A 0.535-kg mass suspended from a spring undergoes simple harmonic oscillations with a period of 1.55 s How much mass, in kilograms, must be added to the object to change the period to 1.75 s?

Answers

Answer 1

0.207 kg or approximately 0.21 kg mass must be added to the object to change the period to 1.75 s.

Given, a mass of 0.535 kg suspended from a spring undergoes simple harmonic oscillations with a period of 1.55 s.

From the given information, we can use the formula of time period of simple harmonic motion as:

T = 2π √(m/k) where T is the time period, m is the mass, and k is the spring constant.

Since we want to find how much mass must be added to change the period from 1.55 s to 1.75 s, we can set up an equation:T1 = 1.55 s, T2 = 1.75 sT1 = 2π √(m/k)T2 = 2π √((m+M)/k)where M is the mass that needs to be added.

From the given information,T1 = 2π √(0.535/k)T2 = 2π √((0.535+M)/k)

Dividing the second equation by the first equation,

T2/T1 = √((0.535+M)/0.535)

Squaring both sides,T2²/T1² = (0.535+M)/0.535

Now we can solve for M,

M = (T2²/T1² - 1) × 0.535M = (1.75²/1.55² - 1) × 0.535M = 0.207 kg

Thus, 0.207 kg or approximately 0.21 kg mass must be added to the object to change the period to 1.75 s. This is because the time period of an oscillating mass is directly proportional to the square root of its mass. By adding mass to the object, we increase its mass and hence increase its time period.

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Related Questions

What are waveform conversion circuits? 2. Where are waveform conversion circuits typically used

Answers

Waveform conversion circuits, also known as signal conversion circuits, are electronic circuits designed to convert one form of an electrical waveform into another form. Waveform conversion circuits find application in a wide range of fields where the modification, conditioning, or transformation of electrical waveforms is necessary to achieve specific objectives.

These circuits modify the characteristics of an input signal to achieve a desired output waveform. The conversion can involve changing the amplitude, frequency, phase, or shape of the waveform.

Waveform conversion circuits are used in various applications where it is necessary to transform signals to match specific requirements. Here are some common areas where waveform conversion circuits are typically used:

Audio Processing: In audio applications, waveform conversion circuits are used to modify audio signals for various purposes. This includes amplifying, filtering, equalizing, or modulating audio waveforms to enhance sound quality, remove noise, or achieve specific audio effects.

Power Electronics: Waveform conversion circuits are extensively employed in power electronics systems for converting and conditioning electrical power. These circuits are used in devices such as inverters, converters, rectifiers, and voltage regulators to transform power waveforms, adjust voltage or current levels, and ensure efficient power transfer.

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Which of the following equations is dimensionally invalid

a. v=x+at
b. x=at^2
c. v=\(\sqrt{2ax}\)
d. v\(v_{f} =v_{i} -at\)

Answers

the answer should be A or D

Two forces acting on an object in the same direction. One is 25N West and the other is 15 N West. What is the net force?

Answers

Answer: 40 N

Explanation: 25N + 15N

Here’s my work to your question
Two forces acting on an object in the same direction. One is 25N West and the other is 15 N West. What

a 10kg box has u of 0.4 with surface if the box accelerates at 1.08 m\s^2 what was the applied force

Answers

Answer:

The distance from Jerusalem to Galilee is approximately 150 km depending on the route you take. You can get a bus from Jerusalem's central bus station to Tiberias, on the edge of the Sea of Galilee. The journey takes about 2-3 hours.Sep 4, 2019

Which switching device creates its own electrical voltage pulse?

Answers

Transistor.

A switching device that creates its own electrical voltage pulse is called a "transistor." Transistors are active semiconductor devices that can amplify or switch electronic signals and electrical power. They consist of three layers of semiconductor material and can operate in different modes, such as common-emitter, common-base, or common-collector configurations.

When a transistor is used as a switch, it can generate its own electrical voltage pulses by controlling the flow of current through it. In the "on" state, the transistor allows current to flow from the collector to the emitter, creating a low resistance path. In the "off" state, the transistor blocks current flow, creating a high resistance path. By switching between these two states rapidly, transistors can generate voltage pulses.

There are different types of transistors, such as bipolar junction transistors (BJTs) and field-effect transistors (FETs). Both types can be used as switching devices and produce their own voltage pulses when appropriately biased and driven by an input signal.

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yo help please i’ll give u a brainliest

yo help please ill give u a brainliest

Answers

Couldn’t really read or see the problem clearly, but from what I think I saw I would say B

a car takes off from rest and covers a distance of 80m on a straight road in 10s. Calculate the magnitude of its acceleration​

Answers

Answer:

The magnitude of the acceleration is 1.6 m/s².

Explanation:

We can find the magnitude of the acceleration by using the following equation:

\( x_{f} = x_{0} + v_{0}t + \frac{1}{2}at^{2} \)

Where:

\( x_{f}\): is the final position = 80 m

\( x_{0\): is the initial position = 0

\( v_{0}\): is the initial speed = 0 (it starts from rest)

a: is the acceleration =?

t: is the time = 10 s

Hence, the acceleration is:

\( a = \frac{2x_{f}}{t^{2}} = \frac{2*80 m}{(10 s)^{2}} = 1.6 m/s^{2} \)

Therefore, the magnitude of the acceleration is 1.6 m/s².

I hope it helps you!          

A. It Implies That M Is Finitely Generated. B. It Implies That M Has Nonzero Elements Of Nonzero Order. C. When Every Non-Null Element Has Null . D. In The Case That The Ring R Is A Body. E. None Of The Above Alternatives Gives A
Which of the following alternatives give a true statement. Justify your answer.
A modulus M over a ring R has a finite basis:
a. It implies that M is finitely generated.
b. It implies that M has nonzero elements of nonzero order.
C. When every non-null element has null .
d. in the case that the ring R is a body.
e. None of the above alternatives gives a true statement.
Which of the following statements are true?
a. If a subset of a module generates that whole module, then the subset cannot be
empty.
b. Every submodule S of a module M verifies the inequality C. Two different subsets of M have to generate two different submodules of M.
d. If S generates a submodule N of the module M, then contains S.
e. Neither statement is true.

Answers

The correct answer is e. None of the above alternatives gives a true statement. None of the statements in options a, b, c, and d are true when it comes to a modulus M over a ring R having a finite basis.

When a modulus M can be formed entirely from a finite set of elements, the modulus M is said to be finitely generated. M's finite basis does not, however, automatically imply that M is finitely generated. A basis is a set of linearly independent elements, and it might not be enough to produce all of the components of the modulus.

According to the assertion in option b, M must include nonzero items of nonzero order if it has a finite basis. This is untrue, though. The smallest positive number k, such that the element raised to the power of k equals the identity element, is referred to as the order of an element.

According to option c, every non-null element in a modulus with a finite basis has a null. Nevertheless, this claim is likewise untrue. It is possible for a modulus with a finite basis to have non-null elements without a null element.

According to option d, a ring R is a body, or a field, and only then can a modulus have a finite basis. However, this assertion is also untrue. Even though the ring R is not a field, a modulus can nonetheless have a finite basis. None of the given alternatives provides a true statement about a modulus M over a ring R having a finite basis.

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Two technicians are discussing a resistance measurement between the can-h and can-l wires. Technician a says this measurement should be done with the ignition switch in the "run" position. Technician b states that a measurement of 0 ohms indicates an open in the network. Which technician is correct?

Answers

Based on the information given, the technician that's correct regarding the resistance measurement between the wires is Technician A.

Who is a technician?

It should be noted that a technician simply means an individual that's in charge of looking after the technical equipment in an organization.

In this case, Technician A is correct. Technician B is incorrect as zero-ohm doesn't indicate an open circuit in the network but rather, a complete circuit.

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the direction of the force of sliding friction is always select one to that of velocity of the object and is select one static friction. State True or False your answer:
a. True
b. False

Answers

The given statement was false as sliding friction is lower than static friction.

what is Sliding friction ?

The friction experienced by two bodies in a comparable sliding motion is referred to as sliding friction. Sliding friction, like any other form of friction, may produce wear and tear on moving bodies.

Kinetic friction is a notion that defines the friction that happens as something slides. Because sliding friction is lower than static friction, moving a moving body is much easier than moving a stationary body (rest).

In contrast, the frictional force associated with a sliding motion is typically substantially larger. Although sliding friction is unaffected by surface area or total area of contact, it is greatly impacted by two factors: the kind of moving objects and their mass.

The given statement was false as sliding friction is lower than static friction.

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If a 1200 N box were lifted off the ground


1. 5 m. How much work would be done

Answers

If a 1200 N box were lifted off the ground for a distance of 5 m, the amount of work done would be 6000 J.

Work (W) is defined as the product of the force (F) applied on an object and the distance (d) over which the force is applied. Mathematically, W = Fd.

In this case, the force applied is the weight of the box, which is 1200 N. The distance through which the box is lifted is 5 m. Therefore, the work done in lifting the box can be calculated as W = Fd = 1200 N x 5 m = 6000 J.

This means that lifting the box requires an input of 6000 Joules of energy.

It is important to note that as work is a scalar quantity and the direction of the force and displacement are parallel, therefore, work done is simply the product of force and displacement.

Additionally, the work done on the box is equal to the potential energy gained by the box, which is at a height above the ground.

Therefore, if the box is allowed to fall back to the ground, it will release the same amount of potential energy as it gained, which will be converted into kinetic energy.

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The X-axis of a position-time graph represents

Answers

Answer:

The motion of an object can be represented by a position-time graph like Graph 1 in the Figure below. In this type of graph, the y-axis represents position relative to the starting point, and the x-axis represents time

Explanation:

Weighing a Bacterium Scientists are using tiny, nanoscale cantilevers 4 micrometers long and 500 nanometers wide-essentially miniature diving boards-as a sensitive way to measure mass. The cantilevers oscillate up and down with a frequency that depends on the mass placed near the tip, and a laser beam is used to measure the frequency. A single E. coli bacterium was measured to have a mass of 710 femtograms = 7.10×10−16 kg with this device, as the cantilever oscillated with a frequency of 17.1 MHz .
Treating the cantilever as an ideal, massless spring, find its effective force constant.

Answers

If we consider the cantilever to be a perfect, massless spring, then K = 5.952N/m is its effective force constant.

How does science define force?

The meaning of the term "force" is obvious. At about this point, it's perfectly permissible to describe a force as shoving or pulling. An object doesn't "have a force in it" or "contain a force." A force is applied to one thing by another.

Why is force such a big deal?

A force can be a push or a pull, and it affects how we go about our daily lives because we can't open or close items, raise our legs or arms or accomplish a lot more without it.

Briefing

Numerous E coli bacteria, m = 7.10 × 10⁻¹⁶

frequency =17.1 MHz

frequency of vibration, F = 1/2π√K/M

17.1×10⁶= 1/2π√K/ 7.10 × 10⁻¹⁶

K/ 7.10 × 10⁻¹⁶ = 7.10 ×10¹⁵

K = 5.952N/m

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what is the height of an inclined plane in order that a circular disk will roll from rest to the bottom with a final velocity of 20 m/s?

Answers

Answer:

30 m

Explanation:

Potential energy = kinetic energy + rotational energy

PE = KE + RE

mgh = ½ mv² + ½ Iω²

For a disk, I = ½ mr².  For rolling without slipping, ω = v/r.

mgh = ½ mv² + ½ (½ mr²) (v/r)²

mgh = ½ mv² + ¼ m v²

mgh = ¾ m v²

gh = ¾ v²

h = 3v² / (4g)

h = 3 (20 m/s)² / (4 × 10 m/s²)

h = 30 m

A 4 kg object is moving 2 m/s to the right. A 6 N pushes to the left for 3 seconds. Calculate the momentum before

Answers

The momentum of an object is defined as the product of its mass and velocity. To calculate the momentum of the object before the 6 N force is applied, we need to know the initial velocity.

Given that the object is moving at 2 m/s to the right, we can consider this as the initial velocity. The mass of the object is given as 4 kg.

The formula to calculate momentum is:

Momentum = mass × velocity

Plugging in the values, we have:

Momentum = 4 kg × 2 m/s

Multiplying 4 kg by 2 m/s gives us a momentum of 8 kg·m/s to the right. This is the momentum of the object before the 6 N force is applied.

It's important to note that momentum is a vector quantity, which means it has both magnitude and direction. In this case, since the object is moving to the right, the momentum is positive, indicating its direction of motion.

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- Explain why an aircraft will tend to lose height
when banking, unless the pilot increases its speed to
provide more lift.

Answers

Answer:

the planes wings are lifting  at an angle to gravity so the plane isn't lifting as much against gravity when it banks.  some of the wing lift is going into turning the plane.   :)   so it needs more lift to bank and stay up

Explanation:

Banking the aircraft no longer regulates the quantity of lift being generated by the wing.

Why an aircraft will tend to lose height when banking?

If the aircraft was making simply sufficient elevate to stay within the air before the bank (because it typically is), then whilst the aircraft has banked the share of elevating acting “upward" will now not be sufficient to equal the plane's weight, so the plane will start to descend.

The ordinary method of the pilot in this example is to increase the entire raise generated by the wing, by means of the growing attitude of attack, till the upward issue of carrying is over again sufficient to maintain up the aircraft.

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When researchers implanted electrodes into a person's hippocampus, they found cells sensitive to what? A. Color B. Temperature C. Location D. Rhyming.

Answers

When researchers implanted electrodes into a person's hippocampus, they found cells sensitive to location. The hippocampus is responsible for spatial navigation and memory, so it makes sense that it would have cells that are sensitive to location.

This discovery has important implications for our understanding of how the brain works and how we form memories of the world around us. It also has potential applications in the development of new treatments for disorders such as Alzheimer's disease, which is characterized by a breakdown in memory function. By understanding how the hippocampus works at the cellular level, researchers may be able to develop new therapies to help people with memory impairments.


When researchers implanted electrodes into a person's hippocampus, they found cells sensitive to "C. Location." These cells are called place cells, and they play a crucial role in spatial navigation and memory formation. Place cells fire in response to specific locations within an environment, creating a cognitive map for navigation. This discovery has significantly contributed to our understanding of how the brain processes and stores information about our surroundings, ultimately helping us navigate through the world.

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A 10 Ohm resistor and a 4 Ohms Resistor are wired in series. What is the equivalent resistance of these two resistors? a. 14 Ohms b.6 Ohms c.2.86 Ohms d. 0 Ohms unless it is connected to a battery. QUESTION 2 A 10 Ohm resistor and a 4 Ohms Resistor are wired in series. What is the voltage drop across the 10 Ohm resistor if they are connected to a 5 V battery? a. 1.4 V b.0V c. 3.6 V d.5V QUESTION 3 A 10 Ohm resistor and a 4 Ohms Resistor are wired in series. How much current flows through the 10 Ohm resistor if they are connected to a 5 V battery? a. 0.5 A b. 0.36 A

Answers

1. The equivalent resistance of a 10 Ohm resistor and a 4 Ohm resistor wired in series is 14 Ohms.

2. The voltage drop across the 10 Ohm resistor, when connected to a 5 V battery, is 3.6 V.

3. The current flowing through the 10 Ohm resistor, when connected to a 5 V battery, is 0.36 A.

1. When resistors are connected in series, the equivalent resistance is the sum of individual resistances. Therefore, the equivalent resistance of a 10 Ohm resistor and a 4 Ohm resistor wired in series is 10 Ohms + 4 Ohms = 14 Ohms.

2. In a series circuit, the total voltage of the battery is distributed across the resistors. Since the resistors are connected in series, the same current flows through both resistors. The voltage drop across a resistor can be calculated using Ohm's law:

\(V = I * R\)

where V is the voltage, I is the current, and R is the resistance. Given a 5 V battery and a total resistance of 14 Ohms, the voltage drop across the 10 Ohm resistor can be calculated as follows:

\(V_{10 }= (10 \ Ohms / 14\ Ohms) * 5\ V = 3.6\ V\)

3. In a series circuit, the current remains constant throughout. The current flowing through the resistors can be calculated using Ohm's law: I = V / R, where I is the current, V is the voltage, and R is the resistance. Given a 5 V battery and a total resistance of 14 Ohms, the current flowing through the circuit is: I = 5 V / 14 Ohms = 0.36 A. Since the same current flows through both resistors in a series circuit, the current flowing through the 10 Ohm resistor is also 0.36 A.

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Which two factors affect the strength of gravitational force?
a.
Distance and mass
b.
Distance and speed
c.
Speed and velocity
d.
Mass and weight

Answers

I think it’s C, sorry if it’s wrong

Answer:

a

Explanation:

The speed, v, of an object moving along a straight line can be given in terms of time, t by v = at +b/(t-c)where a, b, c are constants. Assume, the expression is physically correct. If the dimensions of v are L/T, determine the dimensions of the terms a, b and c. Carefully layout your procedure.

Answers

Given

\(v=at+\frac{b}{t-c}\)

Procedure

Dimensions of v are L/T

The answer would be:

\(LT^{-2},L\text{ and T}\)

The letter a is multiplying to one dimension in time, so it must be a value of distance over two of time. LT^(-2)

The letter b is in the numerator so it must be a distance dimension. L

The letter c is being operated as a subtraction in the denominator so it must be time T

a solid sphere of mass and radius 20kg and 4m is rotating with an angular velocity of 40rad/sec is accelerated uniformly to 60rad/sec in 2sec what is the torque acting on the sphere? (I=0•4MR^2)​

Answers

Answer:

1280Nm

Explanation:

torque= I×alpha(angular acceleration)

so Angular acceleration is found by the following process.

a solid sphere of mass and radius 20kg and 4m is rotating with an angular velocity of 40rad/sec is accelerated

Given a table of values for the exponential function f(x) and a description of the
transformation for the function g(x)
, fill out the table of values based on the original
points for glx), the transformed function.
- 1
0
2
16
3
Reflect over
0
2
4
0-4, -1, -12
1
16
.
64
01, 1, 4, 16, 64
,
4, 1, , 162
0-1, -1, –4, – 16, – 64

Given a table of values for the exponential function f(x) and a description of thetransformation for

Answers

Answer:its D

Explanation:

i did the test and got it right

The transformation function of the given exponential function is -1/4, -1, -4, -16, -64. Hence option D is correct.

What is an exponential function?

An exponential function is a mathematical relation to find exponential growth or decay for the given data. It represents the constant change in independent variables and gives the same proportional change.

The exponential function is expressed as f(x) = exp (x) or eˣ where x is variable and e is constant which is called the base of the equation.  

From the given,

the exponential function f(x) = 1/4, 1,4,16,64

The transformation function G(x) is the inverse of the exponential function and is equal to -1/4,-1, -4,-16,-64.

Hence, the ideal solution is option D.

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A spring has a force constant of 40000 N/m.
How far must it be stretched for its potential energy to be 42 J?
Answer in units of m

Answers

Answer:

0.05m

Explanation:

Given parameters:

Force constant of the spring  = 40000N/m

Potential energy  = 42J

Unknown:

Extension  = ?

Solution:

To solve this problem, use the expression below:

           E.PE  = \(\frac{1}{2}\) k e²  

k is spring constant

e is the extension

              42  =  \(\frac{1}{2}\)  x 40000 x e²  

               e  = 0.05m

How much net force is required make a 10 kg box accelerate at a rate of 5 m/s2?
O2N
0 50 N
0 15 N
0 100 N

Answers

F = (mass)(acceleration)

F = (10)(5)

F = 50

Answer: 50 N

True or False an overtone occurs when two or more sound waves are produced at the same time.

Answers

Answer:

True, overtone occurs when two or more sounds are produced at the same time.

Answer:

This statement is true.

Explanation:

for each of the following cases, indicate whether the work done is positive or negative. explain your answers. a) work done by an applied force in lifting a bucket of water upward. fa mg b) work done by the weight of the bucket c) work done by the applied force and mg if the bucket were lowered.

Answers

The work done in case a) is positive, in case b) is negative and in case c) is positive.

Work is said to be done when the displacement is occur in the direction of the applied force.  

W = F×d×cosθ

Where F is the force, d is the displacement and θ is the angle between the displacement and the direction of the force.

In case a) as the work is done against the direction of the gravity so the work is positive. In case b) the weight of the buckets acts in downwards direction, that is the direction of the acceleration due to gravity. So the work is negative. In case c) the bucket were lowered, it means the displacement is in the direction of the applied force. Hence the work done is positive.

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Mercury has a radius of 2.43x10^6 m, and a mass of 3.2x10^23 kg, what is Mercury's acceleration due to gravity?

Answers

I think that you need the gravitational acceleration of mercury

so we will use Newton's gravitational law :

gravitational acceleration = \(\frac{G * m}{r^{2} }\)

G is the gravitational constant = G = 6.673×10^-11 N m^2 kg^-2

after substitution :

6.673×10^-11 * 3.2x10^23 / (2.43x10^6)^2

using calculator :

gravitational acceleration of mercury = 3.61625 m/s^2

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Se colocan tres objetos, muy cerca uno del otro, dos al mismo tiempo. Cuando se juntan los objetos A y B, se repelen. Cuando se acercan los objetos B y C, se repelen. De los siguientes enunciados, ¿cuál es el verdadero? a) Los objetos A y C tienen cargas del mismo signo. b) Los objetos A y C poseen cargas de signos opuestos. c) Los tres objetos tienen cargas de distinto signo. d) Uno de los objetos es neutro. e) Es necesario llevar a cabo experimentos adicionales para determinar los signos de las cargas.

Answers

Answer:

Los objetos A y C tienen cargas del mismo signo (opcion a)

Explanation:

Hay dos tipos de cargas : cargas positivas y cargas negativas.

La Ley de Coulomb dice que la fuerza electrostática entre dos cargas puntuales es proporcional al producto de las cargas e inversamente proporcional al cuadrado de la distancia que las separa, y tiene la dirección de la línea que las une y se cumple que:

La fuerza ejercida sobre una carga apunta hacia la otra cuando las dos tienen distinto signo (fuerza atractiva). El sentido de la fuerza se dirige hacia el lado opuesto de la carga cuando ambas tienen el mismo signo (fuerza repulsiva).

Es decir que las cargas de igual signo se repelen, mientras que las de diferente signo se atraen.

Entonces, si se juntan los objetos A y B y se repelen significa que la carga es del mismo signo.

Cuando se acercan los objetos B y C, se repelen. Entonces significa que posee carga de igual signo.

Por lo que podes concluir que los objetos A y C tienen cargas del mismo signo (opcion a)

a hydraulic press has an input cylinder 4 inches in diameter and an output cylinder of 10 inches in diameter. if the input piston moves 5 inches, how far does the output piston move?

Answers

To determine how far the output piston moves in a hydraulic press, we can use the principle of Pascal's law, which states that the pressure applied to an enclosed fluid is transmitted uniformly to all parts of the fluid and the enclosing walls.

In this case, we can calculate the displacement of the output piston using the following formula:

Output displacement = (Input displacement) * (Input cylinder area / Output cylinder area)

First, let's calculate the areas of the cylinders using the formula for the area of a circle:

Input cylinder area = π * (input cylinder radius)^2

Output cylinder area = π * (output cylinder radius)^2

Given:

Input cylinder diameter = 4 inches

Output cylinder diameter = 10 inches

Input displacement = 5 inches

Calculations:

Input cylinder radius = input cylinder diameter / 2 = 4 inches / 2 = 2 inches

Output cylinder radius = output cylinder diameter / 2 = 10 inches / 2 = 5 inches

Input cylinder area = π * (2 inches)^2 = 4π square inches

Output cylinder area = π * (5 inches)^2 = 25π square inches

Output displacement = (5 inches) * (4π square inches / 25π square inches)

Output displacement = (5 inches) * (4/25)

Output displacement = 0.8 inches

Therefore, the output piston will move 0.8 inches when the input piston moves 5 inches in a hydraulic press with an input cylinder diameter of 4 inches and an output cylinder diameter of 10 inches.

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The radius of the planet Mercury is 2.43 x 10^6m and its mass
is 3.2 x 10^23 kg. What is the speed of a satellite in orbit
265.000 m above the surface?

The radius of the planet Mercury is 2.43 x 10^6m and its massis 3.2 x 10^23 kg. What is the speed of

Answers

Hey There!_____________________________________Answer:

\(\huge\boxed{Option D}\)

_____________________________________DATA:

Radius of Mercury = \(R_m\) = \(2.43x10^6m\)

Mass of Mercury = \(M_m = 3.2x10^{23}m\)

Distance Satellite above the surface of the Mercury = d = 265,000m

Gravitational Constant =  \(G = 6.67x10^{-11} \frac{N.m^2}{kg^2}\)

_____________________________________SOLUTION:

Since the Satellite is orbiting around the Planet Mercury, due to the centripetal force, and Centripetal force is the force that acts towards the center of the circle, Whereas The gravitational force also acts towards the center of the circle thus we can say that Centripetal force is equal or same as centripetal force.  So,

               

                                             \(F_g =F_C\)

Fg is Given by,

                                           \(F_g = \frac{GM_MM_S}{r^2}\)

Fc is Given by,

                                           \(F_c=\frac{M_SV^2}{r}\)

Where,

            G is Gravitational Constant

            \(M_e\) is mass of Planet Mercury

            \(M_S\) is Mass of Satellite

             r(small letter) is the distance between the center of the Planet Mercury and the satellite.

             V is velocity of satellite

_____________________________________

Now,

                                 \(\frac{GM_MM_S}{r^2} =\frac{M_SV^2}{r}\)

                         

                                 \(V = \sqrt\frac{GM_M}{r}\)

 r can also be written as,

                           

                                  \(V = \sqrt\frac{GM_M}{R_M +d}\)

Substitute the variables,

         

                                  \(V = \sqrt{\frac{(6.67x10^{-11})x(3.2x10^{23})}{2695000}\)

Simplify the equation,

           

                                  V = 2814 \(\frac{m}{s}\)

Approximately,

                                  V = 2800 \(\frac{m}{s}\)

_____________________________________Best Regards,'Borz'
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