Suppose a 65.5 kg gymnast climbs a rope. What is the tension in the rope if she climbs at a constant speed

The kinetic energy of the ball at the highest point of its motion is equal to 90.2 Joules.

Given the following data:

Mass of baseball = 0.150 kg

Speed of baseball = 40.0 m/s

V = v Cos(θ)

V= v cos 30

V= 40 x 0.867

V=34.68 m/s

K.E =1/2 MV^2

K.E= 1/2 x 0.150 x 34.68^2

K.E= 90.2 Joules.

Kinetic energy is a type of energy that an object or particle has due to its motion. When work is done on an object by applying a net force that transfers energy, the object accelerates, thereby gaining kinetic energy.

Kinetic energy has three subcategories: vibration, rotation, and translation. Naturally, the oscillating kinetic energy is caused by a vibrating object. Rotational kinetic energy is generated by moving an object, and translational kinetic energy is caused by the collision of an object.

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The amplitude of the wave is determined from the tension in the wire, speed of the wave, frequency of the wave and average power of the wave.

The amplitude of the wave travelling at the given frequency and power is calculated as follows;

U = (¹/₂)(T/v²)(ω²)(A²)(v)

U = (¹/₂)(T/v)(ω²)(A²)

U = (¹/₂)(T/v)(2πf)²(A²)

where;

Thus, the amplitude of the wave is determined from the tension in the wire, speed of the wave, frequency of the wave and average power of the wave.

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Answer:

don't know the answers sorry

The standard drink measurement should contain 14 grams of pure alcohol in United States of America.

Standard drink measurement can be defined as the measurement of alcohol that is expected by an individual to consume daily without having a bad health effect.

In the United States of America, an amount of 14 grams of pure alcohol which can be found in 12 ounces of beer is regarded as normal.

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The current in the second wire is 1.37 A.

The current in the second wire is calculated from the magnetic force between the two wires.

F/L = (μI₁I₂)/(2πr)

where;

μI₁I₂ = (F/L 2πr)

I₂  = ((F/L 2πr) / (μI₁)

I₂  = (7.7 x ⁻⁵ x 2π x 0.082)/(4π x 10⁻⁷ x 23)

I₂  = 1.37 A

Thus, the current in the second wire is 1.37 A.

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When the train is approaching then the frequency is 239.2 Hz.

This is the total number of times a periodic event happens within a given period of time. Wavelengths are used to measure periodic phenomena, which are frequently waves like sound waves. The frequency is the total number of wavelengths throughout time.

given,

speed of train = 34.5 m/s

Frequency of sound = 215 Hz

speed of sound = 341 m/s

when the train is approaching:

 [tex]f1 = f[/tex]ₓ [tex]\frac{V}{V-Vt}[/tex]

[tex]f1 = 215[/tex]ₓ [tex]\frac{341}{341 + 34.5}[/tex]

f₁ = 239.2 Hz                                

Hence, when the train is approaching then the frequency is 239.2 Hz.

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A current magnetic relay is often used to assist in the starting of the compressor, but most new appliances use positive temperature coefficient (PTC) device.

A compressor can be defined as a mechanical device that is designed and developed to provide power to refrigerators, especially by increasing the pressure on air or other applicable gases.

According to heating, ventilation, and air conditioning (HVAC), a current magnetic relay is mostly used to assist in the starting of the compressor, but many new electrical appliances use positive temperature coefficient (PTC) device.

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Answer:

6 pulse per second

Explanation:

if,

5 secs = 30 pulse

1 sec = 30/5

1 sec = 6

Answer:

1. Solar Nebula

2. The Sun

3. Planetesimals

4. Inner planets

5. Outer planets

Explanation:

A star is formed in a molecular cloud of gas and dust, mainly composed of hydrogen and helium. The Nebular Theory establishes, for the formation of the solar system, that the cloud starts to collapse under its own gravity when it receives a shock wave from a near event, for example, a supernova explosion. That results in the cloud breaking in small pieces, and those pieces constitute a possible future star.

Then it begins to accrete and rotate as a consequence of the angular momentum. In the center of that disk when it reaches the necessary temperature and pressure a protostar will born.

Around the star, in this case the Sun, fragments of dust combine until they get a meaningful size (planetesimals). According with chemical distribution on the disk of the future solar system, rocky and iron were closer to the Sun and gasses and ice were in the outer part of disk. That may explain why the inner planets are terrestrial and the outer planets are giant gasses.

Explanation:

there are 4 phases in which matter could be classified.

1. Solid: an example of this would be the metal copper.

2. Liquid: an example of this would be H2O or water.

3. Gas: an example of this would be oxygen gas or O2

4. Plasma: an example of this would be lightning.

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The lowest constant acceleration needed for takeoff from a 1.80 km runway is 2.8 m/s².

To find the answer, we need to know about the Newton's equation of motion.

=> 10000= 3600a

=> a= 10000/3600 = 2.8 m/s²

Thus, we can conclude that the lowest constant acceleration needed for takeoff from a 1.80 km runway is 2.8 m/s².

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Answer:

the maximum height reached by the object from where it was launched is 0.4591 m

Explanation:

initial speed of the object, u= 3 m/s

The velocity at the maximum height will always be 0.

Therefore,  final velocity, v= 0 m/s  

Using the Newton's  equation of motion,

v^2 - u^2 = 2*g*h(max)

0 - u^2= 2*g*h(max)

h(max) = -u^2 /2* g

where g is the gravitational acceleration.

g= - 9.8 m/s^2

substituting the values in equation,

h(max)= - (3*3) / 2*(-9.8)

h(max) =  0.4591 m

the maximum height reached by the object from where it was launched is 0.4591 m

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The coefficient of aerial expansion for metal b is one-fourth of the coefficient of aerial expansion for metal a.

Note: Most probably your question was to find the relation between the coefficient of aerial expansion for metal a and metal b.

Coefficient of linear expansion:

The ratio of the change in length of a solid to its original length when there is a unit change in temperature at constant pressure is called the coefficient of linear expansion. It is given by the formula,

α=ΔL/(Lo*ΔT)

where α is the coefficient of linear expansion,  ΔL is the change in length Lo is the original length, and ΔT is the change in temperature.

Coefficient of aerial expansion:

The ratio of the change in surface area of a solid to its original surface area when there is a unit change in temperature at constant pressure is called the coefficient of aerial expansion. It is given by the formula,

β=ΔA/(Ao*ΔT)

where β is the coefficient of aerial expansion,  ΔA is the change in surface area, Ao is the original surface area, and ΔT is the change in temperature.

Relation between α and β:

The relation between the coefficient of linear expansion and aerial expansion is given by the formula,

β=2α

Given that metal a has a coefficient of linear expansion four times that of  metal b. It can be written.

α₁=4α₂

where α₁ is the coefficient of linear expansion for metal a and α₂ is the coefficient of linear expansion for metal b.

Then from the above relation, the ratio of the coefficient of aerial expansion β₁ and β₂ for metal a and metal b respectively is,

β₁/ β₂ = 2*(α₁)÷(2*(α₂))

β₁/ β₂= 2*(4α₂)÷(2*(α₂))

β₁/ β₂=4

β₂= β₁/4

Therefore, the coefficient of areal expansion of metal b is one-fourth of the coefficient of aerial expansion of metal a.

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Answer: Horizontal Speed = 4.6 m/s

              Vertical Speed = 1.7 m/s

Explanation:

Jumper's velocity = 5 m/s

Angle = 20 degrees

the angle is theta, so theta = 20 degrees

Theta is the angle between the hypothenuse and the adjacent side.

The horizontal side will be the adjacent side, and the vertical side will be the opposite side.

The hypothenuse = 5 m/s

First, let's calculate the adjacent side (horizontal speed)

We have cosine of theta, which is equal to adjacent side / hypothenuse

So, [tex]cos(20) = adjacent/5[/tex]

Multiply 5 on both sides, to get the 5 on the right side canceled.

5cos(20) = adjacent side.

4.6 = adjacent side

Horizontal Speed = 4.6 m/s

Now, let's calculate the vertical speed.

To do that, we need to calculate the opposite side.

We can calculate the opposite side with the help of sin.

The sin of theta equals to opposite side / hypothenuse

[tex]sin(20)=opposite/5[/tex]

We do the same thing, multiply 5 on both sides.

5sin(20) = opposite

1.7 = opposite

Vertical Speed = 1.7 m/s

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The friction force between the box and the incline if the box does not slide down the incline will be 0.577

The force preventing sliding against one another of solid surfaces, fluid layers, and material components is known as friction. There are several kinds of friction: Two solid surfaces in touch are opposed to one another's relative lateral motion by dry friction.

Given the box resting on the inclined plane above has a mass of 20kg and the The incline sits at a 30 degree angle

We have to find the friction force between the box and the incline if the box does not slide down the incline

Since the frictional force F₁ must equal or exceed gravitational force F₂ down the incline:

F₁ = F₂

μmgcosΘ = mgsinΘ

μ = (mgsinΘ)/(mgcosΘ)

μ = tanΘ

μ = 0.577

Hence the friction force between the box and the incline if the box does not slide down the incline will be 0.577

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:The resistance created by the box's friction with the incline The slope will be 0.577 if the box doesn't descend.

Friction is the force that prevents solid surfaces, fluid layers, and material constituents from sliding past one another. Different types of friction exist. Dry friction opposes the relative lateral motion of two touching solid surfaces.

Given that the 20-kg box lying on the inclined plane above and the incline's 30 degree inclination

If the box does not slide down the incline, we must determine the friction force between them.

Given that the gravitational force F2 down the gradient must be equal to or greater than the frictional force F1,

F₁ = F₂

If mgcosx = mgsinx

equals (mgsinx)/(mgcosx)

μ = tanx

μ = 0.577

Therefore, if the box does not slide down the incline, the friction force between the box and the incline will be 0.577.

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The potential energy of the spring is 6.75 J

The elastic potential energy stored in the spring is given by the equation:

[tex]E= \frac{1}{2} kx^2[/tex]

where;

k is the spring constant

x is the compression/stretching of the string

In this problem, we have the spring as follows:

k = 150 N/m is the spring constant

x = 0.3 m is the compression

Substituting in the equation, we get

[tex]E=\frac{1}{2} (150) (0.3)^2[/tex]

[tex]E=6.75J[/tex]

Therefore. the elastic potential energy stored in the spring is 6.75J .

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The average velocity of the jet during the diversion is 518.75 m/s.

The displacement of the pilot from the starting position is calculated as follows;

d² = 20² + 60² - 2(20)(60) x cos(θ)

where;

θ = (90 - 38) + (90 - 55) = 87⁰

d² = 20² + 60² - 2(20)(60) x cos(87)

d² = 3874.39

d = 62.25 km

V = total displacement/total time

where;

V = (62.25 km)/(0.033 hr)

V = 1,867.5 km/hr = 518.75 m/s

Thus, the average velocity of the jet during the diversion is 518.75 m/s.

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A white automobile is a bad example of a blackbody radiator since it reflects the majority of the light that strikes it.

The same colour as an ideal absorber, an ideal radiator, sometimes known as a blackbody, absorbs all radiation that strikes it. White, on the other hand, is a poor radiator and absorber. Like a mirror, a white object reflects all radiation.

Certainly, a red laser pointer is a poor choice for a black body, for the following reasons: A heated object, like a chunk of red-hot metal from a furnace, produces a black body spectrum.

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Answer:

Explanation:

On return to Earth, gravity once again “pulls” the blood and fluids into the abdomen and legs. The loss of blood volume, combined with atrophy of the heart and blood vessels that can occur in space, reduces the ability to regulate a drop in blood pressure that happens when we stand on Earth.

The total density of the mixture is 0.485 g/cm^3

What is density:

The formula of density:

here,

volume of water, v1 = 30 cm^3

volume of ethanol, v2 = 40 cm^3

density of water, ρ1 = 1 g/cm^3

density of ethanol, ρ2 = 0.85 g/cm^3

so, according to formula,

for water

ρ1 = m1 / v1

m1 = ρ1 * v1

m1 = (1) * (30)

m1 = 30 grams

for ethanol

ρ2 = m2 / v2

m2 = ρ2 * v2

m2 = (0.85) * (40c)

m2 = 34 grams

total mass, M= m1 + m2

M= 30 + 34

M= 64 grams

total volume, V= v1 + v2

V= 30 + 40

V= 70 g/cm^3

Density of the mixture:

ρ = M / V

ρ = 34 / 70

ρ = 0.485 g/cm^3

Hence The total density of the mixture is 0.485 g/cm^3

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Answer:

Tension T1 is less than tension T2.

T1 < T2

Explanation:

According to given data,

mass of box A ( mA) is grater than mass of box B (mB)

we can write,

m(A) > m(B)

Newton's second law states that:

Tension of object is directly proportional to the mass of the system.

T ∝ m

here Boxes A and B are being pulled to the right on a frictionless surface,

so Tension T1 generates due to the mass of box A m(A)

and Tension T2 arises due to mass of the system m(A) + m(B)

Thus tension T1 will be less than tension T2

T1 < T2

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If the force is increased, the crate will become accelerated while if the force is decreased, the crate will decelerate.

Recall that the force is the product of mass and acceleration. Now we know that work is done when the force applied moves a distance. Since the velocity is constant;

W = Fs

F= W/s

F = 350 J/ 12.0 m

F = 29.2 N

If the force is increased, the crate will become accelerated while if the force is decreased, the crate will decelerate.

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The leaf fell at the crooked path instead of straight down because air currents and gravity applied changing and unbalanced forces to the leaf.

An air current is defined as the changes in atmospheric pressure that causes the movement of air from one area to another.

When a leaf is detached naturally from the tree, it won't fall straight down to the floor but will fall a distance away from the tree due to the action of air current and some unbalanced forces.

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The kinetic energy gained by the air molecules is 0.0437 J                

Given:

Mass of a coffee filter, m = 1.5 g

Height from which it is dropped, h = 3 m

Speed at ground, v = 0.7 m/s

Initially, the coffee filter has potential energy. It is given by :

[tex]P =mgh[/tex]

P = 1.5 × 10⁻³ kg × 9.8 m/s² × 3m

P = 0.0441 J

Finally, it will have kinetic energy. It is given by :

[tex]E= \frac{1}{2} mv^{2}[/tex]

[tex]E= \frac{1}{2}[/tex]×[tex]1.4[/tex] × 10⁻³ × (0.7)²

E = 0.000343 J

The  kinetic energy Kair did the air molecules gain from the falling coffee filter is :

E = 0.000343 -  0.0441

  = 0.0437 J

So, the kinetic energy Kair did the air molecules gain from the falling coffee filter is 0.0437 J

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The applied force needed for situation a and b are 211. 31 Newton and 453. 15 Newton respectively.

We have that the force for situation 'a' is on an angle of inclination of 25° with the book of ice.

Thus,

Applied force = mg × sine of angle of inclination

Where mass, m = 50kg

g = acceleration due to gravity = 10m/s^2

Applied force = 50 × 10 × sin 25

Applied force = 50 × 10 × 0. 4226

Applied force = 211. 31 Newton

For situation 'b', the mass of block is adjacent to the book of ice, thus

Applied force = mg × cos of angle of inclination

Applied force = 50 × 10 × cos 25

Applied force = 50 × 10 × 0. 9063

Applied force = 453. 15 Newton

Thus, the applied force needed for situation a and b are 211. 31 Newton and 453. 15 Newton respectively.

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Answer:

b) combine

Explanation:

The energy from the sun is due to Nuclear Fusion where lighter nuclei combine to form heavier and stable nuclei this releasing a lot of energy in this process.

Moment of inertia of single particle rotating in circle is I1 = 1/2 (m*r^2)

The value of the moment of inertia when the person is on the edge of the merry-go-round is I2=1/3 (m*L^2)

Moment of Inertia refers to:

The moment of inertia of single particle rotating in a circle I1 = 1/2 (m*r^2)

here We note that the,

In the formula, r being the distance from the point particle to the axis of rotation and m being the mass of disk.

The value of the moment of inertia when the person is on the edge of the merry-go-round is determined with parallel-axis theorem:

I(edge) = I (center of mass) + md^2

d be the distance from an axis through the object’s center of mass to a new axis.

I2(edge) = 1/3 (m*L^2)

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The charge of the wire is 180 C.

The term charge is defined as the product of the current and the time taken. Thus we can write that;

Q = It

Q = charge

I = current

t = time

Hence;

Q = 3 A * 1 * 60 s = 180 C

Thus the charge of the wire is 180 C

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2N is the frictional force by the floor on the box.

[tex]F=mA[/tex]

where,

F = Horizontal force

m = Mass

a = Acceleration

But, a = 0 as Constant speed = 0 acceleration.

       v = constant

Hence, there should be no net force. The frictional force is opposing the girl's force and should be equal to one another.

Frictional force = 2N

Therefore, the horizontal force applied by a small girl on the box is equal to the frictional force by the floor on the box.

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The new resistance will be 9R

A longer wire should have a higher electrical resistance than a wire with a bigger cross section, and vice versa. The electrical resistance of a wire should also be affected by the material from which it is formed.

The resistance of a wire is R = ρL/A. The volume of a wire is LA. If L increases by 3, then A must decrease by 3 in order for the volume to remain constant. If L increases by 3 and A decreases by 3, then L/A increases by 9 .

Hence the new resistance will be 9R    

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