M = 5.9736 x 10²⁴ kg

r = 638000 + 5000 = 6385000

g = (6.67 × 10⁻¹¹  *  5.9736 x 10²⁴ )(6385000)²

g = 9.77 m/s²

His weight at the mountain top will be:

weight = 100 * 9.77

weight = 977 N

Weight at sea level = 100 * 9.81 = 981 N

Decrease in weight = 981 - 977

Decrease in weight = 4 N

In conclusion, the weight of the man varies according to his distance from the earth.

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A boat moves through the water with two forces acting on it. One is a 1,575-N forward push by the water on the propeller, and the other is a 1,200-N resistive force due to the water around the bow. (Review attachment)

(a) What is the acceleration of the 1,100-kg boat?

______ m/s2

(b) If it starts from rest, how far will the boat move in 20.0 s?

______ m


(c) If it starts from rest, how far will the boat move in 20.0 s?

______ m/s

Answers

(a) The acceleration of the 1,100-kg boat is 0.341 m/s².

(b) The distance covered by the boat is 68.2 m.

(c) The speed of the boat is 6.82 m/s.

Acceleration of the boat

Net force on the boat = 1,575 N - 1,200 N = 375 N

F(net) = ma

a = F(net)/m

a = 375/1100

a = 0.341 m/s²

Distance moved in 20 s

s = ut + ¹/₂at²

s = 0 + ¹/₂(0.341)(20)²

s = 68.2 m

Speed of the boat in 20 s

v = u + at

v = 0 + 0.341(20)

v = 6.82 m/s

Thus, the acceleration of the 1,100-kg boat is 0.341 m/s², the distance covered by the boat is 68.2 m and the speed of the boat is 6.82 m/s.

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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, T in the cable is equal to 323.5 N.

What is the tension?

Tension is force exerted by a cable or string on another object usually a weight suspended from the cable or string

The tension in the cable is found this:

Angle of the boom with horizontal, θ = tan⁻¹(5/10) = 26.56°

The angle of cable with horizontal, B = tan⁻¹(4/10) = 21.80

Taking moments about the pivot:

175.5 * cos 26.56 + 94.7 * cos 26.56 * 0.5 = T (sin(26.56 + 21.80) * 1

T = 241.68/0.747

T = 323.5 N

In conclusion, the tension in the cable is determined by taking moments about the pivot.

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A person standing at the edge of a cliff throws one ball straight up and another ball straight down, each at the same initial speed. Neglecting air resistance, which ball hits the ground below the cliff with the greater speed?​

Answers

Since both balls have the same conditions at the cliffs edge (in downward motion), they will have the same speed just before they reach the ground. Ball B will reach the ground quicker since Ball A had to travel up and then back down again to reach the edge of the cliff.

Haley is trying to pull an object upward. The below forces are acting on the object.

Fp= 5500 N
Fg= 6000 N

Which represents the net force?

Answers

The net force is represented by ↓ 500N.

What is the net force?

The net force is the force that has the same effect in magnitude and direction as two or more forces acting together.

Now we have the forces;

Fp= 5500 NFg= 6000 N

Thus we can obtain the net force as;

5500 N - 6000 N

= - 500 N

Therefore the net force is represented by ↓ 500N.

Missing parts:

Haley is trying to pull an object upward. The below forces are acting on the object.

Fp = 5500N

Fg = 6000N

Which represents the net force?

← 500N

→ 500N

↑ 500N

↓ 500N

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When using a stream table in a classroom setting what are three factors that can be controlled?

Answers

Answer:

These include the slope of the land, the nature of the land surface, the placement of dams, and the direction of topsoil disturbance as created by farming activities. Materials: Students should work in groups of 3 or 4, or as materials allow.

Explanation:

Hope this helps

Based on the way living things are organized ehat level combines to form organ ststems

Answers

Answer:

Higher levels of organization are built from lower levels.

Molecules combine to form cells.

Cells combine to form tissues.

Tissues combine to form organs.

Organs combine to form organ systems,

and organ systems combine to form organisms.

Explanation:

Hope it helps.

Discuss the aspects of either the Gemini Program or the Soyuz Program.

Answers

Answer:

The Gemini program

Explanation:

The Gemini Program was the second human spaceflight program hosted by Nasa in the year 1961. Taking place between mission Mercury and Apollo, the Gemini spacecraft carried two people to space and marked the foundation to the upcoming Apollo mission to Moon. It was a series of missions into the outer orbital which took place between 1965 and 1966. Prior to the Gemini missions, NASA had little to no information about space and space traveling. It was crucial for them to get acquainted with life outside before establishing successful Moon landings. And the series of Gemini missions helped them do just that.

the temperature at which the velocity of sound in air is twice its velocity at 15°C

Answers

With the use of below formula, at 879 °C,  velocity will be double the velocity at 15 °C.

What is the relationship between Velocity and sound ?

The velocity of sound waves in air is proportional to the square root of Thermodynamic temperature. That is, V = K[tex]\sqrt{T}[/tex]

Given that the temperature at which the velocity of sound in air is twice its velocity at 15°C, Let us make use of the formula;

(v2/v1) = √(T2 / T1)

Where

v2 = final velocityv1 = initial velocityT2 = final absolute temperatureT1 = initial temperature.

Recall that absolute temperature = °C + 273.

If v2 = 2 × v1 and temperature in degree Celsius = 15°C, then,

Temperature in Kelvin K = 15 + 273 = 288

Substitute all the parameters into the formula

(2 × v1)/v1 = √(T2/288)

2 = √ (T2 /288)

Square both sides

4 = (T2/288)

T2 = 4 × 288

T2 = 1152K

Temperature in degrees Celsius = 1152 - 273 = 879 °C.

Therefore, at 879 °C,  velocity will be double the velocity at 15 °C.

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Checking the what will reduce the possibility of having to rebuild or replaced the engine?

Answers

Checking the oil will reduce the possibility of having to rebuild or replaced the engine.

what is an engine ?

A device created to transform one or more sources of energy into mechanical energy is known as an engine or motor. Potential energy, heat energy, chemical energy, electric potential, and nuclear energy are all forms of energy that are readily available.

The lubricating function of engine oil is crucial. It shields and stops all the moving parts from rubbing against one another. Metal-on-metal wear would quickly kill your engine without lubrication.

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Three equal positive charges 'q' are at the corners of an equilateral triangle of side 'a'.
a. Assuming that the three charges together create an electric field, find the location of a point other than the obvious one where the electric field is zero.
b. What is the magnitude and direction of the electric field at the top corner due to the two charges at the base?

Answers

(a) The location of a point where the electric field is zero is at the center of the triangle which is equal to ¹/₆√3a.

(b) The magnitude and direction of the electric field at the top corner due to the two charges at the base is  1.732 kq/a².

Position where the electric field is zero

The electric field is zero at the center of the equilateral triangle whose magnitude is equal to √3a/6.

Electric field at top corner due to two charges at the base

E = E₁ + E₂

where;

E₁ is electric field at the left base cornerE₂ is electric field at the right base corner

E = kq/a²[(cos 60i + sin 60j) + (-cos 60i + sin 60j)]

E = kq/a²[2(sin 60j)] = 1.732 kq/a²

Thus, the location of a point where the electric field is zero is at the center of the triangle which is equal to ¹/₆√3a.

The magnitude and direction of the electric field at the top corner due to the two charges at the base is  1.732 kq/a².

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Which best describes the results of Becquerel’s experiments?

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Both forming images when placed in their respective places best describes  Becquerel’s experiments.

What is Becquerel’s experiment?

This was conducted by  Henri Becquerel in which he sought to know how uranium salts are affected by light.

He discovered that the salts emits a penetrating radiation and formed an image in the presence of light but didn't form any in darkness.

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a 5.5kg bowling ball has a weight on earth closest to what in N

Answers

The weight of the body is obtained as 53.9 N.

What is the weight of an object?

The term weight refers to the product of the mass and the acceleration due to gravity.

Now we have the mass  of the body as 5.5kg and the acceleration due to gravity as 9.8 m/s^2.

It the follows that the weight is;

W = mg = 5.5kg *  9.8 m/s^2 = 53.9 N

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Define the term work and state its unit. An ant is dragging a house-fly and the elephant is pushing a big tree which is not moving. Who is doing work, the ant or the elephant? Justify your answer. 922.5 205​

Answers

Ant is performing a work

what is work?

Work is the force applied on an individual with respect to displacement.

Work = Force × displacement

Unit is Nm

Elephant is pushing bt there is no displacement occurred so the work of elephant is zero.

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The ant works, but the elephant does not.

Who works, how do find the ant and the elephant?

Work done = Force × Displacement.

If there are ants and houseflies,

Ants drag the house bug, so they use specific force to move the house bug from one point to another, so we can say they work.

In the case of the elephant and the tree,

When the elephant pushes the tree (applying a force), the tree does not move, i.e., there is no displacement, so there is work.

Work done = Force × Displacement

= Force × 0

= 0

Therefore,

The ant works, but the elephant does not.

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A truck is carrying a refrigerator as shown in the figure. The height of the refrigerator is 158.0 cm, the width is 60.0 cm. The center of gravity of the refrigerator is 67.0 cm above the midpoint of the base.
What is the maximum acceleration the truck can have so that the refrigerator doesn't tip over? (The static friction between the truck and the refrigerator is very large.)

Answers

The maximum acceleration the truck can have so that the refrigerator does not tip over is 1.86m/s².

What is acceleration?

Acceleration is the change in velocity with time.

The maximum acceleration is obtained by taking moments about the tipping point of rotation.

Moment = force * perpendicular distanceClockwise moment = Anticlockwise moment

F₂ * 1.58 m = F₁ * 0.67 m

where

F₂ is tipping force = mass * acceleration, a

F₁ is weight = mass * acceleration due to gravity, g

The weight acts at a distance half the width of the refrigerator = 30 cm or 0.3 m

Height of refrigerator is 158 cm 0r 1.58 cm

m * a * 1.58 = m * 9.81 * 0.30

a = 1.86 m/s²

The maximum acceleration the truck can have so that the refrigerator does not tip over is 1.86m/s².

In conclusion, if the maximum acceleration is exceeded, the refrigerator will tip over.

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An object with a density of 941.0 kg/m3 and a mass of 1039.0 kg is thrown into the ocean. Find the volume that sticks out of the water. (use ρseawater = 1024 kg/m3)

Answers

The volume that sticks out of the water is 83 m³.

To find the answer, we need to know about the archimedes principle.

What's archimedes principle?It says that when an object is on a water surface, the amount of force on the object is equal to the weight of water displaced by it.Mathematically, weight of the object= weight of water displaced

What's the volume of an object remain on the water surface, if the density and mass of the object are 941.0 kg/m³, 1039.0 kg respectively?Let V = volume of the object, v= volume of water displacedV-v = volume that sticks out of the waterWeight of the object = V× density of object × gWeight of water displaced= v× density of water × gAs per archimedes principle, V× density of object × g=v× density of water × gV-v = density of water - density of object

= 1024 - 941 = 83 m³

Thus, we can conclude that the volume that sticks out of the water is 83 m³.

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A hypothetical planet has a mass 2.81 times that of Earth, but the same radius.
What is g near its surface?

Answers

The acceleration due to gravity near the surface of the planet is 27.38 m/s².

Acceleration due to gravity near the surface of the planet

g = GM/R²

where;

G is universal gravitation constantM is mass of the planetR is radius of the planetg is acceleration due to gravity = ?

g = (6.626 x 10⁻¹¹ x 2.81 x 5.97 x 10²⁴) / (6371 x 10³)²

g = 27.38 m/s²

Thus, the acceleration due to gravity near the surface of the planet is 27.38 m/s².

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What is the fastest possible speed called in our universe and what is the equation for it?

Answers

Answer:

The speed of light traveling through a vacuum is exactly 299,792,458 meters (983,571,056 feet) per second. That's about 186,282 miles per second — a universal constant known in equations as "c," or light speed.

[tex]s\frac{d}{t}[/tex]

Explanation:

hope this helps you my friend

The speed of light. Nothing can travel faster than speed because of their massless particles that include photons. The equation is c = 1/(e0m0)1/2 = 2.998 X 108m/s

Calculate the de Broglie wavelength of a 0.56 kg ball moving with a constant velocity of 26 m/s (about 60 mi/h)

Answers

The de Broglie wavelength of a 0.56 kg ball moving with a constant velocity of 26 m/s is 4.55×10⁻³⁵ m.

De Broglie wavelength:

The wavelength that is incorporated with the moving object and it has the relation with the momentum of that object and mass of that object. It is inversely proportional to the momentum of that moving object.

λ=h/p

Where, λ is the de Broglie wavelength, h is the Plank constant, p is the momentum of the moving object.

Whereas, p=mv, m is the mass of the object and v is the velocity of the moving object.

Therefore, λ=h/(mv)

λ=(6.63×10⁻³⁴)/(0.56×26)

λ=4.55×10⁻³⁵ m.

The de Broglie wavelength associated with the object weight 0.56 kg moving with the velocity of 26 m/s is λ=4.55×10⁻³⁵ m.

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please help me with this physics question ASAP​

Answers

Answer:

See below

Explanation:

With switches open, the circuit is a simple series circuit ....the ammeters will have the same readings

V = IR

I = V/R = 5 / (10+5+5) = .25 A

b) With S1 closed   5 ohm and 10 ohm in parallel become = 5 *10 / (5+10) = 3.33 ohm

 then the series circuit current becomes  

     5 v / ( 10 + 3.33 + 5 ) = ammeter 1 = .273 amps

            ammeter 2 will get a portion of this ...the smaller resistor will get 2/3 ...the 10 ohm resistor will get 1/3        .273 *   10 / 15 =.182 amps

Three ropes A, B and C are tied together in one single knot K.
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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Hello!

This is an example of a force summation in the vertical direction.

We have the tension of rope A upward (+), and the equal vertical components of the tensions of rope B and C downward (-).

These forces sum to zero, since the knot is stationary.

[tex]\Sigma F = T_A - T_{By} - T_{Cy} \\\\0 = T_A - T_{By} - T_{Cy}[/tex]

Ropes 'B' and 'C' form equivalent angles from the vertical. (If you were to draw a line from rope A down). We can use right-triangle trig to determine the angle:

[tex]tan^{-1}(\frac{O}{A}) = \theta[/tex]

The ropes are 5 m long and 2 m tall, which are the opposite and adjacent sides respectively:
[tex]tan^{-1}(\frac{5}{2}) = 68.2^o[/tex]

The vertical components are the adjacent sides from this angle, so, we would use cosine.

[tex]0 = T_A - T_Bcos\theta - T_Ccos\theta[/tex]

Rope 'B' and 'C' have the same tensions since they form the same angle with the vertical and are the same length, so we can call them 'T'.

[tex]0 = T_A - 2Tcos\theta[/tex]

Solving for 'T':

[tex]2Tcos\theta = T_A \\\\T = \frac{T_A}{2cos\theta}\\\\T = \frac{65.3}{2cos(68.2)} = \boxed{87.92 N}[/tex]

What is the resistance of a carbon rod at 25.8 ∘C if its resistance is 0.0200 Ω at 0.0 ∘C ?

Answers

0.02020 ohm is the resistance of a carbon rod at 25.8 ∘C if its resistance is 0.0200 Ω at 0.0 ∘C.

What is a resistor?

A resistor is an electrical component that controls or restricts how much electrical current can pass across a circuit in an electronic device. A specified voltage can be supplied via resistors to an active device like a transistor.

The temperature of the resistor varies based on the variation in the temperature. The equation that describes the relationship between the two of them is:

R = R0[1+ alpha(T-T0)]  where:

R is the new resistance we are looking for

alpha is the temperature coefficient of resistance. For carbon rod, alpha = ₋ 4.8 x [tex]10^{-4}[/tex](1/°c)

T0 is the standard temperature =25.8°C

R0 is the resistance at T0 = 0.0200 ohms

T is the temperature at which we want to get R = 0

Substitute in the equation to get R as follows:

R = 0.0200 [1+( ₋ 4.8 x [tex]10^{-4}[/tex]) (0-25.8)] = 0.02020 ohm

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Two planets X and Y travel counterclockwise in circular orbits about a star, as seen in the figure.
The radii of their orbits are in the ratio 4:3. At some time, they are aligned, as seen in (a), making a straight line with the star. Five years later, planet X has rotated through 88.0°, as seen in (b). By what angle has planet Y rotated through during this time?

Answers

Answer:  Two planets X and Y travel counterclockwise in circular orbits about a star, as seen in the figure. The radii of their orbits are in the ratio 4:3. At some time, they are aligned, as seen in (a), making a straight line with the star. Five years later, planet X has rotated through 88.0°, as seen in (b). Then, at an angle 135.48°, the planet Y rotated through during this time.

Explanation: To find the answer, we need to know about the Kepler's third law of planetary motion.

What is Kepler's third law of planetary motion?Kepler's third law of planetary motion states that, the square of the period of revolution is proportional to the cube of the orbital radius of the elliptical path.It can be expressed as,

                                      T² ∝ r³

How to solve the problem?We have given with the ratio of the radii of their orbits as,4:3.planet X rotated through an angle of 88°.thus,

                 [tex]\frac{r_1}{r_2}=\frac{4}{5} \\\frac{T_1}{T_2} =(\frac{r_1}{r_2})^{3/2}\\[/tex]

As we know that,

                  [tex]T=\frac{2\pi }{w}[/tex] where, w is the angular velocity.

Angular displacement is the angle swept by the position vector of a particle in a given interval of time.

                           [tex]\alpha[/tex] =wt.

We can rewrite our equation as,

                   [tex]\frac{T_x}{T_y}=\frac{w_y}{w_x}\\thus,\\\frac{w_y}{w_x}=(\frac{r_1}{r_2})^{3/2}[/tex]

We have to find the angle rotated by planet Y during 5 yrs. So, we can rewrite the above equation in terms of angular displacement.

                     [tex]\frac{\alpha _y}{\alpha _x} = (\frac{r_1}{r_2})^{3/2}\\where,\\\alpha _x=\frac{88^0}{5 yrs} because,\\here, angle \beta_x =88^0.\\[/tex]

Thus, the angle rotated by planet Y during 5 yrs will be  [tex]\beta _y[/tex] =

                     [tex]\alpha _y=\frac{88}{5yrs} *(\frac{4}{3} )^{3/2}=\frac{135.48^0}{5yrs} .\\thus,\\\beta _y=135.48^0.[/tex]

Thus, we can conclude that the angle rotated by planet Y during 5 yrs will be 135.48 degrees.

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The planet Y then rotated through at this time at an angle of 135.48°.

In order to understand the solution, we must be familiar with Kepler's third law of planetary motion.

What does the third law of planetary motion by Kepler say?According to Kepler's third law of planetary motion, the elliptical path's orbital radius is proportional to the cube of the square of the revolution's period.It can be stated as follows:

                              T² ∝ r³

How can the issue be resolved?The ratio of their orbital radii that we have provided is 4:3.Planet X rotated at an 88° angle. thus,

                                  [tex]\frac{R_1}{R_2}=\frac{4}{5} \\\frac{T_1}{T_2}=(\frac{4}{5} ) ^{\frac{3}{2} }[/tex]

As we are aware,

                                [tex]T=\frac{2\pi }{w}[/tex]

where w is the angle of rotation per time.

The angle that a particle's position vector sweeps over in a specific amount of time is known as the angular displacement.

                                     [tex]\alpha[/tex]=wt.

Our equation can be rewritten as,

                                   [tex]\frac{w_y}{w_x} =(\frac{4}{5} ) ^{\frac{3}{2} }[/tex]

We have to find the angle that planet Y rotated at over the course of five years. Consequently, we can express the equation above in terms of angular displacement.

                                   [tex]\frac{\alpha _y}{\alpha _x}=(\frac{4}{3} ) ^{\frac{3}{2} } , where\\\alpha _x=\frac{88}{5yrs} \\[/tex]

So, during a period of five years, planet Y will rotate at an angle,

                           [tex]\alpha _y=\frac{88}{5yrs} *(\frac{4}{3} ) ^{\frac{3}{2} }=\frac{135.48}{5yrs}[/tex]

Thus, we may infer that planet Y will revolve at an angle of 135.48 degrees during the course of five years.

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A closed curve encircles several conductors. The line integral around this curve is (image attached below)
a) What is the net current in the conductors?
b) If you were to integrate around the curve in the opposite direction, what would be the value of the line integral?

Answers

The net current in the conductors and the value of the line integral

[tex]I=\frac{3.2\cdot 10^{-4}}{4\pi \cdot 10^{-7}}=254.77\, A[/tex]The resultant remains same 3.2 *10^4 Tm

This is further explained below.

What is the net current in the conductors?

Generally,

To put it another way, the total current In flowing across a surface S (contained by C) is proportional to the line integral of the magnetic B-field (in tesla, T).

[tex]\oint_C \mathbf{B} \cdot \mathrm{d}\boldsymbol{\ell} = \mu_0 \iint_S \mathbf{J} \cdot \mathrm{d}\mathbf{S} = \mu_0I_\mathrm{enc}[/tex]

[tex]I=\frac{3.2\cdot 10^{-4}}{4\pi \cdot 10^{-7}}=254.77\, A[/tex]

B)

In conclusion, It is possible for the line integral to go around the loop in either direction (clockwise or counterclockwise), the vector area dS to point in either of the two normal directions and Ienc, which is the net current passing through the surface S, to be positive in either direction—but both directions can be chosen as positive in this example. The right-hand rule solves these ambiguities.

The resultant remains the same at 3.2 *10^4 Tm

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It's a snowy day and you're pulling a friend along a
level road on a sled. You've both been taking physics,
so she asks what you think the coefficient of friction
between the sled and the snow is. You've been
walking at a steady 1.5 m/s, and the rope pulls up
on the sled at a 35 ° angle. You estimate that the
mass of the sled, with your friend on it, is 57 kg and
that you're pulling with a force of 75 N

Answers

The coefficient of friction between the sled and the snow is 0.119.

To find the answer, we need to know about the friction.

How to find the coefficient of friction between the sled and the snow?Whenever a body moves over the surface of another body, a force come into play, which acts parallel to the surface of contact and oppose the relative motion. This opposing force is called friction.To solve the problem, we have to draw the free body diagram of the given system.We have given with the following values,

                                     [tex]a=0\\\alpha =35^0\\T=75N\\m=57kg[/tex]

Here, acceleration will be equal to zero, because the velocity is given as constant.

Thus, from the diagram, we can write the balancing equations as follows,

                                      [tex]ma=Tcos\alpha -f\\\where\\f=kN\\\N+Tsin\alpha=mg\\Thus,\\N=mg-Tsin\alpha[/tex]

Substituting N in f and f in the equation of ma, then we get,

                   [tex]ma= Tcos\alpha -k(mg-Tsin\alpha )[/tex]

Substituting values, we get the coefficient of friction as,

                    [tex]0=(75*cos35)-k((57*9.8)-(75sin35))\\\\k((57*9.8)-(75sin35))=(75*cos35)\\\\515.6k=61.44\\\\k=\frac{61.44}{515.6}=0.119[/tex]

Thus, we can conclude that, the coefficient of friction between the sled and the snow is 0.119.

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The sled's coefficient of friction with the snow is 0.119.

We must understand the friction in order to choose the solution.

How can I determine the sled and snow's coefficient of friction?A force that works parallel to the surface of contact and opposes the relative motion is present whenever one body moves over the surface of another body. Friction is the name for this opposing force.We must create the given system's free body diagram in order to solve the issue.The values that we have provided are

                               [tex]\alpha =35\\T=75N\\m=57kg\\a=0[/tex]

Because the velocity is specified as constant in this case, the acceleration will be equal to zero.

Consequently, we can express the balancing equations as follows using the diagram:

                             [tex]ma=Tcos\alpha -f\\ where,f=kN\\N+Tsin\alpha =mg\\ thus,\\N=mg-Tsin\alpha[/tex]

When we substitute N for f and f in the equation for ma, we obtain,

                       [tex]ma=Tcos\alpha -k(mg-Tsin\alpha )[/tex]

By substituting values, we obtain the friction coefficient as.

                                   [tex]k=0.119[/tex]

As a result, we may say that there is 0.119 coefficient of friction between the sled and the snow.

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A 40.0 kg beam is attached to a wall with a hi.nge and its far end is supported by a cable. The angle between the beam and the cable is 90°. If the beam is inclined at an angle of θ = 31.0° with respect to horizontal..
1. What is the horizontal component of the force exerted by the hi.nge on the beam? (Use the `to the right' as + for the horizontal direction.)
2. What is the magnitude of the force that the beam exerts on the hi.nge?

Answers

The tension in the cable is 380.55 N and the vertical component of the force exerted by the hi.nge on the beam is 11.45 N.

Tension in the cable

Apply the principle of moment and calculate the tension in the cable;

Clockwise torque = TL sinθ

Anticlockwise torque = ¹/₂WL

TL sinθ  =  ¹/₂WL

T sinθ  =  ¹/₂W

T = (W)/(2 sinθ)

T = (40 x 9.8)/(2 x sin31)

T = 380.55 N

Vertical component of the force

T + F = W

F = W - T

F = (9.8 x 40) - 380.55

F = 11.45 N

Thus, the tension in the cable is 380.55 N and the vertical component of the force exerted by the hi.nge on the beam is 11.45 N.

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A 1300 kg steel beam is supported by two ropes. (Figure
1)

What is the tension in rope 1?

What is the tension in rope 2?

Answers

Relative to the positive horizontal axis, rope 1 makes an angle of 90 + 20 = 110 degrees, while rope 2 makes an angle of 90 - 30 = 60 degrees.

By Newton's second law,

the net horizontal force acting on the beam is

[tex]R_1 \cos(110^\circ) + R_2 \cos(60^\circ) = 0[/tex]

where [tex]R_1,R_2[/tex] are the magnitudes of the tensions in ropes 1 and 2, respectively;

the net vertical force acting on the beam is

[tex]R_1 \sin(110^\circ) + R_2 \sin(60^\circ) - mg = 0[/tex]

where [tex]m=1300\,\rm kg[/tex] and [tex]g=9.8\frac{\rm m}{\mathrm s^2}[/tex].

Eliminating [tex]R_2[/tex], we have

[tex]\sin(60^\circ) \bigg(R_1 \cos(110^\circ) + R_2 \cos(60^\circ)\bigg) - \cos(60^\circ) \bigg(R_1 \sin(110^\circ) + R_2 \sin(60^\circ)\bigg) = 0\sin(60^\circ) - mg\cos(60^\circ)[/tex]

[tex]R_1 \bigg(\sin(60^\circ) \cos(110^\circ) - \cos(60^\circ) \sin(110^\circ)\bigg) = -\dfrac{mg}2[/tex]

[tex]R_1 \sin(60^\circ - 110^\circ) = -\dfrac{mg}2[/tex]

[tex]-R_1 \sin(50^\circ) = -\dfrac{mg}2[/tex]

[tex]R_1 = \dfrac{mg}{2\sin(50^\circ)} \approx \boxed{8300\,\rm N}[/tex]

Solve for [tex]R_2[/tex].

[tex]\dfrac{mg\cos(110^\circ)}{2\sin(50^\circ)} + R_2 \cos(60^\circ) = 0[/tex]

[tex]\dfrac{R_2}2 = -mg\cot(110^\circ)[/tex]

[tex]R_2 = -2mg\cot(110^\circ) \approx \boxed{9300\,\rm N}[/tex]

A canon ball is shot out of a cannon at an angle of 45 degrees. What is the initial velocity of the cannon ball if its initial horizontal velocity is 8 m/s?

Answers

Answer:

11.31 [m/s].

Explanation:

1. the required velocity can be calculated according to

[tex]V=\frac{V_{horizontal}}{sin45};[/tex]

2. according to the formula above:

V=8*1.41≈11.3137085 [m/s].

Two planets X and Y travel counterclockwise in circular orbits about a star, as seen in the figure.
The radii of their orbits are in the ratio 4:3. At some time, they are aligned, as seen in (a), making a straight line with the star. Five years later, planet X has rotated through 88.0°, as seen in (b).
1. By what angle has planet Y rotated through during this time?

Answers

The angle of the planet is mathematically given as

dY= 704 degrees

What angle has planet Y rotated through during this time?

With Kepler's third rule, which states that a planet's orbit squared is a function of cubed radius, we can prove that this is the case.

Generally, the equation for the period is  mathematically given as

(periodX / periodY)^2 = (radius X / radius Y)^3

Therefore

(pX / pY)^2 = 4^3

(pX / pY)^2 = 64

\sqrt{(pX / pY )^2}= \sqrt{64}

(pX / pY=8

In conclusion, Because it takes 8 times longer to complete one orbit on planet X, planet Y travels 8 times farther than planet X does in the same time period...

planet Y travels ;

dY=8 * 88.0

dY= 704 degrees

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