A crate with a mass of M = 62.5 kg is suspended by a rope from the endpoint of a uniform boom. The boom has a mass of m = 116 kg and a length of l = 7.65 m. The midpoint of the boom is supported by another rope which is horizontal and is attached to the wall as shown in the figure.
1. The boom makes an angle of θ = 57.7° with the vertical wall. Calculate the tension in the vertical rope.
2. What is the tension in the horizontal rope?

A Crate With A Mass Of M = 62.5 Kg Is Suspended By A Rope From The Endpoint Of A Uniform Boom. The Boom

Answers

Answer 1

Answer:

Tension in the vertical rope: approximately [tex]613 \; {\rm N}[/tex].

Tension in the horizontal rope: approximately [tex]3.74 \times 10^{3}\; {\rm N}[/tex].

Assumption: [tex]g = 9.81\; {\rm N \cdot kg^{-1}}[/tex].

Explanation:

Since the system is not moving, the tension in the vertical rope would be equal to the weight of the crate:

[tex]\begin{aligned}\text{weight of crate} &= m\, g \\ &= 62.5\; {\rm kg} \times 9.81\; {\rm N \cdot kg^{-1}} \\ &= 613.25 \; {\rm N}\end{aligned}[/tex].

Note that [tex]\theta = 57.7^{\circ}[/tex] is the angle between the beam (the lever) and the vertical rope. The torque that this vertical rope exert on the beam would be:

[tex]\begin{aligned} \tau &= r\, F\, \sin(\theta) \\ &=(7.65\; {\rm m}) \, (613.25\; {\rm N})\, (\sin(57.7^{\circ})) \\ &\approx 3.965 \times 10^{3}\; {\rm N \cdot m} \end{aligned}[/tex].

This torque is in the clockwise direction.

The weight of the beam ([tex]m = 116\; {\rm kg}[/tex]) would be:

[tex]\begin{aligned}\text{weight of beam} &= m\, g \\ &= 116 \; {\rm kg} \times 9.81\; {\rm N \cdot kg^{-1}} \\ &= 1.138 \times 10^{3}\; {\rm N}\end{aligned}[/tex].

Note that [tex]\theta = 57.7^{\circ}[/tex] is also the angle between the beam and the direction of the (downward) gravitational pull on this. Since this beam is uniform, it would appear as if the weight of this beam is applied at the center of this beam (with a distance of [tex](7.65\; {\rm m}) / 2[/tex] from the pivot.) Thus, the torque gravitational pull exerts on this beam would be:

[tex]\begin{aligned} \tau &= r\, F\, \sin(\theta) \\ &= \genfrac{(}{)}{}{}{7.65\; {\rm m}}{2} \, (1.138 \times 10^{3}\; {\rm N})\, (\sin(57.7^{\circ})) \\ &\approx 3.679 \times 10^{3}\; {\rm N \cdot m} \end{aligned}[/tex].

This torque is also in the clockwise direction.

The tension in the horizontal rope would need to supply a torque in the counterclockwise direction. The magnitude of that torque would be approximately:

[tex]\begin{aligned} & 3.965\times 10^{3}\; {\rm N \cdot m} + 3.679\times 10^{3}\; {\rm N \cdot m} \\ \approx \; & 7.645 \times 10^{3}\; {\rm N \cdot m} \end{aligned}[/tex].

Note the angle between the direction of this tension and the beam is [tex](90^{\circ} - \theta) = 32.3^{\circ}[/tex]. This force is applied  [tex](7.65\; {\rm m}) / 2[/tex] from the pivot. Hence, achieving that torque of [tex]7.645 \times 10^{3}\; {\rm N \cdot m}[/tex] would require:

[tex]\begin{aligned} F &= \frac{\tau}{r\, \sin(90^{\circ} - \theta)} \\ &\approx \frac{7.645\times 10^{3}\; {\rm N \cdot m}}{((7.65\; {\rm m}) / 2) \times \sin(32.3^{\circ})} \\ &\approx 3.74 \times 10^{3}\; {\rm N} \end{aligned}[/tex].


Related Questions

If the boy is pushing with a force of 40.0 N on the box, what is the approximate magnitude of the frictional force?

Answers

The magnitude of the frictional force is 5 N.

The force exerted by the boy on the box is 40.0 N. According to Newton's second law of motion, the net force acting on an object is equal to the product of its mass and acceleration:

F(net) = m*a

where F(net) is the net force, m is the mass of the object, and a is its acceleration.

In this case, the net force acting on the box is the force applied by the boy minus the frictional force:

F(net) = F(applied) - F(friction)

By substituting the values:

F(applied) = 40.0 N

m = 5 kg

a = 7 m/s^2

Now, by using frictional force:

F(friction) = F(applied) - F(net)

F(friction) = F(applied) - ma

                = 40.0 N - (5 kg)(7 m/s^2)

                = 5 N

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a negative charge Q1 = -5.50 is located at a point x1=-6.00 abd. positive chsrge Q2= 6.50 uc is located at point x2= 4.00 m find the magnitude and direction of the electric force between rhe charges

Answers

a negative charge Q1 = -5.50 is located at a point x1=-6.00 abd. positive charge Q2= 6.50 uc is located at point x2= 4.00 m then the magnitude and direction of the electric force between the charges is 3.56 mN and from left to right.

Coulomb's Law, which says that the electric force between two charges is directly proportional to the product of their charges and inversely proportional to the square of their distance, may be used to determine the size and direction of the electric force between the provided charges.

Given:

Q1 = -5.50 μC (negative charge)

Q2 = 6.50 μC (positive charge)

x1 = -6.00 m (position of Q1)

x2 = 4.00 m (position of Q2)

distance between the charges is

Distance (d) = |x2 - x1| = |4.00 m - (-6.00 m)| = 10.00 m

electric force (F) by using Coulomb's Law:

F = (k * |Q1| * |Q2|) / (d^2)

Where k is the electrostatic constant, which is equal to 9 × 10^9 N·m^2/C^2.

Substituting the given values:

F = (9 × 10⁹ N·m²/C² * |(-5.50 μC)| * |6.50 μC|) / (10.00 m)^2

F ≈ 3.2 mN

The magnitude of the electric force between the charges is approximately 3.56 mN.

Since Q1 is negative and Q2 is positive, the electric force acts in the direction from Q1 towards Q2. Therefore, the direction of the electric force is from left to right.

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Which of the following is true about mixtures and compounds?
OA. A compound forms when different substances chemically combine to form a new substance.
B. A mixture contains different substances that are not chemically combined with one another.
OC. Mixtures and compounds are both made of two or more different substances.
D. all of these

Answers

Is the A
Because both made of two or more different substances

You are creating a model showing the distances between colored balls which represent the Earth, the Moon, and the Sun. The Earth is about 240 thousand miles from the Moon and about 93 million miles from the Sun. In your model, represent one million miles with one step. Which of the following statements are correct? Select the two that apply.
A. The ‘Moon’ should be 240 steps away from the ‘Earth’.
B. The ‘Earth’ should be 93 steps away from the ‘Sun’.
C. The ‘Moon’ should be less than one step away from the ‘Earth’.
D. The ‘Earth’ should be 5 steps away from the ‘Sun’.

Answers

A and B are the correct statements. A. The ‘Moon’ should be 240 steps away from the ‘Earth’. The ‘Earth’ should be 93 steps away from the ‘Sun’.

To create a model of the distances between the Earth, the Moon, and the Sun, we represent one million miles with one step. Based on this model:

A. The ‘Moon’ should be 240 steps away from the ‘Earth’. This is a correct statement, as the distance between the Earth and the Moon is about 240 thousand miles. In the model, we represent each million miles with one step, so the distance between the Earth and the Moon in the model would be 240 steps.

B. The ‘Earth’ should be 93 steps away from the ‘Sun’. This is also a correct statement, as the distance between the Earth and the Sun is about 93 million miles. In the model, we represent each million miles with one step, so the distance between the Earth and the Sun in the model would be 93 steps.

C. The ‘Moon’ should be less than one step away from the ‘Earth’. This statement is incorrect, as the actual distance between the Earth and the Moon is much greater than one million miles. In the model, the distance between the Earth and the Moon would be represented by 240 steps.

D. The ‘Earth’ should be 5 steps away from the ‘Sun’. This statement is incorrect, as the actual distance between the Earth and the Sun is much greater than five million miles. In the model, the distance between the Earth and the Sun would be represented by 93 steps.

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2. The second year of Peixotto Media's incorporation, the board of directors
announce that they will issue cash dividends to their shareholders. At this point,
shareholders own 70,000 shares of stock in the corporation. The dividends will be 10
cents per share.
a. How should Savannah journalize the declaration and payment of this dividend? (4
points)
b. Now, imagine that Peixotto Media had chosen to pay its shareholders a stock
Qividend instead of cash dividend. At the time, their stock is valued at $7.25 per
share. They choose to pay a 5 percent dividend. How would Savannah journalize the
declaration and payment of this dividend? (4 points)
c. Elena and Josh both own common stock in Peixotto Media. Elena owns 300
shares and Josh owns 75 shares. Compute the dividends payable to both
shareholders. Show your work. (2 points)

Answers

a. Savannah would debit retained earnings and credit dividends payable for the declaration of a cash dividend, and debit dividends payable and credit cash for the payment, b. To declare and pay a stock dividend, Savannah would debit retained earnings and credit common stock dividend distributable for declaration, then debit common stock dividend distributable and credit common stock for payment, and c. Dividends payable to shareholders like Elena and Josh can be computed by multiplying the number of shares owned by the dividend per share.

Dividends Payable is a liability account used to record the amount of dividends that a company owes to its shareholders but has not yet paid out. It represents the obligation of the company to pay out the declared dividend amount to its shareholders, and the balance is typically cleared out when the dividend payment is made. Companies usually set a record date and payment date to declare and pay dividends respectively.

a. To journalize the declaration and payment of the cash dividend, Savannah would make the following entries:

Declaration:

Debit: Retained Earnings

Credit: Dividends Payable

Payment:

Debit: Dividends Payable

Credit: Cash

b. To journalize the declaration and payment of the stock dividend, Savannah would make the following entries:

Declaration:

Debit: Retained Earnings

Credit: Common Stock Dividend Distributable (70,000 x 5% = 3,500 shares)

Payment:

Debit: Common Stock Dividend Distributable

Credit: Common Stock ($7.25 x 3,500 shares)

c. To compute the dividends payable to Elena and Josh, we would use the following formula:

Dividends Payable = Number of Shares x Dividend per Share

For Elena:

Dividends Payable = 300 shares x $0.10 per share = $30.00

For Josh:

Dividends Payable = 75 shares x $0.10 per share = $7.50

Therefore, To declare and pay a cash dividend, Savannah would debit retained earnings and credit dividends payable for declaration, and debit dividends payable and credit cash for payment. To declare and pay a stock dividend, Savannah would debit retained earnings and credit common stock dividend distributable for declaration, then debit common stock dividend distributable and credit common stock for payment. Dividends payable to shareholders like Elena and Josh can be computed by multiplying the number of shares owned by the dividend per share.

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A falling object accelerates from
-10.0 m/s to -30.0 m/s. How much
time does that take?
(Unit = s)
Remember: Falling = -v
a = -9.80 m/s²
Lost height = -Ay
Be careful with minus signs!!!/for acellus

Answers

It takes 2.04 seconds for the object to accelerate from -10.0 m/s to -30.0 m/s.

Velocity is a measure of an object's speed in a specific direction. It is calculated by dividing the distance traveled by the time taken and specifying the direction of the motion.

We can use the following formula to find the time taken for an object to change velocity under constant acceleration:

Δv = a × Δt

where Δv is the change in velocity, a is the acceleration, and Δt is the time taken.

In this case, the initial velocity is -10.0 m/s, and the final velocity is -30.0 m/s. So, the change in velocity is:

Δv = (-30.0 m/s) - (-10.0 m/s) = -20.0 m/s

The acceleration of the falling object is -9.80 m/s² (negative because the object is falling downward).

Now, we can rearrange the formula to solve for Δt:

Δt = Δv / a

Substituting the values we have:

Δt = (-20.0 m/s) / (-9.80 m/s²) = 2.04 seconds

Therefore, The object accelerates from -10.0 m/s to -30.0 m/s in 2.04 seconds.

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A current of 17.o mA is maintained in a single circular loop with a circumference of 2.0 m .A magnetic field of 0.80 T is directed parallel to the plane of the loop. What is the magnitude of the torque exerted by the magnetic field on the loop?

Answers

The magnitude of the magnetic field's torque on the loop is 0.034 Nm.

When a current-carrying conductor is put in a magnetic field, it experiences a force known as the Lorentz force, which is proportional to the magnetic field's strength and the current running through the conductor. As a result of this force, a torque is imparted to the conductor, which tends to turn it around an axis perpendicular to the conductor's plane.

The following formula can be used to calculate the torque operating on the conductor:

= NIABsin

where is the torque, N is the number of turns, I is the current, A is the area of the loop, B is the strength of the magnetic field, and is the angle between the magnetic field and the plane of the loop.

If the magnetic field is parallel to the plane of the loop, then θ is equal to 0°, and sinθ is equal to 0.

As a result, the torque formula can be shortened to: = NIAB.

When the numbers for N, I, A, and B are entered into this formula, the magnetic field's torque on the loop is found to be:

= (1)(0.017 A)(π(1 m)²)(0.80 T)τ = 0.034 Nm.

As a result, the magnitude of the magnetic field's torque on the loop is 0.034 Nm.

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A 100g apple falls from a ground from a tree and lands on the ground of 6metres
a) what is the force pulling the apple and how large the force is?
b) Calculate the gravity needed.
c) energy transfer takes place.
Gonna rate the answer

Answers

(a) The  force pulling the apple is the weight of the apple and the magnitude is determined as 0.98 N.

(b) The gravity needed is 0.98 N.

(c) The energy transfer that takes place is 5.88 J.

What is the gravity needed?

The gravity needed is calculated as follows;

Fg = mg

where;

m is the mass of the apple, m = 100 g = 0.1 kgg is acceleration due to gravity = 9.8 m/s²

Fg = 0.1 x 9.8

Fg = 0.98 N

The  force pulling the apple is equal in magnitude to force of gravity and the magnitude is determined as 0.98 N.

So the pulling force on the apple is the weight of the apple.

The energy transfer that takes place is calculated as follows;

E = P.E = mgh

E = 0.98 N x 6 m

E = 5.88 J

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Two objects, X and Y, experience external net torques that vary over a period of 5 seconds. Object X has a moment of inertia I0, and Object Y has a moment of inertia 2I0. The average value of the magnitude of the external net torque exerted on Object X from time t=0 to t=5s is torquex. Similarly, the average value for ObjectY is torquey. The magnitudes of the angular momenta L of Objects X and Y versus t are shown in the graph. Which of the following expressions correctly relates torquey to torquex?

Answers

Answer: τy = 2τx

Given: graph of L vs t
Ly = 20 at t = 5
Lx = 10 at t = 5
All L = 0 at t = 0
So change in angular momentum of y is 20 and x is 10

Explanation: ΔL = τ(average) * Δt
Change in angular momentum = average torque * change in time

solve for average torque for each objects
τ(average) = ΔL / Δt

Object y average torque
τy = ΔLy / Δt = 20 / 5 = 4
τy = 4

Object x average torque
τx = ΔLx / Δt = 10 / 5 = 2
τx = 2

Relates τy and τx
2τx = τy


Two objects, X and Y, experience external net torques that vary over a period of 5 seconds. Object X has a moment of inertia I0, and Object Y has a moment of inertia 2I0. The average value of the magnitude of the external net torque exerted on Object X from time t=0 to t=5s is torquex. Similarly, the average value for ObjectY is torquey.

The magnitudes of the angular momenta L of Objects X and Y versus t are shown in the graph. The precise relation between torquey and torquex is torquey = 2 * torquex.

To relate torquey to torquex, we are able to use the concept of angular momentum and torque. Angular momentum is described because the manufactured from the moment of inertia and angular velocity:

L = I * ω

Differentiating this equation with an appreciation of time, we get:

dL/dt = d(I * ω)/dt

Using the product rule of differentiation, we've got:

dL/dt = I * dω/dt + ω * dI/dt

Now, we realize that torque (τ) is described because of the charge of the exchange of angular momentum:

τ = dL/dt

Substituting the expression for dL/dt in terms of angular velocity and second of inertia:

τ = I * dω/dt + ω * dI/dt

Let's denote the common price of torque for item X as torquex. Since object X has a moment of inertia I0, we can write:

torquex = I0 * dω/dt + ω * dI0/dt

Now, let's consider item Y. It has a moment of inertia 2I0. Using the identical expression, we will write:

torquey = (2I0) * dω/dt + ω * d(2I0)/dt

torquey = 2I0 * dω/dt + ω * (2 * dI0/dt)

torquey = 2I0 * dω/dt + 2ω * dI0/dt

Comparing the expressions for torquex and torquey, we will see that:

torquey = 2 * torquex

Therefore, the precise relation between torquey and torquex is;

torquey = 2 * torquex.

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The correct question is;

"Two objects, X and Y, experience external net torques that vary over a period of 5 seconds. Object X has a moment of inertia I0, and Object Y has a moment of inertia 2I0. The average value of the magnitude of the external net torque exerted on Object X from time t=0 to t=5s is torquex. Similarly, the average value for ObjectY is torquey. The magnitudes of the angular momenta L of Objects X and Y versus t are shown in the graph. Which of the following expressions correctly relates torquey to torquex?"

The diagram shows two sets of vectors that result in a
single vector.
R
100 m
200 m
250 m
50 m
What are the first two steps for finding the magnitude of
the resultant vector?
find the square of the first horizontal vector and the
square root of the first vertical vector
O find the square root of the first horizontal vector and
the square root of the second horizontal vector
O find the sum of the two horizontal vectors and the
sum of the two vertical vectors
O find the difference between the two horizontal vectors
and the difference between the two vertical vectors

Answers

The magnitude of the resultant vector is obtained by finding the sum of two horizontal vectors and the sum of two vertical vectors. Thus, option C is correct.

The resultant vector is the single vector that has the same effect in the number of vectors collectively produced. The resultant vector in the horizontal and vertical direction is obtained by drawing a diagonal and hence by using the Pythagoras theorem.

To find resultant vector is obtained by finding the sum of two horizontal vectors and vertical vectors and then using the Pythagoras theorem.

Thus, the ideal solution is option C.

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Move numbers to the boxes to show the factor pairs of 14. Response area with 4 blank spaces Blank space 1 empty times Blank space 2 empty equals 14 Blank space 3 empty times Blank space 4 empty equals 14 Answer options with 14 options. Answer Options 1 2 3 4 5 6 7 8 9 10 11 12 13 1

Answers

Move numbers to the boxes to show the factor pairs of 14:

Blank space 1: 1

Blank space 2: 1

Blank space 3: 2

Blank space 4: 7

A factor pair of a number is a pair of whole numbers that can be multiplied together to give the original number. For the number 14, the factor pairs are (1,14) and (2,7). So, we can put 1 in the first blank, 14 in the second blank, 2 in the third blank, and 7 in the fourth blank to show the factor pairs of 14.

To show the factor pairs of 14 in the given response area with 4 blank spaces, we need to find the two numbers that can be multiplied together to give 14. These two numbers are called factor pairs of 14.

To begin, we can start listing the factors of 14. The factors of 14 are 1, 2, 7, and 14. We can then use these factors to form factor pairs by multiplying them together. The factor pairs of 14 are (1, 14) and (2, 7).

To show these factor pairs in the given response area, we can put the first factor of each pair in the first and third blank spaces, and the second factor of each pair in the second and fourth blank spaces. Therefore, we can put 1 in the first blank, 14 in the second blank, 2 in the third blank, and 7 in the fourth blank to show the factor pairs of 14.

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proof(how this formula comes )
vector
u.v=|u||v|cosβ

Answers

The formula you mentioned is known as the dot product formula or the scalar product formula. It is used to find the angle between two vectors u and v.

Let's start by defining the vectors u and v. Suppose we have two vectors u and v in a two-dimensional space.

u = (u1, u2)

v = (v1, v2)

The dot product of these vectors is defined as:

u . v = |u| |v| cos(β)

where |u| and |v| are the magnitudes of the vectors u and v respectively, and β is the angle between the vectors u and v.

Now, let's derive this formula. The dot product of two vectors u and v is given by:

u . v = (u1 × v1) + (u2 × v2)

The magnitude of a vector is given by:

|u| = sqrt(u1² + u2²)

|v| = sqrt(v1² + v2²)

We can use the dot product and magnitude equations to obtain:

cos(β) = (u . v) / (|u| × |v|)

Multiplying both sides by |u| × |v| gives us:

|u| × |v| × cos(β) = u . v

Therefore, we have derived the dot product formula:

u . v = |u| × |v| × cos(β)

This formula can be used to find the angle between two vectors u and v in any two-dimensional or three-dimensional space.

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The complete question is-

Write the proof of the formula

u.v=|u||v|cosβ

1. A 20 Ohm resistor and a 5 Ohm lamp are connected in a single path, with a 50 amps.
What type of circuit is this:
What is the total resistance of the circuit?
What is the total voltage in this circuit?
What is the current?

Answers

The circuit given is a series resistance circuit.

1) The given circuit is a series resistance circuit.

2) Resistance, R₁ = 20 Ω

Resistance, R₂ = 5 Ω

The effective resistance of the circuit is given by,

Reff = R₁ + R₂

Reff = 20 + 5

Reff = 25 Ω

3) Total resistance of the circuit, R = 25 Ω

Current flowing through the circuit, I = 50 A

Therefore, the voltage across the circuit is,

V = IR

V = 50 x 25

V = 1250 V

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A __ __ is a physical item used as a standard measurement

Answers

A physical standard is a physical item used as a standard measurement

Physical measurement standard explained.

A physical standard is an object that is carefully designed, manufactured and maintained to serve as a reference or benchmark for measurements. It represents a specific quantity or characteristics with a well defined value, making it a point of comparison for other similar measurements. Physical standards are used in various fields, including science, engineering, metrology , and quality control.

Physical standards can take different forms depending on the quantity being measured. For a example a standard kilogram represent the unit of mass and a standard meter represent unit of length.

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when two buses are moving in the same direction with the same velocity then a passenger in one bus finds another bus at rest. give reason.

Answers

If two buses are moving in the same direction with the same velocity, a passenger in one bus would perceive the other bus as being at rest relative to their own frame of reference. This phenomenon is known as relative motion or the principle of relativity.

The reason behind this perception is that both buses are moving with the same velocity. From the perspective of the passenger in one bus, they are also moving at the same speed and in the same direction as their own bus. Therefore, the relative velocity between the two buses is zero, and the passenger perceives the other bus as being stationary.

This perception is similar to how passengers inside a moving train may perceive nearby objects, such as other stationary trains on parallel tracks, as being at rest relative to their own moving train. It's important to note that this perception of relative rest is valid only within the frame of reference of the passenger in one bus. Observers outside the buses, or in a different frame of reference, would see both buses moving with the same velocity.

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in a race a car travels 60 times around a 3.6km track, this takes 2.4 hours.
What is the average speed of the car ?

Answers

To calculate the average speed of the car, we can use the formula:

Average speed = Total distance / Total time

Given information:

Number of laps = 60

Track length per lap = 3.6 km

Total time = 2.4 hours

First, let's calculate the total distance traveled by the car:

Total distance = Number of laps * Track length per lap

Total distance = 60 * 3.6 km

Total distance = 216 km

Now, we can calculate the average speed:

Average speed = Total distance / Total time

Average speed = 216 km / 2.4 hours

Average speed ≈ 90 km/h

So, the average speed of the car is approximately 90 km/h.

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If the magnification is -4 then is the image larger or smaller and is it inverted or upright

Answers

If the magnification is -4 the the image is larger and is it inverted in nature.

The magnification of the body is given is -4, here the signs show the nature of the image and the numerical value is the times to which the object has been magnified. Here, it is inverted because there is negative sign and it is enlarged as the magnification is more than 1.

Therefore, a magnification of -4 indicates that the image is both inverted and larger than the object. The resultant picture will be a larger, inverted version of the object if it is seen via a lens or mirror with a magnification of -4.

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List the following in order of increasing mass: an atomic nucleus, a cell, an electron, a DNA molecule.

Answers

The order of increasing mass is:

An electron < An atomic nucleus < a DNA molecule < a cell.

     An electron is a fundamental particle with a negative charge and has a very small mass of order [tex]10^{-31}\ kg[/tex]. Which makes it the lightest in the group.

     An atomic nucleus consists of protons and neutrons which both individually have larger mass than an electron. The order of magnitude of the nucleus's mass is [tex]10^{-27}\ kg[/tex] or higher.

     A DNA molecule is a polymer chain of nucleotides and it carries genetic information. It contains many atoms, therefore it makes sense that it should have more mass than an atomic nucleus. Each human cell has about DNA of mass of order [tex]10^{15}\ kg[/tex].

     Lastly, A cell has the most mass in the given list since it encompasses everything else in the list.

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Suppose that a car is initially moving at a speed of 100 m / s to the right. Take right a positive. The driver hits the brakes, and the car comes to a stop in a time of 20 s. What is the acceleration of the car?

Answers

The required acceleration of the car, when the driver hits the brake, is [tex]-5 m/s^2[/tex], the negative sign indicates that the car is slowing down.

From the question we can see that the:

initial velocity(u) is + 100 m/s (to the right)

Final velocity (v) is 0 since the car comes to stop

Time (t) is 20 s

We can use the formula

a= (v-u)/t to find the acceleration(a) of the car.

Now Substituting the values in the formula given above we get:

a=(0-100)/20

a= [tex]-5m/s^2[/tex]

Therefore, the acceleration of the car is [tex]-5 m/s^2[/tex]. The negative sign in the answer indicates that the acceleration is in the opposite direction to the initial velocity, which means that the car is slowing down or decelerating.

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PLEASE HELP

S
ai
5
The regular polygon has the following measures.
a = 9√3 m
s = 18 m
Segment a is drawn from the center of the polygon
perpendicular to one of its sides.
What is the vocabulary term for segment a?
What is the area of the polygon?
Round to the nearest tenth and include correct units.

Answers

Segment a, which is drawn from the center of the polygon perpendicular to one of its sides, is called the apothem.

The typical hexagon has a surface area of around 874.6 square meters.

How to determine area of a hexagon?

To find the area of a regular polygon, use the formula:

Area = (1/2) x Perimeter x Apothem

Find the perimeter of the polygon. Since the polygon has n sides, use the formula:

Perimeter = n x s

where s = length of one side.

Since s = 18m, find n by using the formula:

n = 360° / (180° - (360° / n))

where n = number of sides.

Plugging in the values:

n = 360° / (180° - (360° / n))

n = 360° / (180° - (360° / 6))

n = 6

So the polygon has 6 sides, which makes it a hexagon.

Now find the perimeter:

Perimeter = n x s

Perimeter = 6 x 18

Perimeter = 108m

Next, find the apothem, use the formula:

Apothem = s / (2 x tan(π/n))

Plugging in the values:

Apothem = 18 / (2 x tan(π/6))

Apothem = 9√3 m

Now use the formula for the area:

Area = (1/2) x Perimeter x Apothem

Area = (1/2) x 108 x 9√3

Area ≈ 874.6 m²

Therefore, the area of the regular hexagon is approximately 874.6 square meters.

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You will need to know that Force (N) is equal to mass (kg) multiplied by acceleration (m/s2) for this problem. A fearless space explorer has discovered a new planet with a frictionless surface! He pushes a large crate with a mass of 220kg a distance of 5.3 km, as he does so, it accelerates at a rate of 2m/s2. How much work has our intrepid hero done?

Answers

The intrepid hero has done 2.332 x Joules of work in pushing the crate.

To ascertain the work done by the traveler, we first need to find the power he applied on the case. As per Newton's subsequent regulation, force is equivalent to mass times speed increase, so the power applied by the traveler on the container is:

Force = mass x speed increase = 220 kg x 2  = 440 N

Then, we really want to work out the distance the case was moved. The pilgrim pushed the box a distance of 5.3 km, or 5,300 m.

At long last, we can compute the work done by the pioneer utilizing the equation:

Work = force x distance = 440 N x 5,300 m = 2.332 x 10^6 Joules

Thusly, the valiant legend has done 2.332 x  Joules of work in pushing the case.

The space pilgrim takes care of business on the case by applying a power that makes it speed up. The work done is equivalent to the power duplicated by the distance over which the power is applied. Involving the recipe for force, F=ma, and the given qualities for mass and speed increase, we can ascertain the power applied. Then, at that point, involving the recipe for work, W=Fd, and the given distance, we can ascertain the work done. The work done by the adventurer is 2.332 x  J.

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A hot water tap delivers water at the rate of 20kg per minute at 80°C. A cold water tap delivers cold water at the rate of 10kg per minute at 20 °C. If both tabs are open for 3 minutes, calculate the final temperature of the mixture of cold and hot water.​

Answers

The final temperature of the mixture of cold and hot water is 60°C.

To calculate the final temperature of the mixture of hot and cold water, we can use the principle of conservation of energy. The heat gained by the cold water is equal to the heat lost by the hot water.

Given:

Rate of hot water flow (m₁) = 20 kg/min

The initial temperature of hot water (T₁) = 80°C

Rate of cold water flow (m₂) = 10 kg/min

The initial temperature of cold water (T₂) = 20°C

Duration (t) = 3 minutes

Let's calculate the heat gained by the cold water and the heat lost by the hot water using the formula:

Heat gained = mass * specific heat capacity * temperature change

For the cold water:

Heat gained by cold water = m₂ * specific heat capacity * (final temperature - T₂)

For the hot water:

Heat lost by hot water = m₁ * specific heat capacity * (T₁ - final temperature)

Since the heat gained by the cold water is equal to the heat lost by the hot water, we can set up the equation:

m₂ * specific heat capacity * (final temperature - T₂) = m₁ * specific heat capacity * (T₁ - final temperature)

Let's substitute the given values and solve for the final temperature:

10 kg/min * specific heat capacity * (final temperature - 20°C) = 20 kg/min * specific heat capacity * (80°C - final temperature)

Simplifying the equation:

10 * (final temperature - 20) = 20 * (80 - final temperature)

10 * final temperature - 200 = 1600 - 20 * final temperature

30 * final temperature = 1800

final temperature = 1800 / 30

final temperature = 60°C

Therefore, the final temperature of the mixture of hot and cold water after 3 minutes will be 60°C.

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Hi
Please help on question asap if the answer is correct I'll rate you five stars a thanks and maybe even brainliest!

What do you notice about the values?

0.9 amps ÷0.03v=30 ohms.
1.9amps÷0.07v=27.149 ohms
3.1. amps ÷0.10v =31 ohms
3.9. amps ÷ 0.12v =032.5 ohms
5. amps ÷0.15v=33.33 ohms
6.1. amps ÷0.19v=32.1053 ohms

Answers

The resistance values from the givens are having a consistent value ranging from 27 to 33 ohms depending upon the supply of voltage and current.

Ohm's law gives the relation between the voltage, current, and resistance. Ohm's law states that the applied voltage is directly proportional to the current flow in the conductor. Thus, V∝I, V is the voltage and I is the current.

Ohm's law can also be written as, V = IR, where R is the resistance and the unit of resistance is ohm. The resistance is the factor that resists or opposes the current flow in the curcuit. When resistance increases, current flow in the circuit decreases and vice-versa.

From the given values, the resistance values changes when there is a change in voltage and current. The current and voltage have linear relationship, and these calculations make the idealsitic assumptions and can not hold true in practical applicaitons, when woeking with non-ohmic or non-linear components.

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Which statement best suscribes what happens during chemical change?

Answers

Chemical change involves the rearrangement of atoms or molecules in a substance, resulting in the formation of new substances with different properties than the original substance.

A chemical change in a chemical reaction is a process where one or more substances undergo a chemical transformation, resulting in the formation of new substances with different chemical and physical properties than the original substances. During a chemical change, the atoms or molecules of the reacting substances are rearranged through chemical reactions, leading to the breaking and forming of chemical bonds and the release or absorption of energy.

Chemical changes occur when a material's chemical makeup is changed, creating one or more new compounds with qualities that are distinct from those of the original substance. Chemical reactions that result in the breaking and building of chemical bonds occur when the atoms or molecules of the substances involved are reorganized during a chemical shift. The release or absorption of energy in the form of heat, light, or sound is typically accompanied by this process.

Therefore, Rearranging atoms or molecules in a substance causes chemical change, which creates new compounds with differing properties from the original one.

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In the above example, the 9.012 represents the

Answers

The medium in which electromagnetic waves and mechanical waves travel is one of their primary distinctions. Light and other electromagnetic waves, including radio waves, can move through void space without the aid of a physical medium.

They may move through vacuum, air, or other materials and are made up of oscillating electric and magnetic fields. The propagation of mechanical waves, such as sound or water waves, on the other hand, depends on a physical medium.

To transport energy, they rely on particle interactions and displacements in the medium. Since mechanical waves need a physical medium to carry their energy, they cannot move through a vacuum.

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I need help. I don’t understand.

Answers

The voltage drop across R3 is 34.5 volts.

Voltage, also known as electric potential difference, is a measure of the difference in electric potential energy between two points in an electrical circuit, and it is measured in volts. It is the driving force that moves electric charges through a circuit, from a higher potential to a lower potential.

To determine the voltage drop across R3 in this circuit, we need to first find the equivalent resistance of R2, R3, and R4, since they are connected in parallel. We can then find the total resistance of the circuit by adding the equivalent resistance in series with R1, and finally use Ohm's Law to calculate the voltage drop across R3.

The equivalent resistance of R2, R3, and R4 in parallel can be calculated as:

1/R_parallel = 1/R2 + 1/R3 + 1/R4

1/R_parallel = 1/20 + 1/25 + 1/10

1/R_parallel = 0.15

R_parallel = 1/0.15

R_parallel = 6.67 ohm

The total resistance of the circuit can be found by adding R1 and the equivalent resistance in series:

R_total = R1 + R_parallel

R_total = 15 + 6.67

R_total = 21.67 ohm

Now we can use Ohm's Law to calculate the current flowing through the circuit:

I = ET / R_total

I = 30 / 21.67

I = 1.38 A

Finally, we can use Ohm's Law again to calculate the voltage drop across R3:

V_R3 = I * R3

V_R3 = 1.38 * 25

V_R3 = 34.5 V

Therefore, the voltage drop across R3 is 34.5 volts.

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A uniform bar, of mass M, with seven evenly spaced holes is held by sliding the bar over a horizontal peg through one of the seven holes. The peg passes through hole C, and a cylinder hangs from a hook placed through hole B as shown above. The mass of the bar is equal to the mass of the cylinder, and the location of the center of mass of the bar is at the center of hole D. In this configuration, the bar-cylinder system remains motionless but is free to rotate around the peg in hole C. Frictional forces acting on the bar are negligible. In a clear, coherent paragraph-length response that may also contain equations, explain why the bar does not rotate in this configuration.

Answers

In this configuration, the bar-cylinder system is in static equilibrium, which means that the net force and the net torque acting on the system are both zero. The system remains motionless and does not rotate around the peg in hole C because the weight of the cylinder hanging from hole B and the weight of the bar itself create equal and opposite torque around the peg.

To understand why the system is in equilibrium, we can consider the forces and torques acting on the system. Let's assume that the weight of the bar is W, and the weight of the cylinder is also W. When the system is hung in this configuration, the weight of the cylinder hanging from hole B creates a clockwise torque around the peg, while the weight of the bar creates a counter-clockwise torque around the same peg. The two torques cancel each other out, resulting in zero net torque.

The location of the center of mass of the bar at the center of hole D ensures that the weight of the bar acts vertically downward through the center of hole D. Since the peg passes through hole C, the weight of the bar does not act at a distance from the peg, and so it does not create any torque around the peg.

Therefore, the bar-cylinder system remains in equilibrium and does not rotate around the peg in hole C because the weight of the cylinder and the weight of the bar create equal and opposite torques around the peg, resulting in zero net torque. The location of the center of mass of thebar at the center of hole D ensures that the weight of the bar itself does not create any torque around the peg. Hence, the system remains motionless and balanced in this configuration.


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Find the electric field at a point midway between two charges of +40.0x10^-9C and +60.0x10^-9C separated by a distance of 30.0cm

Answers

The total electric field produced by the charges at the midpoint is

8 x 10³ N/C.

Amount of charge on the first particle, q₁ = 40 x 10⁻⁹C

Amount of charge on the second particle, q₂ = 60 x 10⁻⁹C

Distance between the charges, r = 30 cm = 0.3 m

The expression for the electric field due to the charges is given by,

E = 1/4πε₀ x q/r²

At the midpoint between the two charges, d = 0.15 m

So, the electric field produced by the charge q₁ at the midpoint is,

E₁ = 1/4πε₀ x q₁/d²

E₁ = 9 x 10⁹ x 40 x 10⁻⁹/(0.15)²

E₁ = 1.6 x 10⁴ N/C

So, the electric field produced by the charge q₂ at the midpoint is,

E₂ = 1/4πε₀ x q₂/d²

E₂ = 9 x 10⁹ x 60 x 10⁻⁹C/(0.15)²

E₂ = 2.4 x 10⁴ N/C

Therefore, the total electric field produced by the charges at the midpoint is,

E = E₂ - E₁

E = 2.4 x 10⁴- 1.6 x 10⁴

E = 8 x 10³ N/C

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c) A steel ring of radius 444mm is to be slipped on to a brass wheel of radius 450mm. To what maximum temperature
should the steel ring be heated to enable fitting? What will be the stresses in the materials on cooling if the cross-
sectional dimension of the steel ring is 20mm x 5mm and that of the brass wheel is 20mm x 40mm? (E for steel is
200GPa, E for brass is 95GPa and coefficient of expansion for steel is 12 x 10-6/°C (12 Marks)
&
10cm=16m

Answers

According to the information, the steel ring should be heated to a maximum temperature of approximately 50.67°C to enable fitting; and the stresses in the materials on cooling will be approximately 17.04 MPa in the steel ring and 2.11 MPa in the brass wheel.

How to calculate the linear thermal expansion?

To enable fitting, the steel ring needs to expand in size so that its inner diameter matches the outer diameter of the brass wheel. We can use the formula for linear thermal expansion:

ΔL = α * L0 * ΔT

Where ΔL is the change in length, α is the coefficient of linear expansion, L0 is the initial length, and ΔT is the change in temperature. By substituting the given values and solving for ΔT, we find that the steel ring needs to be heated to a maximum temperature of approximately 50.67°C.

How to calculate the stress in the materials?

The stresses in the materials can be calculated using the formula:

Stress = (Force / Area)

Since the dimensions of the cross-sections are given, we can calculate the areas of the steel ring and brass wheel. The force can be calculated using the equation:

Force = Young's modulus * Change in length / Initial length

By substituting the given values for Young's modulus, change in length, and initial length, we can calculate the forces in both materials. Finally, by dividing the forces by their respective areas, we can determine the stresses in the steel ring and brass wheel, which are approximately 17.04 MPa and 2.11 MPa, respectively.

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Some students are using the apparatus below to observe waves in a solid. The frequency of the generator is 19Hz. The wavelength of the waves in the string is 0.2m. Calculate the wave speed. Give your answer to two significant figures.​

Answers

Answer: 3.8

Explanation: speed = wavelength x frequency

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