A 22 kg toboggan is pulled along at a constant speed by a horizontal force of 31N. a) What is the force of gravity on the toboggan? b) What is the coefficient of friction? c) How much force is needed to pull the toboggan if two children each with a mass of 50 kg are sitting on it?

Answers

Answer 1

(a) This is essentially asking for the weight of the toboggan, which is

w = (22 kg) (9.80 m/s²) = 215.6 N ≈ 220 N

(b) Being pulled with constant speed means the toboggan is in equilibrium, so

n + (-w) = 0

where n is the magnitude of the normal force, and

31 N + (-f ) = 0

where f is the magnitude of the friction force.

f is proportional to n by a factor of µ such that

f = µ n

We have

n = w = 215.6 N

f = 31 N

so

31 N = µ (215.6 N)   →   µ ≈ 0.14

(c) Let p denote the magnitude of the required pulling force. The combined mass of the toboggan and children is now 122 kg, so its weight is

w = (122 kg) (9.80 m/s²) = 1195.6 N

which means the normal force is also n = 1195.6 N.

We want to have

p + (-f ) = 0   →   p = f

so we just need to find the magnitude of the friction force using the coefficient from part (b).

p = f = 0.14 (1195.6 N) ≈ 170 N


Related Questions

A 2kg mass moving at 1 m/s has a kinetic energy equal to...?

Answers

Answer:

kinetic energy = 1/2mv2

= 1/2 x 2 x 3^2

= 9J

Explanation:

much like a battery these generate electricity from chemical events

Answers

The term you are looking for is "chemical battery". Chemical batteries work by converting chemical energy into electrical energy through a series of chemical reactions. These reactions take place within the battery's cells, which are composed of two electrodes and an electrolyte.

When the battery is connected to a circuit, the chemical reactions produce an electrical current that can be used to power devices. Chemical batteries are widely used in many applications, including consumer electronics, electric vehicles, and renewable energy systems. They are a crucial component of our modern technological society, and ongoing research is focused on developing more efficient and sustainable battery technologies to meet growing energy demands.

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A force of 36 N pushes a box that is 12.2 kg. The box is sliding horizontally 2.6 m/s to the left. What is the coefficient of friction? (Could you draw a Force Diagram?)

Answers

The coefficient of friction on the box sliding to the left is 0.3.

The given parameters;

applied force , F = 36 Nmass of the box, m = 12.2 kgvelocity of the box, v = 2.6 m/s

The acceleration of the box is calculated as follows;

\(F = ma\\\\a = \frac{36}{12.2} \\\\a = 2.95 \ m/s^2\)

The coefficient of friction on the box is calculated as follows;

\(\mu_k = \frac{a}{g} \\\\\mu_k = \frac{2.95}{9.8} \\\\\mu_k = 0.3\)

Thus, the coefficient of friction on the box is 0.3.

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A force of 36 N pushes a box that is 12.2 kg. The box is sliding horizontally 2.6 m/s to the left. What

The Amoeba she observed under the microscope was...?

Answers

Answer:

a tiny blob of colourless jelly with a drak speck

an object with 40 is lifted up by 8 meters with a pulley how much force is needed to overcome friction

Answers

The force needed to overcome friction of an object lifted up by 8 meters with a pulley with a mass of 40 kg can be calculated using the following equation;`F = m*g*h`

Where F is the main answer and m, g, and h represents the mass of the object, acceleration due to gravity, and the height respectively.:Mass, `m = 40 kg`Height, `h = 8m`

Acceleration due to gravity, `g = 9.8 m/s^2`Force, `F = ?`Using the above-given equation,F = m*g*h= 40 * 9.8 * 8= 3136 NTherefore, the force needed to overcome friction is 3136 N.

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A volleyball player spikes a volleyball over the net. The mass of the volleyball is 0.3 kg. The ball accelerates at 800 m/s2. What is the net force that accelerates the ball?

Answers

The magnitude of net force which is required to accelerate the ball is 240 Newtons.

What is the net force?

The net force is the vector sum of all the forces which are acting on a particle or an object. The net force is a single force which replaces the effect of the original forces which are acting on the particle's motion.

F = m × a

where, F = net force,

m = mass of the object,

a = acceleration of the object

F = 0.3 × 800

F = 240N

Therefore, the net force which is required to accelerate the ball is 240 Newtons.

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Norbu's mobile phone battery was very low. When he searched for his charger, he found that he had forgotten to take his mobile charger with him. He had two thin copper wires with him. Can he use these wires to charge his mobile phone by inserting them directly to the socket? Why?

Answers

Answer: No their are different chargers

No, Norbu cannot use the two thin copper wires to charge his mobile phone by inserting them directly into the socket.

Can he use these wires to charge his mobile phone by inserting them directly to the socket?

Charging a mobile phone requires a proper charger and cable that are designed to regulate the flow of electricity and provide the appropriate voltage and current to the battery. Inserting copper wires directly into a socket is not only unsafe but also highly likely to result in electric shock, short-circuiting, overheating, or even causing a fire.

Using improper methods to charge electronic devices can lead to irreparable damage to the device, risk to personal safety, and damage to the electrical system. It's crucial to always use the correct and safe charging equipment provided by the manufacturer to ensure the safety of both the device and the user.

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4.) What are valence electrons?

Answers

Answer:

Valence electrons are electrons that tend to stay in the highest energy levels of an atom and are involved in chemical bonding.

Answer:Valence electrons are outer shell electrons with an atom and can participate in the formation of chemical bonds. In single covalent bonds, typically both atoms in the bond contribute one valence electron in order to form a shared pair. ... Most atoms do not have eight electrons in their valence electron shell.

Explanation:

hope i helped u have a great day

A 0.50-μF and a 1.4-μF capacitor (C1 and C2, respectively) are connected in series to a 6.0-V battery.

c) Calculate the potential difference across each capacitor assuming the two capacitors are in parallel.

d) Calculate the charge on each capacitor assuming the two capacitors are in parallel.

Answers

The potential to difference across each capacitor assuming the two capacitors are in parallel are;

p.d(0.50-μF) = 4.42Vp.d(1.4-μF) = 1.58V

The charge on each capacitor assuming the two capacitors are in parallel are:

Q(0.5-μF) = 0.58C

Q(1.4-μF) = 1.64C

Capacitors in series and parallel connections

C) The potential difference, p.d for the capacitors connected in series are inversely proportional to the capacitance and are as follows;

p.d(0.50-μF) = (1.4)/(1.9) × 6 = 4.42V

p.d(1.4-μF) = (0.5)/(1.9) × 6 = 1.58V

D) When the connection is parallel, the charge on each capacitor is shared as follows;

First, Total charge, Q = C(total) × V.

where, C(total) = (0.5×1.4)/(1.9) = 0.37-μF.

Q = 0.37 × 6

Q = 2.22C

Hence, the charge is shared as follows;

Q(0.5-μF) = (0.5/1.9) × 2.22 = 0.58C

Q(1.4-μF) = (1.4/1.9) × 2.22 = 1.64C

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a sound wave has a wavelength of 5 meters and a freuqnecy of 1000 cycles per second. the velocity of the sound is

Answers

In order to calculate the velocity of a sound wave, you need to use the formula: velocity = wavelength × frequency.

In this case, you have a wavelength of 5 meters and a frequency of 1000 cycles per second (Hz). Using the given information, you can calculate the velocity of the sound wave by multiplying the wavelength (5 meters) and the frequency (1000 Hz). This gives you a velocity of 5,000 meters per second.

To find the velocity of the sound wave, we can use the formula:
Velocity = Wavelength x Frequency, we are given the wavelength as 5 meters and the frequency as 1000 cycles per second.                            Therefore: Velocity = 5 meters x 1000 cycles/second
Velocity = 5000 meters/second
So the velocity of the sound wave is 5000 meters per second.

In summary, a sound wave with a wavelength of 5 meters and a frequency of 1000 Hz has a velocity of 5,000 meters per second.

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is it better to have opacity in the atomosphere with a giant refracting telescope

Answers

Yes, It is better to have low opacity in the atmosphere when using a giant refracting telescope.

1. Opacity refers to the degree to which the atmosphere obstructs or scatters light. In the context of using a refracting telescope, low opacity is desirable because it allows more light to reach the telescope's optics, resulting in better image quality and increased visibility of celestial objects.

2. A refracting telescope uses lenses to collect and focus light from distant objects. When the atmosphere has low opacity, the lenses can gather a greater amount of light, enhancing the telescope's ability to capture detailed images of stars, planets, and other astronomical phenomena.

3. High opacity in the atmosphere, such as due to pollution, dust, or atmospheric conditions, can significantly degrade the performance of a refracting telescope. It scatters and absorbs light, reducing the amount of light reaching the lenses and causing images to appear faint, blurred, or distorted.

4. Therefore, a giant refracting telescope benefits from a transparent atmosphere with low opacity. Astronomical observatories are often situated in remote locations with minimal light pollution and atmospheric disturbances to maximize the telescope's effectiveness.

5. By minimizing opacity, astronomers can obtain clearer and sharper images, enabling them to study celestial objects with greater precision and detail. This enhances our understanding of the universe and facilitates scientific discoveries in the field of astronomy.

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How can you find the mass of an object that is broken into parts?

Find the weight of the parts, and then add those weights together.

Find the weight of the whole.

Find the mass of the whole.

Find the mass of the parts, and then add those masses together.

Answers

The mass of an object broken into parts can be determined by finding the mass of the parts, and then add those masses together.

To total mass of an object broken into parts can be determined by adding the mass of different parts together.

\(M_t = m_1 + m_2 +\ ---\)

where;

\(M_t\) is the total mass of the objects\(m_1 , \ m_2\) masses of the broken parts

Thus, we can conclude that the mass of an object broken into parts can be determined by finding the mass of the parts, and then add those masses together.

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A 15 kg bowling ball is moving at 5m/s down the bowling lane, calculate its
momentum

Answers

75 kg/m/s^2. Momentum = mass x velocity
Sample Problem: If a 4.5 kg bowling ball is rolled down the bowling lane with a velocity of 6.00 m/s, what is its momentum? Known: mass = 4.5 kg velocity = 6.00 m/ ...

a projectile is launched at 50 m/s at 37 degrees from the horizontal. how long will it be in the air if it returns to the same level it was launched

Answers

The projectile will take 6 seconds to return to the same level it was launched if it is launched at 50 m/s at 37 degrees from the horizontal.

Time taken by projectile to cover entire trajectory is called "Time of flight".

Suppose the initial velocity is u = \(v_{0\) sin Ф

Let the Time of flight is T

As the projectile is reaching the same level of projection, vertical displacement is  y=0

we have, s= u t +1/2 a\(t^{2}\)

0= \(v_{0\) sinФT- 1/2 g\(T^{2}\)

0= \(v_{0\) sinФ- 1/2 gt

so, T = 2\(v_{0\) sinФ/g

Putting values in this formula, we have

T= 2×30/10

T= 6 s

So, Time of flight is 6 seconds.

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The number of planets, besides the earth, that are visible to the unaided eye is

Answers

The answer should be 5 it’s easy

a girl spins around in a circle trying to make herself dizzy. without changing her position, she starts spinning twice as fast. by how much did her rotational kinetic energy change?

Answers

Answer:

It would quadruple

Explanation:

Have a great day!

Answer:

by a lot

Explanation:

Not very helpful lol im really just trying to get points to ask questions

What is photosynthesis??​

Answers

Explanation:

The process in which green plants prepare their food in their body by using carbon dioxide and water in the presence of sunlight is called photosynthesis.

hope it is helpful to you

Hey there!

Photosynthesis is the reaction that converts light energy to chemical energy in sugar and carbohydrates. Humans can't eat sunlight, so we eat plants. Plants convert the energy in the sunlight into chemical energy using chlorophyll. Chlorophyll is a molecule produced by plants, algae, and cyanobacteria, which aids in the conversion of light energy into chemical bonds. It is the green pigment found in the chloroplasts of higher plants. They are a part of our ecosystem, and they are lower on the food chain.

Hope this helps!

Have a great day! :)

the absolute refractory period causes action potential propagation too . a. cease b. begin c. increase d. occur in both direction e. occur in one direction e. occur in one direction

Answers

Option e. "occur in one direction" is the correct answer. The absolute refractory period ensures that action potentials propagate in a unidirectional manner, preventing backward propagation and allowing for the proper transmission of nerve impulses along the axon or muscle fiber.

The absolute refractory period affects action potential propagation by causing it to occur in one direction.

During the absolute refractory period, which follows the initiation and peak of an action potential, the voltage-gated sodium channels are inactivated and unable to open. This prevents the generation of another action potential in the same region of the membrane for a brief period of time.

As a result, the action potential cannot propagate backward (opposite to its original direction) during the absolute refractory period. The inactivated sodium channels prevent the depolarization required for the initiation of another action potential in the region that has just undergone an action potential.

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A solid sphere starts from rest and rolls down a slope that is 5. 1 m long. If its speed at the bottom of the slope is 4. 3 m/s, what is the angle of the slope?.

Answers

the angle of the slope is 10°

what is inclined plane?

An inclined plane is a simple machine with a sloping surface that is used to raise heavy objects. When friction is taken into account, the force required to move an object up an incline is less than the weight being raised. The steeper the slope or incline, the closer the needed force comes to the actual weight.

Given,

Initial velocity U = 0 ( since it starts from rest)

Final velocity V = 5.3 m/s

distance S = 6.4 m

Let us first calculate its acceleration by using  third equation of motion.

\(v^{2} + u^{2}\) =  + 2aS

\(4.3^{2}\)= \(0 + 2 * 5.1a\)

\(18.49 = 10.2aa = 18.49 / 10.2a = 1.8 m / s^{2}\)

To calculate the angle of the slope, use the relationship between acceleration a and g on an inclined plane.

acceleration a = gsin∅

substitute all the values

1.8 = 9.8 sin∅

sin∅ = 1.8/9.8

sin∅ = 0.183

∅ = \(sin^{-1}\)(0.224)

∅ = 10.3 degrees

∅ = 10 degrees (approximately)

Therefore, the angle of the slope is 13 degrees

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A cart of weight 20 N is accelerated across a level surface at 0.15 m/s?. What net force acts on
the wagon?

Answers

The net force that acts on the cart of wagon is calculated as 3N

HOW TO CALCULATE NET FORCE:

The net force of a body can be calculated by multiplying the mass of the body by its acceleration. That is;

Force (N) = weight (N) × acceleration (m/s²)

According to this question, a weight of 20N accelerated across a level surface at 0.15 m/s². The net force can be calculated as follows:

F = 20 × 0.15

F = 3N

Therefore, the net force that acts on the cart of wagon is calculated as 3N.

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(a) i. Consider a charged capacitor. The capacitance, C, is defined as a constant
C = Q/V
where Q is the stored charge and V the voltage. At time t = 0 the capacitor is discharged and the time-dependent current, I(t) = - d * Q(t) / d * t can be described by the following relation,
I(t) = (V(t))/R
where R is the total resistance. Derive an expression for the stored charge as a function of time in terms of R and C and the stored charge at t = 0 , Q_{0} At what time does the stored charge decay to 1/e of its initial value?
ii. Consider a supercapacitor with electrodes made of highly porous activated carbon. The electrodes are square-shaped with side lengths equal to L and the electrode surfaces are oriented along the x - y plane. Assume that the surface roughness in the z-direction perpendicular to the x - y plane can be described by the following cosine function, z(x, y) = A * cos (2pi)/lambda * x
with a wavelength lambda = (2pi) nm and an amplitude A = 1 μm.
Consider another, conventional capacitor with the same dimensions as the supercapacitor but with a flat surface. Determine the ratio, r, for the capacitance of the supercapacitor, C sc and the conventional capacitor, C_{c} , r=C sc /C c . Assume that the voltage and the charge density (= charge stored per area), are the same for both capacitors.
Hints: Parametrize the electrode surface of the supercapacitor, r(x, y) = [x, y, z(x, y)] and calculate the surface area in terms of L noting that L >> lambda integrate 1 dx from 0 to pi * (1 + 10 ^ 6 * sin^2 x) ^ (1/2) \approx 2000

Answers

(a) i. The given relation is:

I(t) = (V(t))/R

Where R is the total resistance. The stored charge can be derived from the current as:

∫I(t) dt = ∫dQ/dt dt

∫I(t) dt = Q(t)

From the relation, I(t) = (V(t))/R, we can write the differential equation as:

dQ/dt + (1/RC)Q(t) = 0

Let us first solve for the homogeneous part of the differential equation, which will be:

dQ/dt + (1/RC)Q(t) = 0

Rearranging, dQ/Q = -dt/RC

Integrating both sides of the equation, we get:

ln(Q) = -t/(RC) + k, where k is a constant

At t = 0, Q = Q₀; Hence k = ln(Q₀)

Substituting k = ln(Q₀), we get:

ln(Q) = -t/(RC) + ln(Q₀)

ln(Q/Q₀) = -t/(RC)

The relation obtained gives the variation of charge Q as a function of time.

ii. The surface area of the electrode can be calculated as follows:

Parametrizing the electrode surface of the supercapacitor:

r(x, y) = [x, y, z(x, y)]

z(x, y) = A cos(2πx/λ)

The surface area can be obtained by calculating the partial derivatives of r(x, y):

r_x = [1, 0, -Azsin(2πx/λ)]

r_y = [0, 1, -Azsin(2πy/λ)]

The surface area, ∫∫(1 + r_x^2 + r_y^2)½ dA = ∫∫(1 + A^2z^2sin^2(2πx/λ) + A^2z^2sin^2(2πy/λ))½ dA

By symmetry, the area can be calculated only for one quarter of the surface, and the result can be multiplied by 4.

The integral for one quarter of the surface:

∫∫(1 + A^2z^2sin^2(2πx/λ) + A^2z^2sin^2(2πy/λ))½ dA = ∫(0, L) ∫(0, L) (1 + A^2z^2sin^2(2πx/λ) + A^2z^2sin^2(2πy/λ))½ dx dy

Putting z(x, y) = A cos(2πx/λ) in the integral:

∫(0, L) ∫(0, L) (1 + A^2cos^2(2πx/λ)sin^2(2πx/λ) + A^2cos^2(2πy/λ)sin^2(2πy/λ))½ dx dy

∫(0, L) ∫(0, L) (1 + A^2cos^2(2πx/λ)(1 - cos^2(2πx/λ)) + A^2cos^2(2πy/λ)(1 - cos^2(2πy/λ)))½ dx dy

The integral can be solved by dividing the integration area into small squares of side length dx and dy.

Substituting the values for A and λ, we get:

∫∫(1 + A^2z^2sin^2(2πx/λ) + A^2z^2sin^2(2πy/λ))½ dA ≈ 0.098 L²

The capacitance for a conventional parallel-plate capacitor is given as:

Cc = εA/d

where ε is the permittivity of free space, A is the surface area of the plates, and d is the distance between the plates.

The capacitance for the supercapacitor can be obtained by considering the total charge Q distributed uniformly over the surface area A of the supercapacitor, and the voltage V applied across the electrode plates. The electric field inside the supercapacitor is non-uniform, but the voltage is assumed to be constant. Thus,

Csc = Q/V

Let us now calculate the ratio of capacitance of the supercapacitor and the conventional capacitor.

The ratio,

rc = Csc/Cc = Q/V * d/εA

where Q is the total charge stored in the supercapacitor. Since the charge density is assumed to be the same for both the supercapacitor and the conventional capacitor, the total charge for both capacitors is the same. Thus, Qsc = Qc.

The voltage across the capacitors is assumed to be the same, and the distance between the electrodes in the supercapacitor is not specified. Hence, we cannot calculate the ratio of capacitance.

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a 30.0-kg crate is pushed across a rough floor by a horizontal force of 100 n. the coefficient of kinetic friction between the crate and the floor is 0.100. if a total of 80.5 j of work is done on the crate, how far was it moved along the floor?

Answers

1.14m far the crate was moved along the floor when a total of 80.5 j of work is done on the crate if the coefficient of kinetic friction is 0.100.

Given the mass of crate (m) = 30kg

The horizontal force applied on crate (f) = 100N

The coefficient of friction between the crate and floor is (µ) =  0.100

The total work done on the crate (W) =  80.5J

The distance the crate was moved along the floor = d

We know that the work done is equal to the force exerted in moving an object to a certain distance such that W = Fd

The force of friction acting on the object Fr = µ*N where N is the normal force = mg such that g = 9.8m/s^2

Then Fr = 0.100 * 30 * 9.8 = 29.4N

The net force exerted on the crate (F) = f - Fr = 100 - 29.4 = 70.6N

distance travelled(d) = W/F = 80.5/70.6 = 1.14m

Hence the distance the crate moved is 1.14m

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At rest, a car's horn has a frequency of
395 Hz. Car A passes car B on the street
in the same direction. If car A is traveling
at 22.0 m/s and car B is traveling
at 19.5 m/s, what frequency does
car B hear when car A honks?

(Speed of sound = 343 m/s)
(Unit = Hz)

Answers

The frequency heard by car A is determined as 398.4 Hz.

What is the frequency heard by car A?

The frequency heard by car A is determined by applying the following equation.

f = fs(v - v₀) / (v - vs)

where;

v is the speed of sound = 343 m/sv₀ is the speed car B = 19.2 m/svs is the speed of car A = 22 m/sfs is the frequency of car A = 395 Hzf is the frequency of car B = ?

f = 395(343 - 19.2) / (343 - 22)

f = 395(1.0087)

f = 398.4 Hz

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Plz help i really dont understand 1. A popular sprinter of mass 60 kg, was running a 100 m race. Her velocity was measured over
a 10.0 s period. The results are recorded in Table 1.
Velocity, v/ms^-1 0.0 2.5 5.0 7.5 10.0 10.0
Time, t/s 0.0 2.0 4.0 6.0 8.0 10.0

a. Use the results from Table 1 to plot a graph of Velocity versus Time
b. Determine the slope of the graph over the first 6.0 s of the race.
c. What quantity does the slope of the graph represent?

Answers

Explanation:

It"s B i think i've might be wrong??

A particle moves with a velocity    1 v 5j 3j 6k ms      under influence of a contact force  F 10i 10j 20k N.      THe instantaneous power applied to the particle is

Answers

Answer:

P = 200 W

Explanation:

The expression for the power is

        P = W / t

the job

       W = F d

   

we substitute

      P = F d / t

      P = F. v

We apply this equation to our case where the velocity is

 v = (5 i + 3j + 6k) m / s

and the force is

 F = (10i + 10j +20 k) N

we substitute in the power equation, remember that the scalar product of the unit vectors is

i.i = j.j = k.k = 1 and the other products are zero

    P = 10 5 + 10 3 + 20 6

    P = 200 W

what is electricity?write any two defects of a simple cell.​

Answers

Answer:

Electricity is the set of physical phenomena associated with the presence and motion of matter that has a property of electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described by Maxwell's equations.

The lightweight wheel on a road bike has a moment of inertia of 0. 097 kg⋅m2. A mechanic, checking the alignment of the wheel, gives it a quick spin; it completes 5 rotations in 2. 4 s. To bring the wheel to rest, the mechanic gently applies the disk brakes, which squeeze pads against a metal disk connected to the wheel. The pads touch the disk 7. 1 cm from the axle, and the wheel slows down and stops in 1. 4 s.


What is the magnitude of the friction force on the disk?

Answers

The magnitude of the friction force on the disk is 0.85 N.

In the given question, the magnitude of the friction force on the disk is 0.85 N. Here is how to solve the problem: Given data: Moment of inertia of the lightweight wheel, I = 0.097 kg m²The number of rotations completed by the wheel, n = 5Time taken to complete the rotations, t = 2.4 sDistance of the brake pads from the axle, r = 7.1 cm = 0.071 mTime taken by the wheel to stop, t1 = 1.4 sNow, the angular velocity of the wheel when it completes five rotations is given by;ω = 2πn/t= 2 × π × 5/2.4 rad/s = 26.18 rad/sWhen the brake pads are applied, the torque acting on the wheel is given by;τ = Iα = I(ω - 0)/t1 = - 0.097 × 26.18/1.4= - 1.82 NmNow, the force of friction acting on the disk can be calculated as;τ = Fr= 0.071F- 1.82Therefore,F= (1.82 + 0.071F)/0.071= 25.7 + FTherefore,F - F = 25.7 orF = 25.7 N/m² = 0.85 N.

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Pls help ASAP now! This is physical science

Pls help ASAP now! This is physical science

Answers

Option A is correct answer

Answer:

A

Explanation:

D and C are both eliminated because it being shaped like a horseshoe has nothing yo do with it and c is wrong cause the core is really hot there for it can not be similar so A because it has north and south poles meaning its magnetic ability

what did edwin hubble study in the andromeda galaxy that proved it was an individual galaxy and not part of our own milky way?

Answers

Edwin Hubble studied the Andromeda galaxy and found that it was an individual galaxy and not part of our own milky way is Hubble discovered this by observing a variable star, known as a Cepheid variable, in the Andromeda galaxy and measured its distance from Earth.

The Cepheid variable was used to measure the galaxy's distance because the star's brightness varied predictably, and the brightness was directly related to its distance from Earth. By studying the Andromeda galaxy, Hubble discovered that it was much farther away from Earth than originally thought, and it was actually a separate galaxy rather than a part of the Milky Way.

This discovery proved the existence of other galaxies outside of our own Milky Way, which was a groundbreaking finding at the time and paved the way for modern astronomy. Overall, Hubble's study of the Andromeda galaxy provided significant evidence to support the theory that the universe was much larger than previously thought and made a huge contribution to our understanding of the universe.

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outlet and at the reactor inlet are of 14.4 m s−1 and 10.7 m s−1, respectively. What is the change of rate of kinetic energy (in W )? a. 102.68 b. −698.78 c. −696.53 d. 696.60 e. −102.68

Answers

We find that the change in kinetic energy is positive and equal to 696.60 W, option d. The formula for kinetic energy is given by KE = 1/2 * mv^2, where m is the mass of the fluid and v is its velocity.

In this case, we are given the velocities at the outlet and the reactor inlet, which are 14.4 m/s and 10.7 m/s, respectively. Since the mass of the fluid is not provided, we can assume it to be constant.

The change in kinetic energy is given by the difference in kinetic energies at the outlet and the reactor inlet, which can be calculated using the formula:

ΔKE = (1/2 * m * v_outlet^2) - (1/2 * m * v_inlet^2)

Simplifying this expression, we get:

ΔKE = 1/2 * m * (v_outlet^2 - v_inlet^2)

Plugging in the given values, we have:

ΔKE = 1/2 * m * (14.4^2 - 10.7^2)

Calculating this expression, we find the answer to be approximately 696.60 W. Therefore, the correct option is d. 696.60.

In summary, the change in the rate of kinetic energy is approximately 696.60 W. This is calculated by taking the difference between the kinetic energy at the outlet and the kinetic energy at the reactor inlet using the formula ΔKE = 1/2 * m * (v_outlet^2 - v_inlet^2). Plugging in the given velocities of 14.4 m/s and 10.7 m/s, we find that the change in kinetic energy is positive and equal to 696.60 W.

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