184) you are standing on a skateboard, initially at rest. a friend throws a very heavy ball toward you. 184) you can either catch the object or deflect the object back toward your friend (such that it moves away from you with the same speed as it was originally thrown). what should you do in order to maximize your speed on the skateboard?

Answers

Answer 1

If the friend throws a very heavy ball toward you , then in order to maximize the speed on the skateboard you should Deflect the ball .

The skateboard is given to be at rest ;

the friend throws a heavy ball towards you ,

Initially, the person is given to be at rest ; so his initial speed(u)  is 0.

if the person catches the ball then person have same final velocity (v).

By the conservation of momentum ;

\(m*u_{b}\) = (M + m)v

v = \(m*u_{b}\) /(M + m) ;

Now when the ball is deflected ;

0 + \(m*u_{b}\) = m(\(-u_{b}\)) + MV ;

V = \(2mu_{b}\) /M ;

here , V > v ;

Therefore , to maximize speed of skateboard the person needs to deflect the ball .

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Related Questions

Suppose 900 kg satellite is orbiting the earth one earth radius above the surface: Q1) Find the force of gravity between the earth and the satellite Q2) Find the orbital period of the satellite_ Q3) Find the tangential velocity required to keep the satellite in orbit: Q4) Find the angular velocity of the satellite:

Answers

(1) The force of gravity between the Earth and the satellite is 8.91 * 10^6 N.

(2)  The orbital period of the satellite is 6,132 seconds i.e. 1 hour and 42 minutes.

(3) The tangential velocity required to keep the satellite in orbit is approximately 7.94 km/s.

(4) The angular velocity of the satellite is 0.0011 radians per second.

(1)  The force of gravity between two objects can be calculated using Newton's law of universal gravitation. The formula is F = (G * m1 * m2) / \(r^2\), where F is the force of gravity, G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between their centers. In this case, the mass of the Earth is much larger than the mass of the satellite, so we can consider the satellite's mass negligible compared to the Earth's mass. Plugging in the values, we get\(F = (6.67 \times 10^{-11} N m^2/kg^2) \times (5.97 \times 10^{24} kg) \times (900 kg) / (6,371,000 m)^2 = 8.91 \times 10^6 \ Newtons\)

(2) The orbital period of a satellite can be determined using Kepler's third law of planetary motion, which states that the square of the orbital period is proportional to the cube of the semi-major axis of the orbit. Since the satellite is orbiting at a radius equal to one Earth radius above the surface, the semi-major axis is the sum of the Earth's radius and the altitude of the satellite. Using the formula \(T = 2\pi \times\sqrt{(a^3 / (G \times M)}\), where T is the orbital period, a is the semi-major axis, G is the gravitational constant, and M is the mass of the Earth, we can calculate the value. Plugging in the values, we get \(T = 2\pi \times\sqrt{6,371,000}\) meters +\((6,371,000 \ m)^3 / (6.67 \times 10^{-11} N m^2/kg^2 \times 5.97 \times 10^{24} kg)\) = 6,132 seconds.

(3) The tangential velocity required to keep a satellite in orbit can be determined using the formula \(v = \sqrt{G \times M / r\) where v is the tangential velocity, G is the gravitational constant, M is the mass of the Earth, and r is the distance between the center of the Earth and the satellite. Plugging in the values, we get v = √((6.67 x 10^-11 N m^2/kg^2 * 5.97 x 10^24 kg) / \(v = \sqrt{\frac{(6.67 \times 10^{-11} N m^2/kg^2 \times 5.97 \times 10^{24} kg) }{(6,371,000 m + 6,371,000 m)}\)) = 7,906 m/sec.

(4) The angular velocity of a satellite in orbit can be calculated using the formula ω = v / r, where ω is the angular velocity, v is the tangential velocity, and r is the distance between the center of the Earth and the satellite. Plugging in the values, we get ω = 7,906 meters per second / (6,371,000 meters + 6,371,000 meters) = 0.0011 radians per second.

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a yound double slit has a slit separation 2.50 on which a monochormatic

Answers

Answer:Assuming that the question is about a Young's double-slit experiment and there was an error in the question, I will provide a complete answer based on my assumption.

A Young's double-slit experiment has a slit separation of 2.50 micrometers. When illuminated with a monochromatic light of wavelength 600 nanometers, an interference pattern is observed on the screen. The distance between the screen and the slits is 1.20 meters.

The interference pattern consists of bright fringes (maxima) and dark fringes (minima) that are evenly spaced and parallel to each other. The spacing between the fringes depends on the wavelength of light and the slit separation. In this case, the distance between adjacent bright fringes (or dark fringes) can be calculated using the equation d sinθ = mλ, where d is the slit separation, θ is the angle between the line perpendicular to the slits and the line from the slits to the fringe, m is an integer representing the order of the fringe, and λ is the wavelength of light.

Assuming that the screen is placed far enough from the slits, the angle θ can be approximated as tanθ = y/L, where y is the distance from the center of the pattern to the fringe, and L is the distance from the slits to the screen. Using these equations and plugging in the values, the distance between adjacent bright fringes can be calculated as 0.000015 meters or 15 micrometers.

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A book weighing 10 kg is preparing to fall off the desk from a 1 meter height. The book's
gravitational potential energy is 980 Joules.
O True
O False

Answers

Answer:

False

Explanation:

gravitational potential energy = mgh

10*10*1 = 100 joules

what is the name of the instrument used to measure amount of substance? ​

Answers

Answer:

The word stoichiometry is a technical chemical term derived from the two Greek roots stoicheion, "element", and metron, "measure". Chemical stoichiometry is the area of chemistry which deals with the quantitative relationships between numbers of atoms involved in matter. Since very large numbers of atoms are needed to make up real objects which we can conveniently handle, the unit of amount of substance contains a large number of atoms. That unit of amount of substance is called the mole.

Explanation:

Answer:

The mole is the SI (stoichiometry) unit for ammount of substance

Explanation:

hope this helps

Membrane. room a has 1 kg air and volume 0.5 m3 , room b has 0.75 m3 air with density 0.8 kg/ m3 . the membrane is broken and the air comes to a uniform state. find the final density of the air.

Answers

The final density of the air, after the membrane is broken and the air comes to a uniform state, can be found by considering the conservation of mass.

In the initial state, Room A contains 1 kg of air with a volume of 0.5 m³. The initial density of the air in Room A is:

Density of air in Room A = Mass of air in Room A / Volume of Room A

                          = 1 kg / 0.5 m³

                          = 2 kg/m³

In the initial state, Room B contains 0.75 m³ of air with a density of 0.8 kg/m³.

To find the final density of the air, we need to calculate the total mass of the air in the combined volume of Room A and Room B, and then divide it by the combined volume.

Total mass of air = Mass of air in Room A + Mass of air in Room B

                = 1 kg + (0.75 m³ * 0.8 kg/m³)

                = 1 kg + 0.6 kg

                = 1.6 kg

Combined volume = Volume of Room A + Volume of Room B

               = 0.5 m³ + 0.75 m³

               = 1.25 m³

Final density of air = Total mass of air / Combined volume

                    = 1.6 kg / 1.25 m³

                    = 1.28 kg/m³

Therefore, the final density of the air after the membrane is broken and the air comes to a uniform state is 1.28 kg/m³.

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Another term for technology is
a.applied science
c. matter
d. pure science
b. energy

Answers

Answer:

a. applied science

Explanation:

\(.\)

a 20-kg object travelling at 20 m/s collides head on with an 18-kg object travelling at 17 m/s.If they were locked together after the collision, what is their velocity?.​

Answers

Answer:

2.47 m/s

Explanation:

Momentum = Mass X Velocity

If they were locked together, it means its a perfectly inelastic collision. Therefore,

Total momentum before = Total momentum after

Total momentum before = (20 X 20) - (18 X 17)

= 94

Total momentum after = 94

Y = Object speed after collision

94 = (20+18)Y

Y = 2.47368421 m/s

what is the definition of density? the measure of mass of a material within a given space. the measure of mass of a material within a given space., defragment, the volume of an object. the volume of an object., defragment, the weight of an object the weight of an object, defragment, the mass of an object.

Answers

the definition of density is: the measure of mass of a material within a given space

The density of an object is the relation that exist between the mass and the space that the object occupies. The general formula of the density is:

ρ = m/v

Where:

v= volumeρ= densitym= mass

For example if we want to know which is the density of a body that has a mass of 100g and a volume of 150 cm³, applying the density formula we get:

ρ = 100 g/150 cm³

ρ = 0.666 g/cm³

What is density?

It is a physical quantity that expresses the ratio of the body mass to the volume it occupies.

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what is the definition of density? the measure of mass of a material within a given space. the measure

a 72.9-kg base runner begins his slide into second base when moving at a speed of 3.93 m/s. the coefficient of friction between his clothes and earth is 0.693. he slides so that his speed is zero just as he reaches the base.(a)how much mechanical energy is lost due to friction acting on the runner?

Answers

The mechanical energy lost due to friction acting on the runner is 1095.7 J.

What is Energy?

Energy is a fundamental concept in physics that refers to the ability of a system to do work. In simpler terms, energy is the capacity of an object or system to perform work, move, or cause changes in matter.

To account for this, we can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy:

W = ΔK

where W is the work done on the runner by friction and ΔK is the change in the runner's kinetic energy.

The work done on the runner by friction is given by:

W = μkmgd

where μk is the coefficient of kinetic friction (0.693), d is the distance over which the runner slides (assumed to be the same as the distance between the bases, 15.24 m), and the other variables are as defined above.

W = (0.693)(72.9 kg)(9.81 m/\(s^{2}\))(15.24 m)

W = 1095.7 J

The change in the runner's kinetic energy is given by:

ΔK = \((1/2)mvf^{2}\) - \((1/2)mvi^{2}\)

where vf is the final speed of the runner (zero) and vi is the initial speed of the runner (3.93 m/s).

ΔK = (1/2)(72.9 kg)\((0 m/s)^{2}\) - \((1/2)(72.9 kg)(3.93 m/s)^{2}\)

ΔK = -1041.9 J

The negative sign indicates that the runner's kinetic energy has decreased, as expected.

Therefore, the actual mechanical energy lost due to friction is:

ΔE = W = 1095.7 J

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a thin uniform bar (length 2.1 m and mass 2.5 kg) has two balls of mass 1.3 kg each glued to its ends. what is the moment of inertia of this object about an axis perpendicular to the center of the bar?

Answers

The moment of inertia of the entire object about an axis perpendicular to the center of the bar, we can use the parallel axis theorem and sum the moment of inertia of the bar and the moment of inertia of the balls:

Moment of inertia = (1/12) * (2.5 kg) * (2.1 m)^2 + 2 * (2/5) * (1.3 kg) * ((2.1 m)/2)^2.


The parallel axis theorem states that the moment of inertia of an object about an axis parallel to and a distance "d" away from an axis through its center of mass is given by the sum of the moment of inertia about the center of mass and the product of the object's mass and the square of the distance "d".

The bar has two balls glued to its ends, so we can consider the bar and the balls separately.

The moment of inertia of the bar about an axis through its center of mass can be calculated using the formula for a uniform rod rotating about its center, which is (1/12) * m * L^2, where m is the mass of the rod and L is the length of the rod.

The moment of inertia of the bar is (1/12) * (2.5 kg) * (2.1 m)^2.

The moment of inertia of each ball about an axis through its center of mass can be calculated using the formula for a sphere rotating about its center, which is (2/5) * m * r^2, where m is the mass of the ball and r is the radius of the ball.

Since the balls have the same mass and are identical, their moment of inertia is the same, so we can calculate it for one ball and then multiply by 2.

The radius of each ball can be calculated using the formula r = L/2, where L is the length of the bar.

The moment of inertia of each ball is (2/5) * (1.3 kg) * ((2.1 m)/2)^2.

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you hold a wire coil so that the plane of the coil is perpendicular to a magnetic field b⃗ .

Answers

When a wire coil is held so that its plane is perpendicular to a magnetic field, an electromotive force (emf) is induced in the coil. This phenomenon is known as electromagnetic induction and is described by Faraday's law of electromagnetic induction.

According to Faraday's law, the magnitude of the induced emf can be calculated using the equation:

emf = -N * dΦ/dt

where emf is the induced electromotive force, N is the number of turns in the coil, and dΦ/dt is the rate of change of the magnetic flux through the coil.

The direction of the induced emf follows Lenz's law, which states that the induced current will flow in a direction that opposes the change in magnetic flux.

It's important to note that the magnetic field must be changing in order to induce an emf in the coil. This can be achieved by moving the coil or changing the magnetic field strength. Additionally, the coil must be a closed circuit for the induced emf to generate a current.

If you have specific values for the number of turns in the coil, the magnetic field strength, and the rate of change of magnetic flux, I can assist you in calculating the induced emf.

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a hydraulic press in a garage is attached to a platform that is used to lift cars. the press includes a small piston that is attached to a fluid-filled pipe, which opens into a larger chamber under the platform (see image below). if the platform has a radius of 3 m and the piston has a radius of 3 cm, how much force (in n) must be applied to the piston in order to raise a 1200 kg car?

Answers

Answer:

.12 kg

Explanation:

Area under car = pi 3^2 = 9 pi  m^2

Area of piston = pi (.03)^2 = .0009 pi m^2

As a ratio:

.0009 / 9 =  x / 1200

x = 1200 ( .0009/9) = .12 kg  

An elephant ran 300 meters in 20 seconds, what was his speed?

Answers

Answer: 40 km/hr ( c )

Explanation:

Distance =20 km

Time =30 min=

60

30

hr=

2

1

hr

∴ Speed =

time

Distance

=

(

2

1

hr)

20 km

⇒ Speed =40 km/hr

Option (C) is correct.

How much total mechanical energy (ME) is in a system if the PE is 10 J and the KE is 40 J? Hint: ME=KE+PE
A. 10 J
B. 40 J
C. 30 J
D. 50 J

Answers

Answer:

D. 50 J

hope it helps you you just need to put the values or substitute the value in me=ke+pe

Answer:

D.\(\pmb{ 50~J}\)

Explanation:

As we know that \(\sf{M_{E}=K_{E}+P_{E} }\)

where,

ME=mechanical energy KE=kinetic energy PE=potential Energy

According to the question

ME=KE+PE

ME=40J+10J

ME=50J

what does the term energy density tell us about the difference between this model and the energy interaction model

Answers

The term energy density tells us that the difference between the particle model and the energy interaction model lies in how the energy is distributed or spread out within a system.What is Energy Density?The amount of energy per unit volume that a substance or system contains is known as energy density.

Energy density is a measure of how much energy is stored in a given volume or mass of a substance or system. It is a vital physical property that affects how a system behaves and how much energy can be extracted from it.Particle Model Vs. Energy Interaction Model The particle model of matter refers to the view of matter as being composed of tiny, indivisible particles that are in constant motion and have kinetic energy. In this model, the behavior of matter is primarily determined by the interactions between these particles.The energy interaction model, on the other hand, views matter as being composed of different forms of energy that can be transferred or transformed from one form to another.

In this model, the behavior of matter is primarily determined by the interactions between different forms of energy.The primary difference between these two models lies in how they distribute or spread out energy within a system. In the particle model, energy is primarily distributed among the particles, while in the energy interaction model, energy is primarily distributed among the different forms of energy that are present in the system. This difference in energy distribution can have significant implications for how a system behaves and how much energy can be extracted from it.

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how much work is done by the spring as it accelerates the block?

Answers

The work done by the spring depends on the spring constant, the displacement of the spring, and the time taken for the block to move. The faster the block accelerates, the more work is done by the spring.

When a spring is compressed or stretched, it contains potential energy that can be transferred to an object when released. The amount of work done by a spring as it accelerates a block is equal to the change in potential energy stored in the spring.
Assuming that the block has a mass of m and is initially at rest, the spring exerts a force on the block given by Hooke's law: F = -kx, where k is the spring constant and x is the displacement of the spring from its equilibrium position. As the spring accelerates the block, the displacement x increases, and so does the force applied by the spring. The acceleration a of the block is given by Newton's second law: F = ma.
The work done by the spring is the product of the force and the displacement: W = Fx.

Substituting F = -kx and \(x = (1/2)at^2\), we get:
\(W = -k(1/2)at^2\)
where t is the time taken for the block to move from its initial position to its final position.
The acceleration a can be calculated from the displacement x and the time t:\(a = 2x/t^2\). Substituting this in the expression for work, we get:
\(W = -kx^2/t^2\)

∴ The work done by the spring depends on the spring constant, the displacement of the spring, and the time taken for the block to move.

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1. If a pair of running shoes would weigh 11.55 newtons on Jupiter, what is the strength of gravity there?
2. If the same pair of shoes weighs 0.3 newtons on Pluto, what is the strength of gravity on pluto?
3.What does the pair of shoes weigh on earth?

Answers

The strength of gravity of planets Jupiter and Pluto are 23.1m/s² and  0.6m/s² respectively.

We are given that,

The mass of the shoes =  m=0.500 kg

The weigh  of the shoes on the Jupiter = W₁=11.55 N

The weigh of the shoes on the Pluto = W₂=0.3 N

Therefore, the weight to mass ratio determines the strength of gravity, or the acceleration caused by gravity.

Then the strength of gravity on Jupiter can be calculated as,

\(g_{j} = \frac{w_{1} }{m}\)

Putting the values in above equation we can get,

\(g_{j} = \frac{11.55N}{0.500kg}\\ g_{j} = 23.1m/s^{2}\)

Since, the gravity strength of planet Jupiter would be 23.1m/s²

The strength of gravity of planet Pluto can be calculated when shoes weigh is 0.3 N,

\(g_{p} =\frac{w_{2} }{m} \\g_{p} = \frac{0.3N}{0.500kg} \\g_{p} = 0.6 m/s^{2}\)

Thus, the gravity strength of planet Pluto may be 0.6m/s².

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Which event causes the least amount of time to go by on the game clock?

Question 3 options:

A three-point shot


A bounce pass


A free throw


An alley-oop

Answers

answer : free throw does

The event that causes the least amount of time to go by on the game clock is a free throw.

In basketball, a free throw is an unhindered shot made from behind a set line.

This throw (free throw) is produced because of a foul caused by an opponent.

The obtention of free throws can be a strategy to win a game.

In conclusion, the event that causes the least amount of time to go by on the game clock is a free throw.

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At his job, Paolo is payed a salary every two weeks to ensure that he reliably shows up for work. This is most like which reinforcement schedule?

= Variable-ratio
= Fixed-ratio
= Variable-interval
= Fixed-interval

Answers

This is most like Fixed-interval reinforcement schedule.

Therefore the answer is Fixed-interval

The scenario described in the question is most similar to a fixed-interval reinforcement schedule, in which reinforcement is delivered after a fixed period of time, such as every two weeks, as long as the behavior occurs.

This type of reinforcement schedule is often used in the workplace to encourage reliable attendance and work performance.

Option variable-ratio, involves reinforcement after a variable number of responses and is often associated with gambling behavior. Option fixed-ratio, involves reinforcement after a fixed number of responses, while option variable-interval, involves reinforcement after a variable amount of time has elapsed.

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A hockey puck has a coefficient of kinetic friction of = .20. If the puck feels a normal force of 5 N, what is the frictional force that acts on the puck?

Answers

Answer: 5 N

Explanation:

Friction is a force that prevents two solid objects from rolling or sliding over one another. Although frictional forces, like the traction required to walk without slipping, may be advantageous, they also pose a significant amount of resistance to motion.

The given parameters;

coefficient of kinetic friction, μk = 0.1normal force of the puck, Fₙ = 5 N

By multiplying the normal force and the coefficient of kinetic friction, the frictional force acting on the puck is calculated.

The frictional force that acts on the puck is calculated as follows;

F= u*f

Substitute the given parameters in the above equation and solve the frictional force.

F=0.2*5

F=  1 N

Thus, the frictional force that acts on the puck is 1 N.

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A hot metal sphere is dropped into a beaker of cold liquid inside an insulated container. The metal and the liquid quickly reach a common final temperature. Let the metal and the beaker of liquid be the system.
a. In this process, does the energy of the system increase, decrease, or stay the same?
- The energy increases.
-The energy decreases.
-The energy stays the same.
b. In this process, does the entropy of the system increase, decrease, or stay the same? -The entropy increases. -The entropy decreases. -The entropy stays the same.

Answers

In a) Energy will stay the same as no transfer or energy while in b) Entropy will increase due to increase in disorder from hot to cold object.

The full solution and explanation:

a. In this process, the energy of the system stays the same according to the Law of Conservation of Energy. The energy that is lost by the hot metal sphere is gained by the cold liquid in the beaker, and no energy is gained or lost by the system as a whole. However, during the process, heat flows from the hot metal sphere to the cold liquid, so there is a transfer of energy.

b. In this process, the entropy of the system increases. Entropy is a measure of the disorder or randomness of a system, and during this process, the heat flows from a hot object to a colder object, which increases the disorder of the system. As a result, the entropy of the system increases, which is consistent with the Second Law of Thermodynamics.

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When a ball is dropped it strikes the ground with a speed of 8 m/s.
•How long was it in the air?

•From what height was it dropped?

Answers

Answer:

13.2 meter

Explanation:

because the initial velocity was zero

The loaded cab of an elevator has a mass of 3.0 x 10 3 kg and moves 200 m up the shaft in 20 s at constant speed. At what average rate does the cable do work on the cab

Answers

The average rate at which the cable does work is 294,000 J/s.

The given parameters:

mass, m = 3000 kgheight, h = 200 mtime of motion, t = 20 s

The average rate at which the cable does work is calculated as follows;

\(P = \frac{E}{t} \\\\P = \frac{mgh}{t} \\\\P = \frac{3000 \times 9.8 \times 200}{20} \\\\P = 294,000 \ J/s\)

Thus, the average rate at which the cable does work is 294,000 J/s.

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With an average mass of only 30.0 gthe mouse lemur of Madagascar the smallest primate on Earth. Suppose this lemur swings on a light vine with a length of 2.4 m, so that the tension in the vine at the bot- tom point of the swing is 0.393 N. What is the lemur's tangential speed at that point?

Answers

Suppose that Reid weighs 72 kg. 2. The mouse macaque of India is the shortest primate on Earth, with an average weight of just 30.0 g. Imagine that this lemur swings 

What does the statistical term "average" mean?

Average. In everyday speech, a average is a specific number chosen to represent a collection of figures. In various settings, various average ideas are utilized. The word "average" frequently refers to the mathematical mean, which is the total of the values divided by the number of numbers being averaged. Statistical terms: mean, median

What are the several definitions of average?

In various settings, various average ideas are utilized. The word "average" frequently refers to the mathematical mean, which is the total of the integers divided by the amount of numbers being averaged. Mean, average, and mode all are considered measures of normal distribution in statistics, and in common parlance, any of these could be referred to as an average figure.

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Which one i need help

Which one i need help

Answers

Answer:

C

Explanation:

When there's a temperature difference between two objects, heat is transferred from the hotter object to the cooler one. What is the name for the state reached when they are both at the same temperature?​

Answers

Answer:

 The state when the two objects have reached the same temperature is known as thermal equilibrium.

what type of equipment is operated by a fluid that is under pressure, such as water or oil?

Answers

Equipment that is operated by a fluid under pressure, such as water or oil, is known as a hydraulic system. These systems use pressurized fluid to transmit power and perform various tasks, like lifting heavy loads or operating machinery. Common examples of hydraulic equipment include excavators, car jacks, and hydraulic brakes.

The type of equipment that is typically operated by a fluid that is under pressure, such as water or oil, includes hydraulic equipment and pneumatic equipment.

These types of equipment use the pressure of the fluid to power various mechanisms and perform tasks, such as lifting heavy objects or moving machinery.

Examples of hydraulic equipment include hydraulic presses, cranes, and excavators, while examples of pneumatic equipment include air compressors, drills, and pumps.

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Does direction matter when determining distance?
yes
no

Answers

Answer:

no

Explanation:

ans should be correct

How do we know how much gravitational force objects have?

Answers

Answer:

understand Newton's second law of motion,F is equal to ma where F is the force ,m is the mass of the object,a is acceleration

A 10. 0 cm object is 5. 0 cm from a concave mirror that has a focal length of 12 cm. What is the distance between the image and the mirror? 3. 5 cm –3. 5 cm 8. 6 cm –8. 6 cm.

Answers

The distance between the image and the mirror is -8.6 cm

What is concave mirror?

A concave mirror has a reflective surface that is curved inward and away from the light source. Concave mirrors reflect light inward to one focal point.

Unlike convex mirrors, the image formed by a concave mirror shows different image types depending on the distance between the object and the mirror.

Let's use the mirror equation to solve the problem:

\(\dfrac{1}{f}=\dfrac{1}{d_o}+\dfrac{1}{d_i}\)

where f is the focal length of the mirror,  the distance of the object from the mirror, and  the distance of the image from the mirror.

For a concave mirror, for the sign convention f is considered to be positive. So we can solve the equation for  by using the numbers given in the text of the problem:

\(\dfrac{1}{12}=\dfrac{1}{5}+\dfrac{1}{d_i}\)

\(\dfrac{1}{d_i}=-\dfrac{7}{60}\)

\(d_i=-8.6\ cm\)

Where the negative sign means that the image is virtual, so it is located behind the mirror, at 8.6 cm from the center of the mirror.

Hence the distance between the image and the mirror is -8.6 cm

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