Suppose an automobile engine can produce 180 N*m of torque, and assume this car is suspended so that the wheels can turn freely. Each wheel acts like a 15.5 kg disk that has a 0.175 m radius. The tires act like 1.9-kg rings that have inside radii of 0.19 m and outside radii of 0.315 m. The tread of each tire acts like a 12-kg hoop of radius 0.335 m. The 14.5-kg axle acts like a solid cylinder that has a 1.95-cm radius. The 32.5-kg drive shaft acts like a solid cylinder that has a 2.9-cm radius.
(a) calculate the angular acceleration in radians per square second, produced by the motor if 95.0% of this torque is applied to the drive shaft, axle, and rear wheels of a car.

The speed of the pendulum at the instant it reaches an angle of 20.6 degrees above the vertical is 3.02 m/s.

A pendulum is a weight suspended from a fixed point that swings back and forth due to the force of gravity.

Based on the given information, we have a pendulum of length 1.06 m and it is released from rest at an angle of 41.2 degrees to the vertical. We need to find the speed of the pendulum at the instant it reaches an angle of 20.6 degrees above the vertical.

To solve this problem, we can use the conservation of mechanical energy. At the highest point of the pendulum's swing, all of its energy is in the form of potential energy, and at the lowest point of its swing, all of its energy is in the form of kinetic energy. Therefore, we can write:

PE_max = KE_min

where PE_max is the potential energy at the maximum height and KE_min is the kinetic energy at the lowest point.

The potential energy of a pendulum is given by:

PE = mgh

where m is the mass of the pendulum, g is the acceleration due to gravity, and h is the height above some reference point.

The kinetic energy of a pendulum is given by:

KE = (1/2)mv^2

where v is the speed of the pendulum.

First, we need to find the vertical height difference between the pendulum's highest and lowest points. To do this, we can use trigonometry:

h = L(1 - cosθ)

where L is the length of the pendulum and θ is the initial angle to the vertical. Substituting the given values, we get:

h = 1.06(1 - cos(41.2°)) = 0.654 m

Next, we can use the conservation of mechanical energy to find the speed of the pendulum at the lowest point of its swing. At this point, all of the potential energy has been converted into kinetic energy, so we can write:

PE_max = KE_min

mgh = (1/2)mv^2

Canceling out the mass, we get:

gh = (1/2)v^2

Solving for v, we get:

v = sqrt(2gh)

where g is the acceleration due to gravity. Substituting the given values, we get:

v = sqrt(2(9.81 m/s^2)(0.654 m)) = 3.78 m/s

Finally, we need to find the speed of the pendulum when it reaches an angle of 20.6 degrees above the vertical. At this point, the pendulum has a potential energy of:

PE = mgh' = mgh cos(20.6°)

where h' is the height of the pendulum at this point. To find h', we can use trigonometry:

h' = L(1 - cosθ')

where θ' is the angle above the vertical. Substituting the given values, we get:

h' = 1.06(1 - cos(20.6°)) = 0.242 m

Substituting the values for h' and solving for the kinetic energy, we get:

KE = PE_max - mgh' = mgh - mgh'

Substituting the known values, we get:

KE = (1 kg)(9.81 m/s^2)(0.654 m) - (1 kg)(9.81 m/s^2)(0.242 m) = 5.11 J

Now, we can solve for the speed at this point:

KE = (1/2)mv^2

5.11 J = (1/2)(1 kg)v^2

v = sqrt((2)(5.11 J)/(1 kg)) = 3.02 m/s

Therefore, The pendulum is moving at a speed of 3.02 m/s when it reaches an angle of 20.6 degrees above vertical.

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Answer:

I beleive the answer is d

Explanation:

This is beause theball starts going back down because the velocity slows down.

Answer:

d

Explanation:

the velocity changes as it goes down

(a) The magnitude of the gravitational force on the rock is 64.68 N and on the pebble is 5.488 x 10⁻³ N.

(b) The acceleration of each object is equal to acceleration due to gravity, = 9.8 m/s².

The gravitational force exerted on each object is calculated by applying Newton's law of universal gravitation as follows;

Fg = Gm₁m₂ / R²

where;

The acceleration of each object will be constant and equal to acceleration due to gravity, the force on each object is calculated by using Newton's second law of motion.

Force on the rock;

F = mg

where;

F = 6.6 kg x 9.8 m/s²

F = 64.68 N

The force on the pebble;

F = mg

F = 5.6 x 10⁻⁴  x 9.8

F = 5.488 x 10⁻³ N

Thus, the acceleration of each object is equal to acceleration due to gravity, = 9.8 m/s².

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Answer:The Moon has a smaller mass than the Earth. If you were to travel to the moon your weight would..

Explanation: It would decrease.

The Moon has a smaller mass than the Earth. If you were to travel to the moon your weight would decrease because the acceleration due by gravity on the moon is less than the acceleration due to gravity on the earth, therefore the correct answer is option C.

It can be defined as the force by which a body attracts another body towards its center as the result of the gravitational pull of one body and another.

In comparison to the Earth, the Moon is less massive. Your weight would drop if you traveled to the moon because the acceleration caused by gravity there is lower than that caused by gravity here on Earth.

As a result of the less gravity on the moon, the weight would decrease.

Thus, the correct answer is option C.

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Answer:

Agree

Explanation:

Regarding the aluminium foil, its actually a transparent material, allowing almost all light to pass through. Non-visible light, such as radio waves, x-rays, and gamma-energy photons, can most definitely can travel through wood too. So yeah agree.

Light can travel through transparent materials which we  can see through.  Materials like, wood, aluminums foil etc. are opaque to light and does not pass light through it. Hence, disagreeing to the statement.

A material is said to be transparent if light can pass through it. Thus light any of the phenomenon like transmission, absorption or reflection. A fraction of light transmitting through the material is absorbed by it.

Mirror, glass, water etc. are transparent and light can transmit through it. These materials can absorb light and reflect a portion. The amount of incident light that is absorbed by the material is dependent on its nature.

Objects that does not pass light through them are called opaque. They cant absorb or reflect light. Objects such as wood, aluminum foil, metals such  as iron etc. are opaque. Thus, the given statement is false.

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Series connection

Net resistance

Explanation:

We need to determine the total resistance also known as the net resistance that is occurring in the circuit.  We need to combine the two resistors that are being used and that will give us the net.

50.0 ohm + 70.0 ohm

120.0 ohm

Answer:  The net resistance is 120.0 ohm

Answer:

Approximately \(5.85 \times 10^{3}\; {\rm J}\) assuming no energy loss to the surroundings of the water in this beaker.

Explanation:

Let \(c\) denote the specific heat of a material. The energy \(Q\) required to raise the temperature of \(m\) (mass) of this material by \(\Delta T\) (change in temperature) is:

\(Q = c\, m\, \Delta T\).

In this question, it is given that the specific heat of water is \(c = 4.18\; {\rm J \cdot g^{-1}\cdot K^{-1}}\). It is also given that the mass of the water in this beaker is \(m = 124.9\: {\rm g}\).

The change in the temperature is:

\(\Delta T = (33.5 - 22.3)\; {\rm K} = 11.2\; {\rm K}\).

Assume that there is no heat loss to the surroundings of the water in this beaker. Energy required to achieve this change in temperature would be:

\(\begin{aligned}Q &= c\, m\, \Delta T \\ &= 4.18 \; {\rm J \cdot g^{-1}\cdot K^{-1}} \times 124.9\; {\rm g} \times (33.5 - 22.3)\; {\rm K} \\ &= 4.18 \; {\rm J \cdot g^{-1}\cdot K^{-1}} \times 124.9\; {\rm g} \times 11.2 \; {\rm K} \\ &\approx 5.85 \times 10^{3}\; {\rm J}\end{aligned}\).

Answer:

rubber band

Explanation:

because it's not necessary while conducting the wire circuit

Answer:

Explanation:

Ideal gas equation- The volume (V) occupied by the n moles of any gas has pressure(P) and temperature (T) Kelvin,

the relationship for these variables PV=nRT where R gas constant is called the ideal gas law

Derivation of the Ideal Gas Equation

Let us consider the pressure exerted by the gas to be ‘p,’

The volume of the gas be – ‘v’  

Temperature be – T  

n – be the number of moles of gas

Universal gas constant – R

According to Boyle’s Law,

it constant n & T, the volume bears an inverse relation with the pressure exerted by a gas.

i.e. v∝1p ………………………………(i)

According to Charles’ Law,

When p & n are constant, the volume of a gas bears a direct relation with the Temperature.

i.e. v∝T ………………………………(ii)

According to Avogadro’s Law,

When p & T are constant, then the volume of a gas bears a direct relation with the number of moles of gas.

i.e. v∝n ………………………………(iii)

Combining all the three equations, we have-

v∝nTp

or pv=nRT

where R is the Universal gas constant, which has a value of 8.314 J/mol-K

A  0.32 kg toy mouse was on a couch that is 0.35 m high, a car picks up the mouse and puts it in a nearby bookcase that is 2.85 m high, and the car did 7.84 J of work.

The work done by the car is calculated by ΔPE = mgh ,

(here the m=mass(0.32 kg)

g = acceleration(9.8 \(m/s^2\))

h= change in height  (2.85 m - 0.35 m = 2.50 m)

ΔPE = 0.32 kg x 9.8 \(m/s^2\) x 2.50 m = 7.84 J

Hence, a 0.32 kg toy mouse was on a couch that is 0.35 m high, a car picks up the mouse and puts it in a nearby bookcase that is 2.85 m high, and the car did 7.84 J of work.

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Answer:

It represents a very large, complex system.

Explanation:

Just took test

The function of the source in an electric circuit is to provide the energy (in the form of a potential difference) necessary for the flow of electric charge, enabling the circuit to operate.The correct answer is option C.

In an electric circuit, the source plays a fundamental role in providing the energy needed for the circuit to operate. It is responsible for establishing an electric potential difference, commonly known as voltage, which drives the flow of electric charge, typically carried by electrons, through the circuit.
The source can be a battery, a generator, or any other device capable of converting some form of energy into electrical energy.

The source acts as an electromotive force (EMF) that creates a potential difference between its terminals. This potential difference drives the electrons to move from the higher potential terminal (positive terminal) to the lower potential terminal (negative terminal).
The source essentially pushes the electrons, establishing an electric field that induces the flow of charge through the circuit.

Moreover, the source maintains a relatively constant voltage across its terminals, ensuring a steady flow of current in the circuit. This allows other components in the circuit, such as resistors, capacitors, and inductors, to perform their respective functions based on the energy supplied by the source.
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The probable question may be:
What is the function of the source in an electric circuit?

A. The source safely opens and closes the circuit.
B. The source is whatever is receiving the energy in the circuit.
C. The source is where the energy comes from in the circuit.

D. The source is what the electrons flow through in the circuit.

The volume of the gas at 101.3 kPa would be approximately 651.25 cm³.

To calculate the change in volume of a gas from an initial pressure to a final pressure, we can use Boyle's law, which states that the pressure and volume of a gas are inversely proportional at constant temperature.

Boyle's law can be expressed as:

P1 * V1 = P2 * V2

Where:

P1 = Initial pressure (80.8 kPa)

V1 = Initial volume (817 cm³)

P2 = Final pressure (101.3 kPa)

V2 = Final volume (to be calculated)

Let's plug in the values into the equation and solve for V2:

80.8 kPa * 817 cm³ = 101.3 kPa * V2

V2 = (80.8 kPa * 817 cm³) / 101.3 kPa

V2 ≈ 651.25 cm³

Therefore, the volume of the gas at 101.3 kPa would be approximately 651.25 cm³.

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8.27 x 1013 meres is the orbital radius.

Jupiter's mass, 1.9 x 1027 kg, and the time interval, 16.9 days, are equal to 1.46 x 106 seconds. The radius is needed, thus r. Solution

The moon must be held in its orbit by a gravitational force equal to the centripetal force between Jupiter and the moon.

6.67 x 10⁻¹¹ N/m²kg

2 x 1.9 x 10/27 x 1.46 x 10'6 / 4 r = 6.85 x 102'7 G = 6.67 x 10'11 N/m2kg2 r = 8.27 x 10'7

The second-largest moon in Jupiter's orbit and the third-largest moon in the solar system is called Callisto. Of all the objects in our solar system, its surface has the most craters.

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Answer:

She will be going at 11.01 m/s when she reaches the bottom.      

Explanation:

We can find the speed at the bottom by equating the total work with the change in energy:

\( W = E_{f} - E_{i} \)   (1)

There is no energy conservation because there is a force of friction on her way down.  

By entering \(W = -F_{\mu}*d\), where \(F_{\mu}\) is the force of friction (is negative because it is in the opposite direction of motion) and d is the displacement, into equation (1) we have:

\(-F_{\mu}*d = E_{f} - E_{i}\)  

In the initial state, we have kinetic and potential energy and in the final state, we have only kinetic energy.

\(-F_{\mu}*d = \frac{1}{2}mv_{f}^{2} - (\frac{1}{2}mv_{i}^{2} + mgh)\)  

Where:

m: is the total mass = 40 kg

\(v_{f}\): is the final speed =?

\(v_{i}\): is the intial speed = 5 m/s

g: is the gravity = 9.81 m/s²

h: is the height = 10 m

\( -20 N*100 m = \frac{1}{2}40 kg*v_{f}^{2} - \frac{1}{2}*40 kg*(5 m/s)^{2} - 40 kg*9.81 m/s^{2}*10 m \)    

By solving the above equation for \(v_{f}\) we have:

\( v_{f} = 11.01 m/s \)      

Therefore, she will be going at 11.01 m/s when she reaches the bottom.                                    

I hope it helps you!                      

If truck and car moving with same velocity then the car will cover less distance , if the force of breaking is same .

The velocity of the truck and car are given to have equal velocity ,

the braking force is also equal ,

we know that , the mass of the truck(M)  is greater than mass of the car(m) ;

So , the truck will have more momentum ;

we know that momentum is = mass × velocity ;

let the velocity of car and truck be "v" ;

substituting the values in the momentum formula ;,

we get ; Mv > mv ;

Therefore , the car will cover less distance .

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The net force on an object will be equal to 27.1 N. The net force is in the right direction.

Force can be described as the influence that changes the state of the body of motion or rest. The SI unit of force is Newton and force is a vector quantity. Force can change the direction as well as the speed of the moving object.

The force can be calculated from the product of the mass (m) and acceleration (a) of an object. The mathematical equation of the second law of motion for force is written as:

F = ma

The force P is acting in the left direction or pulling the object in the left direction. The force Q pulls the object in the right direction.

The net force  \(=F_{P} -F_{Q}\) = 12.5 - 39.6

The net force = 27.1 N   in the right direction.

Therefore, the net force of 27.1 N  on the object is pulling the object in the right direction.

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Your question is incomplete, most probably complete question was,

An object is pushed to the left with a force of P and pushed to the right with a force of Q. where P = 12.5 and Q = 39.6.

What is the net force on the object? If the net force is to the right, enter a positive value and if it is to the left, enter a negative value.

Answer:

She fell out of a tree

Explanation:

The answer to the first part of the question is 24 V and the answer to the second part of the question is 48 V.

The formula which relates Charge, Capacitance and Voltage is

Charge = Capacitance × Voltage

Q = CV

where Q denotes the charge, C denotes the capacitance and V denote the voltage.

Using the above formula the charge on the capacitance will be

Q = CV

C = 10 mF

V = 24 V

Q = 240 mC

Charge on capacitance is 240 mC.

Now after we disconnect the battery

C = 10 mF (will remain same)

Q = 240 mC

V = Q/C

V = 240/10 V

V = 24 V

So after we removed the battery, The voltage will remain same.

Now we know that parallel plate capacitor formula is

C = ε(A/d)

from here

C ∝ 1/d, and as there is no loss of charge we can say that V ∝ 1/d

Form C ∝ 1/d and V ∝ 1/C we can state that

V ∝ d   {where d is the measurement of separation between the plates}

so if we double the distance between the plates then, the voltage will also get double.

Previously our voltage was 24 V, now if we double the distance between the plates the voltage will also get double, and it will become 48 V.

So, the voltmeter will take a reading of 24 V if voltmeter is connected across the two plates without discharging them, and if we double the plate separation then it will take 48 V as reading.

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Answer:

Unbalanced

Explanation:

Sound waves are a type of mechanical wave that propagate through a medium, typically air but also other materials such as water or solids.

Frequency: the frequency of a sound wave refers to the number of cycles or vibrations it completes per second and is measured in Hertz (Hz).

Amplitude: the amplitude of a sound wave refers to the maximum displacement or intensity of the wave from its equilibrium position. It represents the loudness or volume of the sound, with larger amplitudes corresponding to louder sounds and smaller amplitudes corresponding to softer sounds.

Wavelength: the wavelength of a sound wave is the distance between two consecutive points in the wave that are in phase, such as from one peak to the next or one trough to the next. It is inversely related to the frequency of the wave.

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The candidate's speed (m/s), given that the candidate experiences a centripetal acceleration that is 2.8 times the acceleration due to gravity is 17.4 m/s

We understood that the centripetal acceleration is related to speed and radius according to the following formula:

a = v² / r

Cross multiply

v² = ar

Take the square root of both sides

v = √ar

Where

Withe the above formula, we can determin the speed of the candidate. Details below:

v = √ar

v = √(27.44 × 11.05)

v = 17.4 m/s

Thus, the speed of the candidate is 17.4 m/s

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Answer:

10.88kJ

Explanation:

Given data

mass= 10kg

heigth= 111m

Applying

PE= mgh

assume g= 9.81m/s^2

substitute

PE= 10*9.81*111

PE=10889.1 Joules

PE=10.881kJ

Hence the potential energy is 10.88kJ

Answer:

445 kPa

Explanation:

Use for conversion rates:

101.325 kPa = 760 mmHg = 14.7 psi

2637.5 mmHg × (101.325 kPa / 760 mmHg) = 351.6 kPa

13.6 psi × (101.325 kPa / 14.7 psi) = 93.7 kpa

The total pressure is:

351.6 kPa + 93.7 kPa = 445.3 kPa

Rounded to three significant figures, the pressure is 445 kPa.

The horizontal displacement of the backpack as it falls is 765 m.

From the question given above, the following data were obtained:

The horizontal displacement of the backpack can be obtained as follow:

s = ut

s = 85 × 9

Horizontal displacement = 765 m

From the calculation made above, we can see that the horizontal displacement (i.e distance from the car) were the backpack will land is 765 m. Thus, the backpack will not land on your car. Hence, you do not need to move the car.

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Answer:

Inductance of a coil(L) = 0.44 H (Approx)

Explanation:

Given:

coil produces emf = 2.40 V

Old current = -27 mA

New current = 33 mA

Time taken = 11 mS

Find:

Inductance of a coil(L)

Computation:

Inductance of a coil(L) = -emf / [Δi / Δt]

Inductance of a coil(L) = -2.4 / [(-33 - 27) / 11]

Inductance of a coil(L) = -2.4 / [-5.4545]

Inductance of a coil(L) = 0.44 H (Approx)

Answer:

ac = 204 [m/s²]

Explanation:

To solve this problem we must use the following equation that relates the tangential velocity to the radius of rotation.

ac = v²/r

where:

v = tangential velocity = 15 [m/s]

r = radius = 1.1 [m]

Now replacing we have:

ac = (15)²/1.1

ac = 204 [m/s²]

Answer:

Explanation:

KE= ½mv²

m = 2KE/v²

m = 2(106)/2.01²

m = 52.47394...

m = 52.5 kg

The mass of the ball will be equal to m= 0.05 kg

Kinetic energy is the energy of motion. An object that has motion - whether it is vertical or horizontal motion - has kinetic energy. There are many forms of kinetic energy - vibrational (the energy due to vibrational motion), rotational (the energy due to rotational motion), and translational

The formula for kinetic energy will be given as

\(\rm KE=\dfrac{1}{2}mv^2\)

It is given that

KE= 106 J=0.106 KJ

Velocity= 2.01 m/s

So the mass will be

\(0.106=\dfrac{1}{2}m(2.01)^2\)

\(m=\dfrac{0.106\times 2}{(2.01)^2}\)

\(m=0.05 \ kg\)

Thus the mass of the ball will be equal to m= 0.05 kg

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Answer: a + b = (-2,5)

Explanation: I'm assuming that these are 1-dimensional matrices or vectors.

So,

a + b = [ a(x) + b(x), a(y) + b(y) ]

        = [ (3) + (-5) , (2) + (3) ]

        = [ (-2) , (5) ]

a +b = (-2,5)