What is work and give an example?

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Answer 1
Working is how you have gotten to your answer and example is an different question with similar ways to work it out

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a group of ten friends, each of mass 50kg, want to test the strength of a trampoline. at their highest jump, each friend is 2m above the trampoline. they all land on the trampoline at the same time and decelerate at a constant rate to a point of zero velocity over a period of 0.5s. the trampoline has a threshold of 5000n, above which it breaks. do the friends succeed in breaking their trampoline? neglect air resistance and the distance the trampoline sags as a result of the friends landing.

Answers

Calculate the striking trampoline.

What is zero velocity?

The zero-velocity surface is a notion connected to the N-body gravity problem. It represents a surface that a body with the specified energy cannot traverse because it would have zero velocity there. George William Hill made the initial proclamation about it.

What is resistance?

A circuit's opposition to current flow is measured by its resistance. The Greek letter omega () stands for ohms, which are used to measure resistance. Georg Simon Ohm (1784–1854), a German physicist who examined the connection between voltage, current, and resistance, is the subject of the name "Ohm."

mass of each friends= 50kg

number of friends =10

total mass= 50×10=500kg

now initial velocity before, falling =0

let final velocity be V

v²-μ²= 2as

⇒v²+2as=2as(μ=0)

∴V=[tex]\sqrt{2as}[/tex]=[tex]\sqrt{2*9.8*2}[/tex]  ( acceleration due to gravity =9.8m/s²) ( s=2m given)

=6.26ms⁻¹

∴The velocity of the friends, just before striking the trampoline= 6.26ms⁻¹

Now after striking the trampoline, the velocity of the people decelerate to 0, in a time interval 0.5s.

∴deceleration= 6.26/ 0.5= 12.52ms⁻²

∴Force required to decelerate=mass× deacceleration

=500×12.52

=6260.99

=6261N

but that trampoline has a threshold of 500N, which is less than force required to stop, the people.

hence the friends succeed in striking the trampoline.

Therefore, the friends succeed in striking the trampoline.

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what does power mean in terms of electrical energy

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Answer:

Electricity is the rate at which electrical energy is converted into motion, heat, or other forms such as electromagnetic fields.

a skateboard rolls down a hill and the wheels do not slip against the pavement. does the static friction force of the pavement on the wheels do any work on the skateboard? g

Answers

The static friction force of the pavement on the wheels will not do any work on the skateboard.

Static friction is a variable resisting force that is equal and opposite to the external force until it exceeds the motion threshold when sliding begins.

It is also called as self adjusting force.

If the skateboard is rolling at a constant speed without any other forces acting on it, then there is no tendency to slip between the wheel and the surface, so there is no frictional work. Friction will only try to prevent slipping between the 2 surfaces.

On an inclined plane, the wheels will tend to slide down, and if there were no friction, it would again slide between the wheels and the inclined surface. Perhaps friction will always try to counteract the slip, so here it acts upward on the slope to try to prevent the skateboard from sliding down the slope. This has the effect of applying a moment to the skateboard causing it to roll.

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10. A stone falls freely from the top of a tower 250.0 m above the ground. Calculate its
velocity half-way through the fall. [g=10.0 ms 2]

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Answer:

50 m/s

Explanation:

Half of its Potential Energy (mgh) will have been converted to Kinetic Energy  ( 1/2 mv^2)

1/2 mgh = 1/2 mv^2

gh = v^2

10(250) = v ^2      v = 50 m/s

The velocity of the stone halfway through the fall will be approximately 50.0 m/s.

To calculate the velocity of the stone halfway through its fall, we can use the kinematic equation for free fall

v² = u² + 2as

Where:

v is the final velocity,

u is the initial velocity,

a is the acceleration due to gravity (g),

and s is the distance fallen.

Given that the stone falls freely, the initial velocity u is 0 since it starts from rest.

The distance fallen halfway through the fall can be calculated by dividing the total distance fallen by 2.

s = 250.0 m / 2 = 125.0 m

Plugging these values into equation, now we solve for v:

v² = 0² + 2 × 10.0 m/s² × 125.0 m

v² = 0 + 2500 m²/s²

Taking the square root of both sides to find v:

v ≈ √2500 m²/s²

v ≈ 50.0 m/s

Therefore, the velocity of the stone halfway through the fall is approximately 50.0 m/s.

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A large block of stone is held at a height of 15meters having gained 4500 j of gpe. how much does it weigh?

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The weight of the large block of stone is 300 Newton. The result is obtained by dividing the gravitational potential energy by the height.

What is gravitational potential energy (GPE)?

Gravitational potential energy is the energy stored in an object due to its position in a gravitational field. GPE can be expressed as

PE = mgh

Where

PE = gravitational potential energym = mass of an objectg = acceleration of gravityh = height of an object

Given

h = 15 mPE = 4500 J

How much does it weight?

The weight of an object is the mass times the acceleration of gravity.

W = mg

So, with the GPE equation, the weight is

PE = mgh

PE = W × h

4500 = W × 15

W = 4500 ÷ 15

W = 300 Newton

Hence, the weight of the large block of stone is 300 Newton.

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if the net acceleration is downward but has a magnitude less than g, then which has the larger magnitude, the force f or the tension in the rope?

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If the net acceleration is downward but has a magnitude less than G, the force of F has a larger magnitude than the tension in the rope.

How to determine the net acceleration?

We do know thаt the net force equаls mаss times the аccelerаtion. Now if we tаke the block аs а system, meаning we mаke use of the equаtion, mаss times аccelerаtion equаls net force, on the block. Now the lаst element of the rope is pulling the block upwаrds. This is becаuse the block pulls the rope down, hence due to newton's third lаw the rope too should pull the block, but in opposite directions, thаt is upwаrds. Hence the tension аcts upwаrds on the block. Therefore the net force is weight downwаrds аnd tension upwаrds, this equаls mаss times аccelerаtion,

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a constriction in a pipe reduces its diameter from 6.5cm to 2.7cm. where the pipe is wider, the fluid velocity is 8m/s. find the fluid velocity where the pipe is narrow. answer in units of m/s

Answers

The velocity of the fluid where the pipe is narrow s 46.36m/s.

The diameter of the larger end of the constriction pipe is 6.5 cm and the diameter of the narrow end of the pipe is 2.7cm.

According to equation of continuity, the volume of the fluid incoming is equal to the volume of the fluid outgoing.

So, we can write,

A₁V₁ = A₂V₂

A₁ and V₁ are the area and speed at the larger end and A₂ and V₂ are area and speed at the narrow end.

Putting values,

π(6.5/2)².8 = π(2.7/2)².V

V = 46.36m/s

The velocity of the fluid where the pipe is narrow is 46.36m/s.

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a 75.9 kg bobsled is pushed along a horizontal surface by two athletes. after the bobsled is pushed a distance of 7.9 m starting from rest, its speed is 7.5 m/s. find the magnitude of the net force on the bobsled. answer in units of n.

Answers

The magnitude of the net force on the bobsled is found to be 270 Newton.

The mass of the bobsled is 75.9 Kg, the bobsled is pushed by two athletes till a distance of 7.9 m with a speed of 7.5m/s.

The work energy theorem says,

The work done by a force is equal to the total change in kinetic energy of the body.

Let us say that the bobsled starts from rest, so, we can write,

Fs = 1/2MV²

F is the net force on the bobsled,

s is the distance to which it is moved,

M is the mass of the bobsled,

V is the speed of the bobsled.

Putting values,

F(7.9) = 0.5 x 75.9 x 7.5 x 7.5

F = 270 N.

The net force on the bobsled is 270 N.

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A stater glides off a frozen pond onto a patch of ground at a speed of 3.1 m/S. Here she is stowed at a constant rate of 3.00 m/*, How fast is the skater moving when she has slid 0.42 m across the ground?

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A stater glides off a frozen pond onto a patch of ground at a speed of 3.1 m/S. Here she is stowed at a constant rate of 3.00 m/s .  The skater will move at a speed of v = 1.01 m/s , when she has slid 0.42 m across the ground

The branch of physics that defines motion with respect to space and time, ignoring the cause of that motion, is known as kinematics. Kinematics equations are a set of equations that can derive an unknown aspect of a body’s motion if the other aspects are provided.

using kinematics equation

[tex]v^{2} - u^{2} = 2as[/tex]

[tex]v^{2} = u^{2}[/tex] + 2as

   = [tex](3.1)^{2}[/tex] - 2 * 3 * 0.42

v    = 1.01 m/s

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a 110 g hockey puck sent sliding over ice is stopped in 15 m by the frictional force on it from the ice. (a) if its initial speed is 6.0 m/s, what is the magnitude of the frictional force? (b) what is the coefficient of friction between the puck and the ice?

Answers

The frictional force where k is the unitary force of kinetic friction acting on an object and k is the coefficient of kinetic friction. For the vast majority of surfaces, K is less than S.

Explain about the magnitude of the frictional force?

The weight of the object and the roughness of the surface in contact determine how much frictional force is generated. The friction force will grow as the roughness increases.

The weight of the object bearing normal to the surface times the coefficient of friction for the contacting surfaces gives the amount of the friction force. The force's direction is perpendicular to the surface and is in opposition to any forces acting on the box.

The amount of kinetic friction is inversely proportional to the amount of normal force and the degree of roughness between the sliding surfaces. The amount of static friction is inversely proportional to the amount of normal force and the degree of roughness between the sliding surfaces.

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two wheels, a and b, are both shaped like uniform disks and have the same overall mass, but wheel a has twice the radius of wheel b. how do we calculate the moments of inertia (around the axis of symmetry) for each wheel?

Answers

The ratio of I sub A to I sub B is 4.

How can you calculate the ratio of A to B?

A/B would be your formula if you were comparing one data point (A) to another data point (B). This indicates that you are multiplying information A by information B. For instance, your ratio will be 5/10 if A is 5 and B is 10. How do we determine each wheel's moments of inertia (around the axis of symmetry) I is equal to 1 over 2 times m times R squared is used to compute the moments of inertia for both masses and radii. We simply use a common factor to cancel. So 4:2=2:1 . The simplest representation of the ratio 4 to 2 is the ratio 2 to 1. Additionally, since each pair of numbers has the same relationship, the ratios are equivalent.

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In the period 6 inner transition element series, the 4f orbitals begin to be filled after the element _____.

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In the period 6 inner transition element series, the 4f orbitals begin to be filled after the element Lanthanum(La) and Cerium(Ce).

The d and f Block elements in the groups of 3 to 11 are also called transition elements and inner transition elements respectively. 4f and 5f orbitals of f-block elements are steadily in the latter of two long periods.

Inner transition element:

Inner transition elements are those elements in which the last electron enters the f-orbital. The elements in which the 4f and the 5f orbitals are progressively filled are called f-block elements. These includes lanthanoids( Z = 58 - 71) and actinoids (Z = 90 - 103).

Therefore period 6 inner transition elements begin with Lanthanum and Cerium.

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determine what fraction of the kinetic energy of the ball before collision is lost during teh collsion. what happens to it?

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1/2 m₁v₁²(m₁ / m₁+ m₂ ) is the fraction of Kinetic energy lost during an inelastic collision.

From the concept of law of conservation of energy, In an elastic collision when two objects collide with a particular velocity then the kinetic energy before the collision will be the same after the collision as well but that's not the case in an Inelastic collision where there's always loss of kinetic energy.

In case of inelastic collision,

pi = pf

here p = momentum

m₁v₁ = (m₁ + m₂)v₂

v₂= m₁v₁ / (m₁ + m₂) ------- equation 1

Ki = Kf

1/2m₁v₁² = 1/2 (m₁+m₂) v₂²

Put the value of v₂ from equation 1

1/2mv² = 1/2 (m₁ + m₂) [m₁v₁ / m₁+m₂]²

=> 1/2  (m₁v₁)² / ( m₁+m₂ )  

∴ Fraction of Kinetic energy lost

= 1/2 m₁v₁² - 1/2 (m₁v₁)² / (m₁+m₂)

=> 1/2 m₁v₁²( m₁ / m₁ + m₂ )

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A 0. 0850-kg arrow is fired horizontally. If the bowstring exerts an average force of 89. 0 n on the arrow over a distance of 0. 782 m, with what speed does the arrow leave the bow?.

Answers

40.47 m/s is the speed of the arrow leaving the bow. When 0.0850 kg arrow fired horizontally, and If bowstring exerts average force of 89.0 N on the arrow over distance of 0. 782 m.

What is velocity?

The primary indicator of object's position and speed is its velocity. It is distance that object travels in one unit of time. Displacement of item in one unit of time is definition of velocity.

By Newton's second law of motion,

F = ma

m is the mass of the arrow (kg) = 0.0850 kg

a is the acceleration of the arrow (m/s²)

F is the force applied (N) = 89.0 N

F= ma

a = F/m

a = 89.0/ 0.0850

∴ a= 1,047.059 m/s²

Now, object have acceleration, and the object will move in non-uniform motion. so the formula applied is:

[tex]v_{t}[/tex] = [tex]v_{0}[/tex] + at

[tex]v_{t}^{2}[/tex] = [tex]v_{0}^{2}[/tex] + 2×a×d

∴ d = [tex]v_{0}[/tex]×t +1/2× a ×t²

here,

[tex]v_{0}[/tex] = initial speed (m/s) = 0 m/s (arrow stationary in bowstring)

[tex]v_{t}[/tex] = final speed (m/s)

a = acceleration (m/s²) = 1,047.059 m/s²

t = interval (s)

d = distance (m) = 0.782 m

[tex]v_{t}^{2}[/tex] = [tex]v_{0}^{2}[/tex] + 2×a×d

[tex]v_{t}^{2}[/tex] = 0² + 2 × 1,047.059 × 0.782

 [tex]v_{t}^{2}[/tex] = 1637.6

[tex]v_{t}[/tex] = [tex]\sqrt{1637.6}[/tex]

[tex]v_{t}[/tex] = 40.47 m/s

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Waves that move the medium at right angles to the direction in which the waves travel.

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Transverse waves  are waves that move the medium at right angles to the direction in which the waves travel.

Types of Waves in Physics

Waves are defined to be oscillations or vibrations about a fixed point, accompanied by the transfer of energy travelling from one medium to another. There are mainly two types of mechanical waves, namely longitudinal waves and transverse waves.

Longitudinal waves are waves in which the movement of the particles in the medium is in the same dimension as the wave’s movement direction. Examples of longitudinal waves include compression wave and sound waves. Transverse waves are waves in which the medium moves at an angle to the wave’s direction. Examples include stringed instruments and light waves.

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a flight attendant pulls her 2 kg flight bag a distance of 23 m along a level airport floor at a constant velocity. the force she exerts is 8 n at an angle of 30 degrees above the horizontal. find the work she does on the flight bag.

Answers

Work done on the flight bag will be 182.20 J.

Work done defined as the product of force and distance covered due to applied force.

The mass of flight bag m = 2 kg

Therefore the weight of the bag will be 2*g = 2*10 = 20 N

(g = acceleration due to gravity = 9.81 m/s2)

The distance covered by the bag is, d = 23 m.

The magnitude of force exerted on bag is, F = 8 N.

The angle of inclination with horizontal = [tex]\alpha[/tex] = 8°

The work done on the flight bag is given by the equation:

W = F * d *Cos [tex]\alpha[/tex]

W = 8 * 23 * Cos8

W = 182.20 J

Thus, the work done by the attendant on the flight bag is 182.20 J.

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when there is no wind, an airplane is flying 70 m/s with its nose pointed due north. a wind begins blowing toward the west with a constant speed relative to the ground of 18 m/s. what is the direction and speed of the plane relative to the ground?

Answers

The relative velocity of the plane with respect to the ground will be 72.57 at an angle of tan⁻¹(0.25) from the north.

The speed of the airplane when there is no wind is 70 m/s in the north direction.

The speed of the wind is 18m/s related to the ground in the direction of West.

As we know, that both west and north are perpendicular to each other, the resultant speed by the observer on the ground will be observed in the direction of the resultant of both the speeds.

Let us say that we is the resultant of both the speeds,

Because the two speeds are perpendicular to each other the resultant is given by,

R = √((70)²+(18)²)

R = 72.27m/s.

The angle with north,

Tan A = 18/70

Tan A = 0.25

So, the speed of the airplane from the ground will be observed as 72.27 degrees and at an angle of tan ⁻¹(0.25) from the north.

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Light passes straight through two vertical polarizers. The axes of the filters are aligned parallel to each other. How does the light that passes through the second filter compare to the light that passed through the first filter?.

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Light passes straight through two vertical polarizers. The axes of the filters are aligned parallel to each other. The way the light that passes through the second filter compared to the light that passed through the first filter is that all of the light will pass through both polarizers.

What is a polarizer?

A polarizer, also known as a polariser, is an optical filter that allows light waves of one polarization to pass while blocking light waves of other polarizations. It may convert an undefined or mixed polarization light beam into a polarized light beam by filtering it.

Calcite, a naturally occurring mineral, is used to make the majority of birefringent polarizers. Calcite is common in polycrystalline form, but optical-grade calcite is scarce, making birefringent polarizers more expensive than most other varieties.

Remember that polarising filters can lower the amount of light reaching your camera's sensor by up to two or three f-stops, so avoid using them in low-light settings.  This includes photography during blue hour, at night, and when capturing the Aurora Borealis.

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A crane is shown below. It is lifting a load of 5000N. The counterweight weighs 4400N and distance y is 9m. What must distance x be if the crane is balanced? Give your answer to one decimal place.

Answers

The distance x must be 7.92 m for the crane to be balanced according to principle of conservation of energy.

What is the distance x?

The distance x can be determined by applying the principle of conservation of energy as shown below.

According to this principle of conservation of energy;

the input work (energy) = output work (energy)

F₁d₁ = F₀d₀

where;

F₁ is the input forced₁ is the input distanceF₀ is the output forced₀ is the output force

(4400) x (9) = 5000x

39600 = 5000x

x = 39600/5000

x = 7.92 m

Thus, the crate a balanced condition, the output work must be equal to the input work.

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A car traveling at 5m/s brakes and skids through a displacement of 6m. if it slows down at the rate of 2m/s/s, determine the length of time during which it breaks.

Answers

When a car travels at 5m/s and brakes at the rate of 2 m/s², the length of time to travel 6 m is 2 or 3 seconds.

Use the equation of motion for deceleration:

s = u . t - 1/2. a t²

Where:

s = distance

u = initial velocity

t = travel time

a = acceleration (minus sign means deceleration)

Parameters given in the problem:

s = 6 m

u = 5 m/s

a = 2 m/s²

Plug these parameters into the formula:

6 = 5t - 1/2. 2 . t²

t² - 5t + 6 = 0

(t - 3) (t - 2) = 0

t = 3  or  t = 2

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Help!!! 23 points label these as Element, compound, mixture of elements, and mixture of compounds

Answers

The given images are labelled as either element, compound, mixture of elements or mixture of compounds accordingly.

The answers are marked according in order of the images as follows:

ElementsCompoundsMixture of elementsMixture of compoundsCompoundsCompounds

If there are only single type of atoms present without being in contact with another atom, it is called as elements. If one atom is in contact with another atoms it is a compound. If there are more than one type of element, it is a mixture of elements. If there are more than one type of compound, it is a mixture of compounds.

Therefore, the given images are labelled as either element, compound, mixture of elements or mixture of compounds accordingly.

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a car with a mass of 1,020.0 kg accelerates from 0 to 94.0 km/h in 10.0 s. the driver applies the brakes when the car is moving at 94.0 km/h, and the car comes to rest after traveling 38.0 m. what is the net force (in n) on the car during its deceleration? (assume the car is traveling in the positive direction. indicate the direction with the sign of your answer.)

Answers

The net force on the car during its deceleration =  9139.2 N

What is deceleration?

Deceleration is actually inversely related to acceleration. We know that acceleration is the rate at which an object is speeding up, and deceleration is the rate at which an object is slowing down. For example, when you brake while driving, deceleration is used to slow the vehicle.

Given, m= 1020 kg

u= 0 m/s

V = 94 km/h or 26.1 m/s

t = 10 s

For deceleration

u = 26.1 m/s

v = 0

S = 38 m

by equation of motion ;

v² = u² + 2as

0 = 26.1² + 38a

a = - 8.96 m/s²

Net force during deceleration:

F= m*a

F= 1020 × 8.96

F = 9139.2 N

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According to the first law of thermodynamics, work done by a system will cause _________ in the internal energy, assuming that no heat is transferred to or from the system.

Answers

According to the first law of thermodynamics, work done by a system will cause decrease in the internal energy, assuming that no heat is transferred to or from the system.

First law of thermodynamics says that energy can neither be created nor it can be destroyed, it can only be transferred from one form to another form. This is also a law of conservation of energy.

It means if there is any work done by any system then that system has burned its energy to do the work. so when energy is used to do the work , there will be decrease in the internal energy of the system, and that will be equal to the workdone.

ΔU = ΔW

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is training for cross country in the fall she ran 5 miles east then she turned and ran 5 miles west. draw and label the vectors that show each segment of her tripand the resulant dispacement vector. find her resulant displacement

Answers

5j-5i is her resultant displacement.

velocity in east= 5i

velocity in west=5j

resultant magnitude=√5i+√5j

displacement =5j-5i

Displacement is the shortest distance, but distance is the length of everything covered. A vector quantity with a magnitude and a direction is displacement. The vector (or straight line) separation between an initial and final position is described by this term. Therefore, all that is needed to determine the resulting displacement is to know these two positions.

Calculate the inverse tangent of the ratio of the components of the displacement in the y- and x-directions to find the direction of the displacement vector.

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How much gravitional potential energy would a 65.0kg rollerblader have at the top of a hill that is 45.0 meters high

Answers

Roller balder will have 28,665 J gravitational potential energy at the top of a hill that is 45.0 meters high

gravitation potential energy = m*g*h

mass = 65 kg

g = 9.8 [tex]m/s^{2}[/tex]

h = 45 m

gravitation potential energy  = 65 * 9.8 * 45 = 28,665 J

Roller balder will have 28,665 J gravitational potential energy at the top of a hill that is 45.0 meters high

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a prescription for corrective lenses reads -5 d for each lens. these corrective lenses are group of answer choices diverging with focal length equal to 20 cm. diverging with focal length equal to 5 m. diverging with focal length equal to 5 cm. converging with focal length equal to 5 cm. converging with focal length equal to 5 m. converging with focal length equal to 20 m.

Answers

These corrective lenses have a 20 cm focal length and are diverging.

P=1/(f(m)) and "hence P= 1/(0.2)=10/2" and "therefore P=5 D" indicate that the lens has a 5 dioptre power.

What is a diverging lens?A lens that, after exiting the lens, produces parallel light beams to spread out and deviate from the optical axis.A lens that, as from a virtual image, produces a beam of parallel rays to diverge after refraction; a lens with a negative focal length.By extending the traces of the light rays traveling through the lens to a focal point behind the lens, negative lenses diverge parallel incident light beams to create an illusion of an image. These lenses typically feature at least one concave surface and are thinner in the middle than they are on the edges. When passing through a concave lens, light rays parallel to the principal axis appear to diverge from a point on the principal axis.

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A student travels on a motorcycle and moves at a constant speed of 80 k/h for 15 m, determine the distance traveled in that time​

Answers

Uniform line movement

Data:

V = 80km/h

T = 15m = 0.25 h

d = ?

We perform a conversion from minutes to hours.

           15 m * 1 h/60 m = 0.25 h

The formula for uniform motion is:

                      V = d/t

We clear for distance:

                  d = v * t

                  d = 80 km/h * 0.25 h

                  d = 20 km

The distance traveled in that time is 20 km.

in a collision between two unequal masses, how does the impulse imparted to the smaller mass by the larger mass compare with the impulse imparted to the larger mass by the smaller one? 3) a) they are equal. b) it is larger. c) it is smaller. d) the answer depends on the ratio of the masses. e) the answer depends on how fast they are moving

Answers

In a collision between two unequal masses, the smaller mass by the larger mass compare with the impulse imparted to the larger mass by the smaller one they are equal.

Any incident where two or more bodies exert forces on each other quickly is referred to as a collision in physics. In physics, collision, which is also known as impact, is the abrupt, forceful coming together in close proximity of two bodies, such as, for instance, two pool balls, a golf club and a ball, a hammer and a nail head, two railroad cars when coupled, or a falling object and a floor. In physics, a collision occurs when particles, aggregates of particles, or solid bodies move in the same direction and get close enough to each other to interact and have an impact on one another. Distracted driving is the most frequent reason for an auto accident. Speeding, disobeying traffic signs, making improper turns, and driving while intoxicated or drugged-up are additional risk factors for car accidents.

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A resistor, an inductor, and a capacitor are connected in series to an ac source. What is the phase angle between the voltages of the inductor and capacitor in this rlc circuit?.

Answers

The phase angle between the voltages of the capacitor and inductor in rlc circuit is 180°.

The phase angle is the component of a periodic wave. It is the shift between the AC current and the voltage on the measured impedance. The two elements of phase angle are reactance(X) and resistance (R).

The phrase for phase angle is, Xₐ = sinωt

where Xₐ= phase angle

ω = wavelength of the wave in 1 revolution

t = time period of 1 revolution

The instantaneous voltage ΔvR is in phase with the current, ΔvL leads the current by 90°, while ΔvC lags behind the current by 90°. The instantaneous values of these three voltages do add algebraically to give the instantaneous voltages across the RLC combination.

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how can we deducve the presence and measure the mass of a supermassivce black hole in the center of a galaxy

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Astronomers can study how clusters of stars and gas move around the galactic center in nearby galaxies and use those movements to calculate the mass of the central black hole.

How can we calculate the black hole's mass at the galactic center?

By monitoring the star motions in the galaxy's center, Webb will calculate the black hole's mass. Astronomers will calculate the mass of that black hole using NASA's James Webb Space Telescope. The outcome may appear to be unimportant, but a black hole's mass controls how it feeds and interacts with its surroundings.

Black holes are discovered when nearby material, such as gas, is pulled by gravity into a disk around the black hole. The gas molecules in the disk of the black hole are spinning so quickly that they heat up and release X-rays. From Earth, one can observe these X-rays.

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