A roller coaster travels around a vertical 8-m radius loop. Determine the speed at the top of the loop if the normal force exerted by the seats on the passengers is equal to ¼ of their weight.

Answer:

The work done by friction was [tex]-4.5\times10^{5}\ J[/tex]

Explanation:

Given that,

Mass of car = 1000 kg

Initial speed of car =108 km/h =30 m/s

When the car is stop by brakes.

Then, final speed of car will be zero.

We need to calculate the work done by friction

Using formula of work done

[tex]W=\Delta KE[/tex]

[tex]W=K.E_{f}-K.E_{i}[/tex]

[tex]W=\dfrac{1}{2}mv_{f}^2-\dfrac{1}{2}mv_{f}^2[/tex]

Put the value of m and v

[tex]W=0-\dfrac{1}{2}\times1000\times(30)^2[/tex]

[tex]W=-450000 \ J[/tex]

[tex]W=-4.5\times10^{5}\ J[/tex]

Hence, The work done by friction was [tex]-4.5\times10^{5}\ J[/tex]

Answer:

(4xy+5ab)(4xy-5ab)

Explanation:

16[tex]x^{2}[/tex][tex]y^{2}[/tex]-25[tex]a^{2}[/tex][tex]b^{2}[/tex]

4^2 is 16 and 5^2 is 25,

Also, (x-a)(x+a) = x^2-a^2

So, this factorized is:

(4xy+5ab)(4xy-5ab)

Hope this helps!

Answer:

240 s or 4 minutes.

Explanation:

Given that

Volume of the cubic vat is 15.7³ = 3869.893 ft³

Density of the liquid is 1.31 g/mL

For easier calculations, we need to convert the density from g/mL to ft³

conversion factors shall be CUBED in order to do it!

We know that

1 inch = 2.54 cm, and

1 foot = 12 in

This means that

1.31 g/cm³ * 2.54³ cm³/in³ * 12³ in³/ft³

= 37095.069 g/ft³

Lastly,

We use this conversion method

1 second/ 2300 grams * 37095.069 g/ft = 16.13 ft³/s

Bringing down the volume of the cube, we use it to divide, and thus

3869.893 / 16.13 = 240 seconds

240 seconds = 4 minutes

Answer:

Fx = 121.24lb

F = 140lb

Explanation:

Since we are not given the angles subtended by the force, we can assume it to be 30 degrees.

The y component of the force expressed by the formula:

Fy = Fsintheta

Given the y-component of the force F to bee 70lb

70lb =  Fsintheta

Get magnitude of the force

F = 70/sin theta

F = 70/sin 30

F = 70/0.5

F = 140lb

Get the x-component of the force

Fx = Fcos theta

Fx = 140cos 30

Fx = 140(0.8660)

Fx = 1,212.4lb

Hence the  x-component of the force sis 121.24lb

Note that the angle used was assumed. Other values can as well be used

Answer:

it has constant angular velocity

Explanation:

an object moving in a uniform circular motion moves with constant angular velocity about a point

Answer:

umm  becuase it is a test and you need them

Explanation:

Answer:

Wedge

Explanation:

A knife is used to cut things into pieces or even cut two items apart.

Now, it is classified as a Wedge because a Wedge is defined as a simple machine that is used in pushing two objects apart. Some examples include axes, knives & chisels.

Answer:

[tex]E = -6 \ N/C[/tex]

Generally given that the electric field is negative it mean that its direction is opposite to that of the force    

Explanation:

From the question we are told that

   The charge on the small object is [tex]Q = -4.00 \ nC = -4.00 *10^{-9} \ C[/tex]

   The force is  [tex]F = 24 \ nN = 24 *10^{-9} \ N[/tex]

    Generally the magnitude of the electric  field is mathematically represented as

       [tex]E = \frac{F}{Q}[/tex]

=>    [tex]E = \frac{ 24 *10^{-9}} {-4 *10^{-9 }}[/tex]

=>     [tex]E = -6 \ N/C[/tex]

Generally given that the electric field is negative it mean that its direction is opposite to that of the force    

Answer:

The tennis ball will have more kinetic energy

Explanation:

It will have more kinetic energy because the tennis ball is more heavier than a wiffle ball. Furthermore, objects that are heavy will have more kinetic energy than objects that are light. Therefore, the tennis ball is the correct answer.

The tennis ball will have more kinetic energy as compared to the wiffle ball, because tennis ball is more heavier.

The energy possessed by any object due to virtue of its motion is known as kinetic energy. The standard expression for the kinetic energy is given as,

[tex]KE = \dfrac{1}{2}mv^{2}[/tex]

Here,

m is the mass of balls.

v is the speed of balls.

Clearly the kinetic energy of any object is dependent on the mass and velocity. So with same velocity, the heavier object will have more kinetic energy. Since, the tennis ball is more heavier as compared to the wiffle ball, therefore kinetic energy of tennis ball will be more.

Thus, we can conclude that the tennis ball will have more kinetic energy as compared to the wiffle ball, because tennis ball is more heavier.

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The question is incomplete. Here is the complete question.

Suppose the mass of a loaded elevator is 1600 kg.

(a) What force, in Newtons, must be supplied by the elveator's cable to produce an acceleration of 0.745 m/s² upwards against a 185N frictional force?

(b) How much work, in joules, is done by the cable in lifting the elevator 21m?

(c) What is the final speed, in meters per second, of the elevator if it starts from rest?

(d) How much work, in kilojoules, went into thermal energy produced by friction?

Answer: (a) F = 1377 N

              (b) W = 28917 J

              (c) v = 5.6 m/s

              (d) W = 3.885 kJ

Explanation:

(a) According to Newton's Second Law: [tex]F_{net}=m.a[/tex], in which, [tex]F_{net}[/tex] is the vetorial sum of all the forces in a system and its unit is [F] = kg.m/s² or newton (N).

In the elevator's case, and assuming going upwards is positive:

[tex]F-F_{f}=m.a[/tex]

F - 185 = 1600(0.745)

F = 1377 N

For an elevator to produce an acceleration of 0.745m/s² upwards, the cables have to supply a force of 1377 newtons.

(b) Work is the energy transferred to an object while is being moved. It is calculated as: W = F.s. Its unit is [W] = N.m or Joule (J)

In the elevator's cable:

W = 1377.21

W = 28917 J

The work done by the elevator's cable is W = 28917 joules.

(c) Acceleration is variation in velocity along time. Since we know the displacement of the elevator:

[tex]v^{2}=v_{0}^{2}+2a\Delta x[/tex]

where:

v₀ is initial velocity, which is this case v₀=0 because it starts from rest;

a is acceleration;

Δx is the displacement

Replacing values:

[tex]v^{2}=2(0.745)(21)[/tex]

[tex]v=\sqrt{31.29}[/tex]

v = 5.6 m/s

Final speed of the elevator is 5.6 m/s.

(d) [tex]W=F_{f}.s[/tex]

W = 185(21)

W = 3885 J

Work transferred into thermal energy because of friction is W = 3.885 kJ.

Answer:

    [tex]\frac{V}{2av}[/tex]

Explanation:

From the question we are told that

Volume V

Contains N particles

Leaks from a small hole of area A

Generally the equation for Flow rate is given as

Volume Flow Rate  [tex]V_r = A * v[/tex]

Mathematically we find the  time taken to flow half way which is given by

          [tex]\frac{(V/2)}{A*v}[/tex]

Therefore the  time taken is

           [tex]\frac{V}{2av}[/tex]

The most dense thing inside the column is the little star. It's pink, and it's resting on the bottom of the cylinder.

The red part under the star is the solid base that the cylinder is standing in. It's probably wood or plastic, it's not free to move, and it's not involved in the experiment.

Answer: That is not meant to be red, it‘s the bottom of the beaker. The star is at the very bottom of the beaker. it’s just the base of the beaker.

Answer:

312hz

Explanation:

thanks me later

Answer:

Since sea water contains alot of salt the density of the sea water is higher as to the river water . So it makes it easier to swim in sea water

Answer:

which items are matter?

battery , mobile phone

Answer:

The water kept in an earthen pot seeps into the small pores in the pot and evaporates from the surface of the pot. The heat required for evaporation is taken from water inside the pot, thus cooling the water stored inside. This is the reason why on hot summer days water remains cool in earthen pot.

Answer:

D. Involves mold filling with minerals and sediment

Explanation:

The given part  y is in the inter region of the circle labelled cast and imprints. Thus, it belongs to both. Cast fossils are a type of imprint fossils which are filled with minerals from sediments and hardens to form the fossils. Thus, option d is correct.

Fossils are decomposed plants or animals or their imprints indicating their actions such as footprints, shells etc. There are broadly two types of fossils namely body fossils and trace fossils.

Body fossils are decomposed body parts of animals or plants such as bones, tree branches, skull etc. Trace fossils are imprints of the animals or plants such as footprints, shells, caves, skin etc.

Imprint fossils are the impression of any activities or behaviour of living things. shell, leaf, caves etc are imprint fossils. Cast fossils are formed by filling of imprint fossils with minerals reached from water and sediments and hardened to fossils. Therefore, the given area is cast fossil and option d is correct.

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Answer:

Q = 675 [J]

Explanation:

We can calculate the amount of heat transfer by means of the following expression that includes the mass and temperature change in a body as a function of the specific heat.

[tex]Q=m*C_{p}*(T_{initial}-T_{final})[/tex]

where:

m = mass = 25 [gr]

Cp = specific heat = 0.9 [J/g*°C]

Tinitial = 55 [°C]

Tfinal = 25 [°C]

[tex]Q=25*0.9*(55-25)\\Q=675 [J][/tex]

Answer:

maxed out

Explanation:

Answer:

acceleration remains constant at g= 9.8m/s²

velocity however ...increases

Answer:

(C). The magnitude of electric force acting on the raindrop is 0.1 N.

Explanation:

Given;

charge of the raindrop, Q = 10  μC = 10 x 10⁻⁶ C

electric field strength, E = 10,000 V/m

The electric force acting on the raindrop is given as;

F = EQ

where;

F is the electric force

Substitute the given values and solve for F.

F = (10,000)(10 x 10⁻⁶)

F = 0.1 N

Therefore, the magnitude of electric force acting on the raindrop is 0.1 N.

Answer:

The answer is  "-72 k".

Explanation:

Please find the complete question in the attached file.

Given point:

[tex]A=(0,0,0)\\B=(0,8,0)\\C=(9,8,0)\\D=(9,0,0)[/tex]

[tex]\bar{AB} = (0i+8j+0k)-(0i+0j+0k)= 8j\\\\\bar{AC} = (9i+8j+0k)-(0i+0j+0k)= 9i+8j\\\\[/tex]

Calculating the area:

[tex]Area=\left|\begin{array}{ccc}i&j&k\\0&8&0\\9&8&0\end{array}\right|[/tex]

       [tex]=i[8(0)-8(0)]-j[(0-0)]+k[(0-9(8))]\\\\=i[0-0]-j[(0)]+k[(0-72)]\\\\=i[0]-j[(0)]+k[(-72)]\\\\=-72 \ k[/tex]

Answer:

h = 5.09 m

Explanation:

Applying the Law of conservation of energy to this situation, we can write:

[tex]Kinetic\ Energy\ Gained\ by\ the\ Cart = Potential\ Energy\ Lost\ by\ the\ Cart\\\frac{1}{2}mv^2 = mgh\\\\h = \frac{v^2}{2g}[/tex]

where,

h = height of the hill = ?

v = speed of cart at the end = 10 m/s

g = acceleration due to gravity = 9.81 m/s²

Therefore,

[tex]h = \frac{(10\ m/s)^2}{(2)(9.81\ m/s^2)}\\\\[/tex]

h = 5.09 m

Answer:

Telescopes have changed the way scientists study the Solar System. Before telescopes, people were only able to observe the Universe with their naked eyes. ... If it were not for telescopes, scientists would not be able to detect possible threats to Earth or predict comet's sightings.

Explanation:

400 years ago, before telescopes, our understanding of the universe was very different.

This is what was believed:

We live on a spherical ball orbited by the rest of a finite, spherical universe.

Earth does not move. It is the center of the universe.

Our Sun orbits the Earth, as do all the other planets and the Moon.

The stars are distant objects, always perfect and unchanging.

How did telescopes & associated technologies unlock the secrets of the universe and

help us toward the understanding we have today where Earth is no longer at the center of

the universe? Instead, we know that ours is a small planet orbiting a star in the suburbs

of a large galaxy filled with billions of other stars and planets, surrounded by billions of

other galaxies becoming increasingly ever distant from each other by the expansion of

space.

This is the story of how telescopes continuously changed our understanding of the

universe and our place in it - transforming our view of our universe. And we still have

much more to discover!

2. Before telescopes, we could only use our eyes and a variety of measuring instruments to

plot the positions and movements of objects in the sky to create a limited understanding

of our universe. We had no way to know what these objects actually were and little

evidence for our relationship to the cosmos.

Answer:

Answer is in photo

Explanation:

Answer:

0.32m/s2

Explanation:

obtained from a=wr2 where w=anular speed

r-radius

Centripetal acceleration refers to the acceleration experienced by an object moving in a circular path. The centripetal acceleration of the ball is approximately [tex]9.86 m/s^2.[/tex]

Centripetal acceleration is a result of the inward force known as the centripetal force that keeps the object moving in a curved path. This force is necessary to counteract the tendency of the object to move in a straight line tangent to the circle.

To find the centripetal acceleration of the ball, we can use the formula:

centripetal  acceleration = [tex](angular speed)^2 * radius[/tex]

First, let's convert the angular speed from revolutions per second to radians per second. Since 1 revolution is equal to [tex]2\pi[/tex] radians, we have:

angular speed in radians per second = [tex]0.500 rev/s * 2\pi rad/rev[/tex]

angular speed in radians per second =[tex]\pi rad/s[/tex]

Now, we can substitute the values into the formula to calculate the centripetal acceleration:

centripetal acceleration = [tex](\pi rad/s)^2 * 0.800 m[/tex]

centripetal acceleration = [tex]\pi ^2 * 0.800 m[/tex]

Using the approximation[tex]\pi = 3.14[/tex], we can calculate the centripetal acceleration:

centripetal acceleration = [tex](3.14)^2 * 0.800 m[/tex]

centripetal acceleration =[tex]9.86 m/s^2[/tex]

Therefore, the centripetal acceleration of the ball is approximately [tex]9.86 m/s^2.[/tex]

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Answer:

Gravitational Potential Energy of both will be equal

Explanation:

The gravitational potential energy is given by the following formula:

[tex]P.E = mgh[/tex]

where,

P.E = Gravitational Potential Energy

m = mass of object

g = acceleration due to gravity

h = height of object

Therefore, the gravitational potential energy of an object depends only upon the height of the object and its mass.

Since, both masses and the heights achieved by both people is equal. Therefore, their gravitational potential energies will also be equal