a block with mass m1 is placed on an inclined plane with slope angle α and is connected to a second hanging block that has mass m2 by a cord passing over a small, frictionless pulley. the coefficient of static friction is μs and the coefficient of kinetic friction is μk

Answers

Answer 1

The mass m2 for which block m1 moves up the plane at constant speed once it is set in motion is:

                      m2 = m1 (sinα + μkcosα)

The tension in the cord should be [tex]m_{2}[/tex]g so the that the hanging block over a frictionless pulley  can move at constant speed. This tension in the cord should the component of gravitational force and the force of friction.

Now

[tex]m_{2}[/tex]g = ([tex]m_{1}[/tex]g(sinα) +μk([tex]m_{1}[/tex]g)cosα)

[tex]m_{2}[/tex]g = [tex]m_{1}[/tex]g(sinα +μkcosα)

[tex]m_{2}[/tex]  = [tex]m_{1}[/tex] (sinα + μkcosα)

So the mass [tex]m_{2}[/tex]  for which m1 moves up the plane at constant speed once it is set in motion is:

                        m2 = m1 (sinα + μkcosα)

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Related Questions

Which of the following does not need to be considered when selecting a bow?

A. Is the bow made by hand?
B. Will you shoot right or left handed?
C. Will the bow be used for target shooting, hunting or both?
D. Can the bow be held without straining?

Answers

Answer:

A. Is the bow made by hand?

Explanation:

Hope this helps.

how do Mars’s surface and atmosphere differ from Earth’s?

Answers

Answer:Mars is about half the size of Earth by diameter and has a much thinner atmosphere, with an atmospheric volume less than 1% of Earth's. The atmospheric composition is also significantly different: primarily carbon dioxide-based, while Earth's is rich in nitrogen and oxygen.

Explanation:

Answer:The atmosphere of Mars is much thinner than Earth's. The average surface pressure is only about 610 pascals (0.088 psi) which is less than 1% of the Earth's value. The currently thin Martian atmosphere prohibits the existence of liquid water at the surface of Mars, but many studies suggest that the Martian atmosphere was much thicker in the past.

Explanation:

a parallel-plate capacitor has the volume between its plates filled with plastic with dielectric constant k. the magnitude of the charge on each plate is q. each plate has area a, and the distance between the plates is d. for related problemsolving tips and strategies, you may want to view a video tutor solution of a spherical capacitor with dielectric.

Answers

The Electric Field of the capacitor is given by E = q/kaε, Voltage is given by V = qd/kaε and the capacitance is given by kaε/d.

The magnitude of charge on each plate is given by q, area between the plates is given by a, dielectric constant is given by k, distance between the plates is d. The area of the enclosed charge 'a' is given by

q(enclosed) = σa(q/a)a, where σ is surface charge density given by q/a.

Now, according to gauss law, E = q/kaε.

Since, voltage = Electric field × Distance

V = E×d

V = (q/kaε)×d

V = qd/kaε

Now, the capacitance = Charge/Voltage

C = q/V

C = q/(qd/kaε)

C = kaε/d.

Thus, the value of Electric Field, Voltage and Capacitance are E = q/kaε, V = qd/kaε and C = kaε/d respectively.

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Complete Question

A parallel-plate capacitor has the volume between its plates filled with plastic with dielectric constant K. The magnitude of the charge on each plate is Q. Each plate has area A, and the distance between the plates is d.1. Use Gauss's law to calculate the magnitude of the electric field in the dielectric.2. Express your answer in terms of the given quantities and appropriate constants.3. Use the electric field determined in part A to calculate the potential difference between the two plates.4. Express your answer in terms of the given quantities and appropriate constants. Use the result of part B to determine the capacitance of the capacitor.5. Express your answer in terms of the given quantities and appropriate constants.

A teacher tells his class that a train is moving at 40 miles per hour. Does this tell them the speed of the train, the velocity of the train, or both?

Answers

This tell them the speed of the train.

Why is speed classified as a vector or a scalar quantity?

Because it has no specified direction and just magnitude, speed is a scalar number. The amount and direction of velocity are both vector variables.

Speed, as a scalar number, is the pace at which an item travels. The average speed is defined as the distance (a scalar number) divided by the time ratio. Speed is oblivious to direction. Velocity, on the other hand, is a vector quantity that is conscious of its direction.

Speed is described as the rate at which distance changes over time. It has a distance by time dimension. Thus, the SI unit of speed is defined as a combination of the fundamental units of distance and time.

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students work together during an experiment about newton’s laws. the students use a setup that consists of a cart of known mass connected to one end of a string that is looped over a pulley of negligible friction, with its other end connected to a hanging mass. the cart is initially at rest on a horizontal surface and rolls without slipping when released. the inertia of the cart's wheels is negligible. students have access to common laboratory equipment to make measurements of components of the system.

Answers

The tension in the string gets doubled when we double the mass of the cart as well as of the mass that hangs from the string.

We know, Newton's Second law states that the force applied to a body is directly proportional to the mass and the acceleration of the body, i.e.,

F = ma

where F is the force applied to the body or the tension in the cart, m is the mass of the body and a is the acceleration of the body.

Since, the mass of the cart is doubled, the tension on the string becomes:

[tex]F_{2}[/tex] = (2m)a

[tex]F_{2}[/tex] = 2ma

[tex]F_{2}[/tex] = 2F

Therefore, the tension in the string also gets doubled.

Complete Question: students work together during an experiment about newton’s laws. the students use a setup that consists of a cart of known mass connected to one end of a string that is looped over a pulley of negligible friction, with its other end connected to a hanging mass. the cart is initially at rest on a horizontal surface and rolls without slipping when released. the inertia of the cart's wheels is negligible. students have access to common laboratory equipment to make measurements of components of the system. The students double the mass that hangs from the string. They also replace the original cart with a new cart that has double the mass. By doubling both masses, how will the tension in the string and the acceleration of the cart change?

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A ball travels along a straight path, perpendicular to a wall. The ball bounces off the wall and returns with the same magnitude of momentum, p, with respect to a ground observer at rest. What expression shows the change in momentum as observed by the ground observer?.

Answers

From the question, we can see that the momentum is a vector thus the change in the momentum with respect to the ground observer ought to be zero.

What is momentum?

The term momentum has to do with the  product of the mass and the velocity of a body. Let us recall that the momentum of a body is a vector quantity thus we have to consider the magnitude as well as the direction of the vector.

With this said, we are going to consider the question more critically. We are told that; a  ball travels along a straight path, perpendicular to a wall. The ball bounces off the wall and returns with the same magnitude of momentum, p, with respect to a ground observer at rest.

Looking at the fact that the momentum of the body is a vector and we have seen told that the ball bounces off the wall and returns with the same magnitude of momentum the  it follows that the change in the momentum is zero.

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Missing parts;

A ball travels along a straight path, perpendicular to a wall. The ball bounces off the wall and returns with the same magnitude of momentum, p, with respect to a ground observer at rest. What expression shows the change in momentum as observed by the ground observer?

a. 0

b 0.5p

c 2p

d 1.5p

Imagine that you are comparing three different ways of having a ball move down through the same height. In which case does the ball reach the bottom with the highest speed?.

Answers

When comparing three different ways of having a ball move down through the same height each circumstance, the acceleration varies.

How gravity works on earth ?

The Earth's mass is what generates gravity. Your body's mass is affected by the combined gravitational pull of all of its mass. That is what gives you authority. If you were on a planet with a lower mass than Earth, you would also weigh less than you do now.

Every object in the universe that has mass is drawn to every other object, regardless of their size or location. Gravity exists whether you are on the Moon, the Earth, or far out in space. Gravity does not require air or an atmosphere to operate.

Acceleration due to gravity :

The acceleration of a body brought on by the force of the earth's gravitational field is known as the acceleration due to gravity, or simply g. This force can be expressed mathematically as mg, where m is the body mass.

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A boat travels north across a river at a velocity of 22 meters/second with respect to the water. the river's velocity is 2.2 meters/second to the east. what is the resultant velocity of the boat, as measured from the land? a. 24.2 meters/second northeast b. 35.5 meters/second north c. 22.1 meters/second northeast d. 28.7 meters/second east

Answers

The resultant velocity of the boat would be 22.11  meters/second northeast.

What is Velocity?

Velocity is the overall distance an object travels in a given amount of time.

As stated in the question that A boat crosses a river heading north at a speed of 22 meters per second relative to the water. To get the board's resulting velocity, we should know the river's eastward velocity, which is 2.2 meters per second.

velocity of the river = 2.2 meters/second to the east

velocity of the boat = 22 meters/second

The resultant velocity of the boat = √(22² + 2.2²)

                                                         = 22.11  meters/second.

Thus, The boat's final velocity would be 22.11 meter/second towards northeast.

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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS

A liquid has a mass of 25 grams (g) and a volume of 10 milliliters (mL). What is the density of the liquid?

A. 4.0 g/ml
B. 0.4 g/ml
C. 2.5 g/ml
D. 250 g/ml

Answers

Answer:

C. 2.5 g/ml

Explanation:

Divide mass by volume

A bicycle moves at an initial velocity of 5m/s accelerating constantly at 2.5m/s^2, what would be the displacement of the bicycle after 6.5 seconds?

Answers

The displacement of the bicycle is 85.3125m

Displacement of the bicycle may be defined as the change in position of the bicycle. It is a vector quantity so that it has direction and magnitude.

We are given that,

The initial velocity of the bicycle = u = 5m/s

The acceleration of the bicycle is = a = 2.5 m/s²

The time taken by the bicycle = t = 6.5 seconds

Therefore, to get the value of displacement of the bicycle by the equation of motion which is written as,

S = ut + (1/2) at²

Where, S is displacement, u is initial velocity, a is acceleration and t is time taken by the bicycle.

Since , putting the values in above equation then we get,

S = {5m/s × 6.5sec} +{ (1/2) × 2.5m/s² × (6.5 sec)²}

S = 32.5 m + 52.8125m

S = 85.3125m

Therefore, the bicycle would be moves 85.3125m

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a 1160 kg car traveling south at 24.0 m/s with respect to the ground collides with and attaches to a 2590 kg delivery truck traveling east at 16.0 m/s .

Answers

V=1160*24S/3750 + 2590*16E/3750 is the final velocity.

How to find the final velocity?

Given,

An 1160 kg car traveling south at 24.0 m/s

A 2590 kg delivery truck traveling east at 16.0 m/s gets collided and attached to the car.

Solution:

The momentum is conserved here

1160*24 S + 2590*16 E =(1160+2590)V

V = 1160*24 S + 2590*16 E/3750

V=1160*24S/3750 + 2590*16E/3750

The final velocity is V=1160*24S/3750 + 2590*16E/3750.

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Describe how the womans nervous system coordinates the reflex action

Answers

The nervous system in a woman can coordinate the reflex action due  skin receptors sense a stimulus, sensory neurons transmits the electrical impulses, motor neurons address it to the effect, and finally producing a response.

What is the reflex action?

Reflex action can be defined as an involuntary response to different environmental conditions, which are collectively called stimuli. These conditions may lead to a change in the body temperature and they are useful to adapt to a changing environment, which is a fundamental issue in adaptive responses.

The nervous system may manage reflex actions in this system by using specific cell receptors located at the epidermis (skin cells).

Therefore, we can conclude that the reflex action is a coordinated response of the nervous system associated with the detection of environmental stimuli that lead to the activation of effector cells and sensory neurons.

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isabella drops a pen off her balcony by accident while celebrating the successful completion of a physics problem. assuming air resistance is negligible, how many seconds does it take the pen to reach a speed of 19.62 \,\dfrac{\text {m}}{\text s}19.62 s m ​ 19, point, 62, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction? \text {s}s

Answers

If the air resistance is negligible, it will take 2 seconds to reach the ground.

What is air resistance?

Air resistance is the force that opposes an object's relative motion as it moves through the atmosphere. By working against the incoming flow's speed, these drag forces make the object travel more slowly. In contrast to other resistance forces, drag has a direct relationship with velocity because it is the portion of the net aerodynamic force that operates in the opposite direction from the direction of the movement.

As given in the question,

(initial vertical velocity) u = 0,

Air resistance is neglected,

g = 9.8 m/s².

The time (t), required for the pen to reach a vertical velocity of 19.62 m/s is given by:

19.62 m/s = 0 + (9.8 m/s²)*(t s)

t = 19.62/9.8 = 2.00 s

Answer:  2.0 s

Therefore, it will take 2 seconds for pan to reach the speed of 19.61 m/s.

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Complete Question

Isabella drops a pen off her balcony by accident while celebrating the successful completion of a physics problem. Assuming air resistance is negligible, how many seconds does it take the pen to reach a speed of 19.62 m/s?


Robert is looking at four galaxies:
an irregular galaxy the he calls "Calliope";
a spiral galaxy that he calls "Medea";
an elliptical galaxy that he calls "Minerva";
and a lenticular galaxy that he calls "Ariadne";
Which of these four is the youngest? A.Medea B.Ariadne C.Minerva D.Calliope

Answers

The youngest is Calliope.

What are  characteristics of a spiral galaxy?a prominent feature of the spiral arms that make up this flat, spinning disc of stars and interstellar debris.an elliptical galaxy-like stellar bulge with an older star-heavy core region.a star dispersion in the form of a bar.a halo of almost spherical stars, many of which are found in globular clusters.The majority of spiral galaxies have a flat, spinning disk of stars around a central bulge. Older, fainter stars make up the bulge in the center, which is thought to house a supermassive black hole. A bar structure runs through the core of almost two-thirds of spiral galaxies, including the Milky Way.

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What advice did the interviewee offer for students interested in his/her career?

Answers

The advice the interviewee offered for students interested in his/her career was to be hardworking and persistent.

What is a Career?

This is referred to as the chosen profession or occupation of an individual and is characterized by the individual taking the required courses or training which are needed in the execution of the tasks related to it.

The advise which was offered to the students was to be hardworking and persistent as there are lots of challenges and obstacles which one will face on the journey and will help overcome them and achieve the desired result in practicing the career.

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Find the y-component of this
vector:
22.3 m
77.1°
Remember, angles are measured from
the +x axis.

Answers

To find the y component you can draw a right triangle, and label the known information and what you are trying to find. You can use sin to find the answer
Sin(77.1 degrees)=y/22.3
(22.3)(sin(77.1 degrees))=y

21.7371746305 meters = y component

The figure shows a steady electric current passing through a wire with a narrow region. What happens to the drift velocity of the moving charges as they go from region a to region b and then to region c ?.

Answers

The drift velocity increases from A to B and decreases from B to C.

A drift velocity in physics is the average speed that charged particles—like electrons—achieve within a material as a result of an electric field. An electron will typically move randomly across a conductor at the Fermi velocity, producing an average velocity of zero. Applying an electric field causes a little net flow in one direction to be added to this random motion; this is the drift. Free electrons gain velocity in the direction opposite the electric field between collisions when a potential difference is applied across a conductor (and lose velocity when moving in the direction of the field), acquiring a velocity component in that direction in addition to their random thermal velocity.

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9. Twelve identical 2 W light bulbs are connected in series to a 240 V mains supply. The current in ampere through each lamp is (A) 0,05 (B) 0,1 (C) 6 (D) 10​

Answers

Since they are connected in series, the current in ampere through each lamp will be  0.01 A approximately. None of the options is correct.

What is Electrical Power ?

Electrical power is the rate at which electrical work (or electrical energy) is done. It is measured in Watt.

Given that twelve identical 2 W light bulbs are connected in series to a 240 V mains supply. The current in ampere through all the lamp will be the same because they are connected in series.

Power P = IV

Where

P = 2 WV = 240 VI = ?

Substitute all the parameters into the formula.

2 = I × 240  

I = 2 / 240

I = 0.0083 A

Therefore, the current in ampere through each lamp is 0.0083 A

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After the big bang occurred, the universe
a. shrank in size.
b. became denser.
c. became hotter.
d. began to cool.
I

Answers

It should be noted that after the big bang occurred, the universe "Became Denser" (Option B)

What is the explanation for this?

According to the Big Bang Theory, after the explosion which triggered the transformation of radiation into matter, gravity pulled dark matter together which in turn attracted normal matter.

Hence, it is right given the above analogy that the Universe became denser.

It should be mentioned that the big-bang hypothesis is a widely accepted account of the universe's evolution. Its defining characteristic is the universe's birth from a condition of great heat and density—the so-called big bang, which occurred 13.8 billion years ago.

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The data below were collected by scientists testing the force of gravity between two objects.
Distance Mass 1 Mass 2 Force
(kg) (kg)
(m)
(N)
0.10
100 150
0.00010
0.10
150
150
0.00015
0.10
100
300 0.00020
0.10
200
200
0.00027
0.10
200
300 0.00040
What do the data in the table support?
OA. The force of gravity between two objects is determined by the object with less mass.
OB. The force of gravity depends on the masses of the objects interacting.
OC.
The force of gravity between two objects is determined by the object with more mass.
D.
The force of gravity only depends on the distance between the objects interacting.

Answers

The data table supports that: Option B, "the force of gravity depends on the masses of the objects interacting." is the correct answer.

What is gravity?

Gravity, also sometimes called as gravitation, is the non-changing force of attraction that binds everything together in mechanics. Being the weakest known force in nature, it has little effect on determining the intrinsic properties of common objects.

In the given data table, the distance is same in all five cases, but we can see that the force of gravity is increasing with increase in mass of any one of the object or both of them. We can also understand it as the force of gravity is increasing with the increase in combined mass of both objects.

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When we rolled carts down a ramp, we measured the length of the ramp, the height of the lower part of the ramp, the height of the upper part of the ramp, and how long it took for the cart to reach the bottom of the ramp. Then we changed the height of the upper part of the ramp and measured how long it took for the cart to reach the bottom of the ramp.

Which variable was the Independent Variable in that situation?
How do you know it's the Independent Variable?

Answers

The force of gravity can more easily overcome the force of friction if the ramp is steep. Obviously, gravity causes an object on an incline to move faster down the slope than an object on a flat slope. Because of the increased height, falling takes longer.

What exactly is an independent variable?In mathematical modeling, statistical modeling, and experimental sciences, dependent and independent variables are variables. Dependent variables are so named because their values are studied in an experiment under the assumption or demand that they are dependent on the values of other variables due to some law or rule. In research, the best way to identify dependent and independent variables is to use the sentence "The Independent variable causes a change in the Dependent variable.Multiple independent variables are frequently included in experiments by researchers. The factorial design is the most common approach, in which each level of one independent variable is combined with each level of the others to generate all possible conditions.

Hence, The force of gravity can more easily overcome the force of friction if the ramp is steep.

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find the ratio of the masses m1/m2 . express your answer in terms of some or all of the variables a , μ , and θ , as well as the magnitude of the free-fall acceleration g .

Answers

The ratio of the masses is m1/m2.In terms of some or all of the variables a, μ, and θ, as well as the magnitude of the free-fall acceleration g.

m1/m2 = a+g(sinθ+μcosθ)/g−a

Acceleration describes the speed and direction changes in velocity over time. Acceleration refers to the change in speed or direction of an item or points traveling straight forward. Due to the constant change in direction, motion on a circle accelerates even while the speed is constant.

To be a vector quantity, acceleration must have both a magnitude and a direction. As a vector quantity, velocity is also. A time interval's velocity vector change divided by that interval's duration is the definition of acceleration. The limit of the ratio of the change in velocity over a certain period to that period as that period approaches zero is used to determine instantaneous acceleration.

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A simple machine is a machine that does work with only |two movements| of the machine
true or false
If false write the true answer

Answers

Answer:

hope it helps

Explanation:

The answer for this is true. The movements correspond.

sarah just bought a telescope and is telling you all about what she saw last night, but she keeps mentioning that every object she pointed it towards seemed to have a fuzzy glow. what type of telescope was she most likely using?

Answers

From the description, the  type of telescope was she most likely using is the radio telescope.

What is a telescope?

The telescope is the kind of device that could be used to find the and see the objects that are in the outer space. There are several kinds of telescopes such as;

radio telescoperefracting telescopecompound telescope reflecting telescope

The radio telescope is the kind of telescope that is able to convert the radio signals into a format that could be used study the parameters that concern the universe. The clarity of the telescope is most times dependent on the location of the person using the telescope.

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Missing parts;

Sarah just bought a telescope and is telling you all about what she saw last night, but she keeps mentioning that every object she pointed it towards seemed to have a fuzzy

glow. What type of telescope was she MOST likely using?

A. radio telescope

B. refracting telescope

C. compound telescope

D. reflecting telescope

Answer:

She is most likely using a refracting telescope.

Explanation:

These telescopes are easily accessible to the general public and are popular for new astronomers but may produce a fuzzy glow around objects they magnify.

Johnny is getting into building and launching model rockets. In designing a rocket, he has to select an engine based on how much force it produces. If his rocket has a mass of 5.00 kg and he wants it to have an acceleration of 28.8 m/s2, how much force in Newtons does the engine need to produce? (Answer should have 3 significant figures.)

Answers

In designing a rocket to select an engine based on how much force it produces, the engine need to produce 144 N force.

Equation :

Force applied on launching model rockets is calculated by the formula,

F = m*a

where,

F is the force of engine

m is the mass

a is the acceleration

The given data are :

m = 5 Kg

a = 28.8 m/s²

F = ?

Now, putting the values in the formula we get,

F = 5 Kg x 28.8 m/s²

F = 144 N

So,  In designing a rocket to select an engine based on how much force it produces, the engine need to produce 144 N force.

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a rabbit is moving in the positive x-direction at 1.50 m/s when it spots a predator and accelerates to a velocity of 10.9 m/s along the negative y-axis, all in 1.80 s. determine the x-component and the y-component of the rabbit's acceleration. (enter your answers in m/s2. indicate the direction with the signs of your answers.)

Answers

x-component of the rabbit's acceleration ax = -0.833m/s

y-component of the rabbit's acceleration ay =  -6.06m/s

How does acceleration work?

Acceleration is the rate of change in both speed and direction of velocity over time. When anything moves faster or slower in a straight line, it is said to have been accelerated. Because the direction is always shifting, motion on a circle accelerates even while the speed is constant.

Along x axis

Vox = velocity along the positive x-direction = 1.50 m/s

Vfx = 0m/s

ax = (Vfx-Vox)/T

ax=(0-1.5)/(1.8)

ax=-0.833m/s

x-component of the rabbit's acceleration ax = -0.833m/s

Along y axis

Voy = 0 m/s

Vfy = velocity along the negative y-axis -10.9m/s

ay=(Vfy-Voy)/T

ay= (-10.9-0)/(1.8)

ay = -6.06m/s

y-component of the rabbit's acceleration ay =  -6.06m/s

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Find the final velocity of the particle if it is initially moving along the x-axis with a velocity of −1.85 m/s

Answers

Although part of your question is missing, the complete question is "Find the final velocity of the particle if it is initially moving along the x-axis with a velocity of −1.85 m/s. The force shown in the force-time graph acts on a 2.4kg object."

The final velocity of the particle is 1.43 m/s.

The impulse of force is the product of the resultant force and duration of time under the impulse-momentum theorem.

Δρ = ΔF + Δ t = area under F-t curve.

area = area of rectangle + area of triangle( 1/2 base ×height )

area = (2× 3) + 1/2 (2×2) = 8 N

To find the final velocity, Δρ = mass × Δvelocity

let the final velocity be v'

∴  8 = 2.4 × ( v' - (-1.85))

2.4v' = 8- 4.44

v' = 1.43 m/s.

Hence the final velocity of the particle is 1.43 m/s.

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1. A cannon launches a shell with mass 100 kg toward a target. When the shell is at a height of 12 m its
velocity is 45 m/s. What is total mechanical energy of the shell?

Answers

Potential energy plus kinetic energy are combined to form mechanical energy. According to the principle of mechanical energy conservation, mechanical energy is constant in an isolated system when only conservative forces are acting on it.

E mechanical = U + K

E mechanical = mechanical energy

U = potential energy

K = kinetic energy

Mechanical energy, also known as kinetic energy or potential energy, is the energy that an object possesses when it is in motion or the energy that an object stores due to its location.

Renewable energy is also fueled by mechanical energy. In order to efficiently produce electricity or convert energy, many sources of renewable energy depend on mechanical energy.

Applying,

Mechanical Energy (M.E.) = ((1/2)mv²) + (m × g × h)

                                          = ((1/2)*100*45²)+(100*9.8*12)

                                          = 101250+ 11760

                                          = 113010 J

m is the object's mass, v is its speed, g is its gravitational acceleration, and h is its height above the ground.

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what force does a trampoline have to apply to a 45.0-kg gymnast to accelerate her straight up at 7.50 m/s2 ? note that the answer is independent of the velocity of the gymnast—she can be moving either up or down, or be stationary.

Answers

The force required will be 337.5 N

We have given the mass of the gymnast m = 45 kg

We have to find the force applied to the gymnast so that he can accelerate with the acceleration of 7.50m/sec^2

According to newtons law force on any object is given by F = ma, where m is mass and a is acceleration

So the force on the gymnast will be equal to F = 45×7.50  337.50 N

For acceleration of 7.50m/sec^2, we have to apply a force of 337.5 N

Acceleration is defined in mechanics as the rate of change of an object's velocity with respect to time. The orientation of an object's net force determines the orientation of its acceleration. Newton's Second Law states that the magnitude of an object's acceleration is the result of two causes:

the net balance of all external forces acting on that object — the magnitude of this net resulting force is related to its sizeThe magnitude is inversely related to the mass, depending on the materials used to make the thing.

The rate of acceleration is expressed in meters per second squared.

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calculate the 76- kg pilot's effective weight (the force with which the seat pushes up on him) at the bottom of the circle, and at the top of the circle (assume the same speed).

Answers

The minimum radius of the circle is 5249m

The 76kg pilot's effective weight at the bottom of the circle is 5214N

The pilot's effective weight at the top the circle is 3724N

Here's the complete question:

a jet pilot takes his aircraft in a vertical loop.

a) if the jet is moving at a speed of 2000 km/h at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0g's

b) calculate also the 76kg pilot's effective weight ( the force with which the seat pushes up on him) at the bottom of the circle.

c) calculate the pilot's effective weight at the top the circle. (Assume the same speed.)

a) To determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0g's.

v =2000 km/h

v = 2000/3.6 m/s

v = 555.6 m/s

centripetal acceleration, a

a = v²/r

Therefore

6g = v²/r

r = v²/(6g)

r =555.6²/(6*9.8)

r = 5249 m

b) The 76kg pilot's effective weight at the bottom of the circle

   76*(6g + g) = 76*7*9.8 = 5214 N

c) The pilot's effective weight at the top the circle.

    76*(6g-g) = 76*5*9.8 = 3724 N

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