A bowl of 426 g of water is placed ina microwave oven that puts out 700 watts (J/s). How long would it take in seconds to increase the temperature of the water from 12.0°C to 45.7°C

Answers

Answer 1

Approximately 26.7 seconds

A bowl of 426 g of water is placed in a microwave oven that puts out 700 watts (J/s). How long would it take in seconds to increase the temperature of the water from 12.0°C to 45.7°C?

Given values:

Mass of water, m = 426 g = 0.426 kg

Initial temperature, T1 = 12.0 °C = (12.0 + 273) K

Final temperature, T2 = 45.7 °C = (45.7 + 273) K

Power of the microwave oven, P = 700 W

Heat capacity of water, c = 4.184 J/g.

We need to find the time it will take to heat the water from T1 to T2.

Use the formula,

Q = mc(T2 - T1)

Here, Q is the heat absorbed by the water.

As we know, Power = Energy / timeSo, Q = Pt

where t is the time it will take to heat the water.

So, putting the values in the formula, we get, Pt = mc(T2 - T1) => t = mc(T2 - T1) / P

Here, m = 0.426 kgc = 4.184 J/g.K = 4.184 * 10³ J/kg.KT1 = (12.0 + 273) K = 285 KT2 = (45.7 + 273) K = 319.7 KP = 700 Wt = 0.426 × 4.184 × (319.7 - 285) / 700= 26.7 s

Therefore, it will take approximately 26.7 seconds to increase the temperature of the water from 12.0°C to 45.7°C.

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Related Questions

why does polishing the surface of a metal extend fatigue life

Answers

Answer:

they are machined with shape characteristics which maximize the fatigue life of a metal.

Explanation:

they are highly polished to provide the surface characteristics which enable the best fatigue life.

A block of wood is kept on table top. The mass of wooden block is 5 kg and its dimensions are 40cmx20cmx10cm. 1. Calculate the area of the wooden block in cm2 and in2. 2. Calculate the volume of the wooden block in cm3 and in3. 3. Compute the density of the wooden block in g/cm3 and lb/in3. 4. Compute the pressure. 5. Compute the pressure on top surface of the wooden block. 6. Compute the pressure on the bottom surface of the wooden block. 7. Compute the force on top surface of the wooden block. 8. Compute the force on the bottom surface of the wooden block. 9. What is the difference between the force on the bottom and the force on top?

Answers

Let's calculate the values based on the given information:

The area of the wooden block can be calculated by multiplying the length and width of one of its faces:

Area = Length * Width

Area = 40 cm * 20 cm

Area = 800 cm²

To convert to square inches, we can use the conversion factor 1 inch = 2.54 cm:

Area in square inches = Area in square centimeters / (2.54 cm/inch)²

Area in square inches = 800 cm² / (2.54 cm/inch)²

Area in square inches ≈ 124.03 in²

The volume of the wooden block can be calculated by multiplying its length, width, and height:

Volume = Length * Width * Height

Volume = 40 cm * 20 cm * 10 cm

Volume = 8000 cm³

To convert to cubic inches, we can use the conversion factor 1 inch = 2.54 cm:

Volume in cubic inches = Volume in cubic centimeters / (2.54 cm/inch)³

Volume in cubic inches = 8000 cm³ / (2.54 cm/inch)³

Volume in cubic inches ≈ 488.19 in³

The density of the wooden block can be calculated by dividing its mass by its volume:

Density = Mass / Volume

Density = 5 kg / 8000 cm³

To convert to grams per cubic centimeter (g/cm³), we can use the conversion factor 1 kg = 1000 g:

Density in g/cm³ = Density in kg/cm³ * 1000 g/kg

Density in g/cm³ = (5 kg / 8000 cm³) * 1000 g/kg

Density in g/cm³ ≈ 0.625 g/cm³

To convert to pounds per cubic inch (lb/in³), we can use the conversion factor 1 kg = 2.20462 lb and 1 inch = 2.54 cm:

Density in lb/in³ = Density in kg/cm³ * (2.20462 lb/kg) / (2.54 cm/inch)³

Density in lb/in³ = (5 kg / 8000 cm³) * (2.20462 lb/kg) / (2.54 cm/inch)³

Density in lb/in³ ≈ 0.036 lb/in³

Pressure is defined as force divided by area. In this case, we need more information to calculate the pressure. If the block is subjected to a specific force, we can divide that force by the appropriate surface area to find the pressure.

The pressure on the top surface of the wooden block depends on the force applied to it. Without information about the applied force, we cannot calculate the pressure.

Similarly, the pressure on the bottom surface of the wooden block depends on the force applied to it. Without information about the applied force, we cannot calculate the pressure.

The force on the top surface of the wooden block depends on the pressure applied and the surface area. Without information about the pressure or force applied, we cannot calculate the force.

The force on the bottom surface of the wooden block depends on the pressure applied and the surface area. Without information about the pressure or force applied, we cannot calculate the force.

Without the values for forces on the top and bottom surfaces, we cannot determine the difference between them.

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The area of the wooden block is 2800 cm² and 434.96 in².The volume of the wooden block is 8000 cm³ and 487.61 in³.The density of the wooden block is 0.625 g/cm³ and 0.0226 lb/in³.The pressure on the wooden block is 0.06125 N/cm² and 0.0089 psi.The pressure on the top surface of the wooden block is 0.06125 N/cm² or 0.0089 psi.The pressure on the bottom surface of the wooden block is 0.06125 N/cm² or 0.0089 psi.The force acting on the top surface of the wooden block is 49 N.The force acting on the bottom surface of the wooden block is 49 N.The force on the bottom surface is equal in magnitude to the force on the top surface.

1. The area of the wooden block can be calculated using the formula for the surface area of a rectangular prism: SA = 2(lw + lh + wh), where l, w, and h are the length, width, and height of the block, respectively. Using the given dimensions, we can find the surface area in cm²:

SA = 2(40 × 20 + 40 × 10 + 20 × 10)

SA = 2(800 + 400 + 200)

SA = 2(1400)

SA = 2800 cm²

To convert cm² to in², we can use the conversion factor 1 in² = 6.45 cm². So, the area in in² is:

2800 ÷ 6.45 = 434.96 in² (rounded to two decimal places)

2. The volume of the wooden block can be calculated using the formula for the volume of a rectangular prism: V = lwh. Using the given dimensions, we can find the volume in cm³:

V = 40 × 20 × 10

V = 8000 cm³

To convert cm³ to in³, we can use the conversion factor 1 in³ = 16.39 cm³. So, the volume in in³ is:

8000 ÷ 16.39 = 487.61 in³ (rounded to two decimal places)

3. The density of the wooden block can be calculated using the formula: density = mass/volume. The mass of the block is given as 5 kg. To convert this to grams, we can use the conversion factor 1 kg = 1000 g. So, the mass in grams is:

5 kg × 1000 g/kg = 5000 g

Using the volume calculated in part 2, we can find the density in g/cm³:

density = 5000 g/8000 cm³

density = 0.625 g/cm³

To convert g/cm³ to lb/in³, we can use the conversion factor 1 g/cm³ = 0.0361 lb/in³. So, the density in lb/in³ is:

0.625 g/cm³ × 0.0361 lb/in³/g/cm³ = 0.0226 lb/in³

4. The pressure on the wooden block is given by the formula: pressure = force/area. To find the pressure, we need to know the force acting on the block. Since the block is simply resting on the tabletop, the force acting on it is due to its weight. Using the formula for weight: w = mg, where w is weight, m is mass, and g is the acceleration due to gravity (9.8 m/s²).

To find the weight in newtons (N), we can use the conversion factor 1 kg = 9.8 N. So, the weight of the block is:

5 kg × 9.8 N/kg = 49 N

Using the area of the block's base (40 cm × 20 cm = 800 cm²), we can find the pressure in N/cm²:

pressure = 49 N/800 cm²

pressure = 0.06125 N/cm²

To convert N/cm² to psi, we can use the conversion factor 1 psi = 6894.76 N/m². So, the pressure in psi is:

0.06125 N/cm² × (1 m²/10,000 cm²) × (1 psi/6894.76 N/m²) = 0.0089 psi (rounded to four decimal places)

5. The pressure on the top surface of the wooden block is the same as the pressure calculated in part 4: 0.06125 N/cm² or 0.0089 psi.

6. To find the pressure on the bottom surface of the block, we can use the formula: pressure = force/area. Since the bottom surface has the same area as the top surface, the pressure will also be the same: 0.06125 N/cm² or 0.0089 psi.

7. The force acting on the top surface of the wooden block is simply its weight, which we calculated to be 49 N in part 4.

8. The force acting on the bottom surface of the wooden block is also its weight, which we calculated to be 49 N in part 4.

9. The force on the bottom surface is equal in magnitude to the force on the top surface.

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What is the centripetal acceleration acting on a 19 kg ball if it is being spun around by a tension force of 125 N?

Answers

Answer:

Explanation:

The centripetal acceleration:

aₙ = F /m = 125 /19 ≈ 6.6 m/s²

a motetcycle was heading south at 90 m/s and then it turned west and went 35 m/s what is the velocity of the motercycle

Answers

A motorcycle was heading south at 90 m/s and then it turned west and went 35 m/s , the velocity of the motorcycle is 62.5 m/s. This is average velocity.

What is velocity?

Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. 60 km/h northbound). Velocity is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of bodies.

Velocity is a physical vector quantity; both magnitude and direction are needed to define it. The scalar absolute value (magnitude) of velocity is called speed, being a coherent derived unit whose quantity is measured in the SI (metric system) as meters per second (m/s). If there is a change in speed, direction or both, then the object is said to be undergoing an acceleration.

Given

initial velocity , x=90m/s

final velocity , y=35m/s

formula for average velocity is \(\frac{1}{2}\) (x + y)

substituting the values

average velocity is 62.5m/s

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Which source should you NOT consult to validate an advertisement's claim?
A.
peer-reviewed scientific journals
B.
websites of government agencies
C.
your doctor
D.
website of the product manufacturer

Answers

Answer:

I believe D

Explanation:

Of course the manufacturer would most likely be biased to the product the have created, but the other sources would have no reason to. Hope this helps!

A boat takes 4 hours for travelling downstream from point A to point B and coming back to point A upstream. If the velocity of the stream is 2 Kmph and the speed of the boat in still water is 4 kmph, whit is the distance between A and B

Answers

Answer:

d = 6 km

Explanation:

In this case we have the relative speed of the boot changes, suppose that the boat and the river have the same direction when the boat goes from A to point B

       vbr = vrt + vbt

        vbr = 2 + 4

        vbr = 6 km / h

        v₁ = 6 km / h

velocity is constant

         v₁ = d / t₁

         t₁ = d / v₁

when the boat returns to the starting point the speed is both opposite

        vbr = vbt - vrt

        vbr = 4-2

        vbr = 2 km / h

        v₂ = 2 km / h

as the speed is constant

         t₂ = d / v₂

they also indicate that the total time is 4 h

       t₁ + t₂ = 4

we substitute

       4 = d / v₁ + d / v₂

       4 = d (1 / v₁ + 1 / v₂)

       d = 4 / (1 / v₁ + 1 / v₂)

let's calculate

       d = 4 / (1/6 + 1/2)

       d = 4 / 0.6666 67

       d = 6 km

A ball is moving at 9.9 m/s and has a momentum of 20.1 kg m/s. What is the balls mass in kg ? Round your answer to 1 decimal place

Answers

The mass of the ball in kg is 2.5.

Here is how to calculate it:

We can use the formula for momentum, which is:p = mvWhere:p = momentum = mass = velocity

Rearranging the formula, we have:m = p/v

Given that the momentum of the ball is 20.1 kg m/s and its velocity is 9.9 m/s,

we can substitute these values into the formula to find the mass of the ball:m = 20.1 kg m/s ÷ 9.9 m/sm = 2.03 kg

Round off the mass to 1 decimal place, and we have:m = 2.5 kg

Therefore, the mass of the ball in kg is 2.5.

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an airplane propeller is 1.80 m in length (from tip to tip) with mass 90.0 kg and is rotating at 2800 rpm (rev/min) about an axis through its center. you can model the propeller as a slender rod.
What is its rotational kinetic energy?
Suppose that, due to weight constraints, you had to reduce the propeller's mass to 75.0% of its original mass, but you still needed to keep the same size and kinetic energy. What would its angular speed have to be, in rpm?

Answers

The rotational kinetic energy of the propeller with the original mass is approximately 7.99 × 10⁵ joules.

In order to maintain the same kinetic energy with a reduced mass of 75.0%, the propeller's angular speed would 56.03 rpm.

To calculate the rotational kinetic energy of the propeller, we'll use the formula:

Rotational Kinetic Energy (KE) = (1/2) * I * ω²

Where:

KE is the rotational kinetic energy

I is the moment of inertia of the propeller

ω is the angular velocity of the propeller

Calculate the moment of inertia (I)

For a slender rod rotating about its center, the moment of inertia is given by:

I = (1/12) * m * L²

Where:

m is the mass of the propeller

L is the length of the propeller

Calculate the rotational kinetic energy (KE₁) with the original mass

To calculate the kinetic energy, we need to convert the angular velocity from rpm to radians per second (rad/s)

KE₁ = (1/2) * I * ω₁²

KE₁ = (1/2) * 18.0 kg·m² * (293.66 rad/s)²

KE₁ ≈ 7.99 × 10⁵ J

Determine the new mass of the propeller

Calculate the new angular velocity (ω₂) to maintain the same kinetic energy

To calculate the new angular velocity, we'll use the same formula as before, but solve for ω₂:

KE₂ = (1/2) * I * ω₂²

Since we want the new kinetic energy (KE₂) to be the same as the original (KE₁), we can equate the two equations:

(1/2) * I * ω₁² = (1/2) * I * ω₂²

Simplifying and solving for ω₂:

ω₂² = (ω₁² * m₁) / m₂

Where:

ω₁ is the original angular velocity

m₁ is the original mass

m₂ is the reduced mass

\(w_2 = \sqrt{w_1^2 * m_1) / m_2)}\)

ω₂ = \(\sqrt{293.66 rad/s)^2 * 90.0 kg / 67.5 kg)}\)

ω₂ ≈ 350.55 rad/s

Convert the new angular velocity to rpm

To convert ω₂ from radians per second to rpm:

ω₂rpm = ω₂ * (1 min/60 s) * (1 rev/2π rad)

ω₂rpm = 350.55 rad/s * (1 min/60 s) * (1 rev/2π rad)

ω₂rpm ≈ 56.03 rpm

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An astronaut is moving in space when a big explosion occurs about 50 meters behind him. How will the astronaut come to know about the explosion?
Choose:--
From the sound of the explosion
From the light due to the explosion
From light and sound due to the explosion
From the vibrations due to the explosion

Answers

Answer:

The correct answer is B.

The astronaut will know due to the light from the explosion.

Explanation:

Sound and vibrations require a medium such as air to travel through. Space, there is no air. Only a vacuum. So sound and vibrations are unable to travel. Light requires no medium to travel. It can go through a vacuum.  

Therefore the Astronaut will see a bright flash of light as it travels from the explosion to outer space. It is also important to note that light can travel very far because nothing else interacts with its wave particles and as such, it cannot be impeded.

Cheers!

a parallel plate capacitor has a charge of 6.0 uc when charged by a potenial difference of 1.25 v. what is the capacitance?

Answers

The capacitance of a parallel plate capacitor is 4.8 μF when charged with a potential difference of 1.25 V and a charge of 6.0 μC. In this calculation, the units are consistent.

The capacitance of a parallel plate capacitor can be calculated using the formula C = Q/V, where C is the capacitance, Q is the charge, and V is the potential difference. In this case, the charge is given as 6.0 μC and the potential difference is 1.25 V.

Substituting the given values into the formula, we have C = (6.0 μC) / (1.25 V). To simplify the units, we convert microcoulombs to coulombs by dividing by 10⁶, which gives C = (6.0 × 10⁻⁶ C) / (1.25 V).

Evaluating the expression, we find C = 4.8 × 10⁻⁶ F. Therefore, the capacitance of the parallel plate capacitor is 4.8 microfarads.

It is important to note that in this calculation, the units are consistent. The charge is in coulombs, the potential difference is in volts, and the capacitance is in farads.

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What is the experimental group(s)?
A. The group(s) that represents the normal conditions.
B. The group(s) that gets the special treatment​

Answers

I think it B The group(s) that gets the special treatment.I hope this is correct.

How can the Fitness Logs help you in this class?
OA. They can't; the Fitness Logs are only useful to your teacher.
B. They help you evaluate yourself for your final grade.
C. They let you keep track of your thoughts, feelings, and progress.
D. They show your parents how much you're learning.

Answers

Answer:B

Explanation:They help you evaluate yourself for your final grade.

a dont make sense, d dont make sense, B or C. B!

what is the main difference between a substance going through a physical change and one going through a chemical ?

Answers

Answer: Physical changes only change the appearance of a substance, not its chemical composition. Chemical changes cause a substance to change into an entirely substance with a new chemical formula. Chemical changes are also known as chemical reactions.

Answer:

just give the other person brainlyest

Explanation:

How to find the acceleration?

Answers

Answer:

speed/time

Explanation:

Answer:

a= (Vf - Vi)

         t

To find acceleration (a) you need to subtract the finale velocity (Vf) minus the initial velocity (vi) divided by time (t) as shown in the equation above.

f the crate starts from rest 8.95 mm up along the plane from its base, what will be the crate's speed when it reaches the bottom of the incline

Answers

Answer:

Its speed would be increasing.

Explanation:

How will the equations of motion for an object moving with a uniform velocity change?.

Answers

If an object is moving with uniform velocity, it means that its speed and direction remain constant over time.

In this case, the equations of motion, which describe the relationship between an object's displacement, velocity, acceleration, and time, will not change.

The equations of motion for an object moving with uniform velocity are:

Displacement (s): s = ut + (1/2)at²

Final velocity (v): v = u + at

Velocity-time relationship: v = (s - u) / t

Displacement-velocity relationship: s = (v + u) / 2 * t

Acceleration (a): a = 0

In these equations:

s represents the displacement of the object.

u is the initial velocity of the object.

v is the final velocity of the object.

t is the time taken for the motion.

a denotes the acceleration of the object, which is zero in the case of uniform velocity.

Since the acceleration (a) is zero, the terms involving acceleration disappear from the equations, simplifying them. The equations reduce to:

Displacement (s): s = ut

Final velocity (v): v = u

Velocity-time relationship: v = s / t

Displacement-velocity relationship: s = v * t

In summary, when an object moves with uniform velocity, the acceleration term in the equations of motion becomes zero, simplifying the equations accordingly.

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Trying to help my brother but i dont remember question 8. Pls help, thank you

Trying to help my brother but i dont remember question 8. Pls help, thank you

Answers

Answer:

I can't read it if you zoom in its still blurry

Explanation:

read the question to me and I'll try to answer it thx

Which type of resources do we have a limited supply of?

Answers

Explanation:

The resources that we value—time, money, labor, tools, land, and raw materials—exist in limited supply. There are simply never enough resources to meet all our needs and desires.

Explanation:

Time, money, labor, land , and raw materials

A tennis ball is thrown vertically upward. It reaches the maximum height in 1.25 sec. What is the initial speed of the ball as it leaves the person's hand (m/s)? (neglect air resistance)

Answers

h= max

v= 0

t= 1.25

Vf= 0 at max height

vf = vi + at

0 = vi - 9.8 * 1.25

vi = 12.25 m/s

A 1.50 kg rock is thrown up into the air from ground level, reaches a maximum height of 7.00 m, then returns to the ground. Calculate the rock's momentum as it strikes the ground

Answers

Answer:

17.565 kgm/s

Explanation:

Momentum = mass × velocity

I = mv..................... Equation 1

But we can calculate the value of v  using the equation of motion under gravity.

v² =  u²+2gs............. Equation 2

Where u = initial velocity, s = maximum heigth, g = acceleration due to gravity.

Given: u = 0 m/s (at the maximum heigth), s = 7.0 m.

Constant: g = 9.8 m/s²

Substitute these values into equation 2

v² = 0²+ 2×7×9.8

v² = 137.2

v = √137.2

v = 11.71 m/s.

Also given: m = 1.50 kg

substitute these values into equation 1

Therefore,

I = 1.5×11.71

I = 17.565 kgm/s

What is 64 °F in °C?

Answers

64°F is equivalent to 17.78°C.

A temperature unit developed from the SI (International System of Units) is Celsius (symbol: °C).

Prior to the adoption of the metric system, Fahrenheit (symbol: °F) was a commonly used measurement of temperature.

To convert Fahrenheit (°F) to Celsius (°C) we have to first subtract 32 from Fahrenheit and then multiply it by .5556 or 5/9.

We have to convert 64 degrees Fahrenheit (°F) to Celsius (°C),

We can use the following formula:

°C = (°F - 32) x 5/9

As per the given information,

°F = 64

By placing the value 99.3 for °F, we get:

°C = (64 - 32) x 5/9

°C= 32 x 5/9

°C = 160/9

°C = 17.78 (rounded to two decimal places)

Therefore, 64°F is equivalent to 17.78°C.

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Question :-   What is 64°F in °C?

anyone please help me I need help please guys PTS 1000

Calculate X and Y in the given diagram

anyone please help me I need help please guys PTS 1000Calculate X and Y in the given diagram

Answers

Answer:

it was helpful to you dear

anyone please help me I need help please guys PTS 1000Calculate X and Y in the given diagram

A simple circuit has 5V battery power source and a 20 Ω resistor. What is the power?

4 W
1.25 W
15 W
100 W
0.25 W
20 W

A simple circuit has 5V battery power source and a 20 resistor. What is the power? 4 W1.25 W15 W100 W0.25

Answers

The power in the given simple circuit with a 5V battery power source and a 20 Ω resistor is 1.25 W.

To calculate the power in a simple circuit, we use the formula P = (V^2) / R, where P represents power, V is the voltage, and R is the resistance. In the given scenario, the circuit has a 5V battery power source and a 20 Ω resistor. Plugging in these values into the formula, we can calculate the power.

P = (5V)^2 / 20 Ω

Simplifying the expression, we have:

P = 25V^2 / 20 Ω

Dividing 25 by 20, we get:

P = 1.25V^2 / Ω

Therefore, the power in the circuit is 1.25 W (watts). This means that the circuit is dissipating energy at a rate of 1.25 joules per second.

The power value of 1.25 W indicates the rate at which electrical energy is transformed or transferred in the circuit. It represents the amount of work done or the amount of energy converted per unit of time. In this case, the power value suggests that the circuit is consuming or dissipating 1.25 joules of energy every second.

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(a) calculate the buoyant force on a 2.20 liter helium balloon.

Answers

The buoyant force on a 2.20 liter helium balloon can be calculated by multiplying the volume of the balloon by the density of the displaced air and the acceleration due to gravity. Assuming standard temperature and pressure (STP) conditions of 0°C and 1 atm, the density of air is approximately 1.29 g/L.

Buoyant force = volume of balloon × density of displaced air × acceleration due to gravity

Buoyant force = 2.20 L × 1.29 g/L × 9.81 m/s²

Buoyant force = 28.3 N

Therefore, the buoyant force on a 2.20 liter helium balloon is approximately 28.3 N. This means that the balloon experiences an upward force of 28.3 N due to the difference in density between the helium in the balloon and the surrounding air, allowing it to float in the air.

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how to make a brainliest questions Or how to Get them?

Answers

Answer:

Select the crown at the bottom of an answer where the speech bubble icon is.

A tennis balls in the air and the potential energy increases. At the same time, it’s kinetic energy___because the velocity____

a.) increases;increases
b.) decreases; increases
c.) decreases;decreases
d.) increases;decreases

Answers

Answer:

A

Explanation:

More potential energy equals more kinetic

What was mollys constant speed if she was running 10 metes in 5 seconds

Answers

Answer:

Answer: b

Explanation:

Average Speed = Total Distance Total Time

Total Distance

Total Time

= 10m

    _  

    5 s

= 2 m/s

Which wave measure is changing by the greatest amount in the image?

A. amplitude
B. wavelength
C. speed
D. frequency

Which wave measure is changing by the greatest amount in the image?A. amplitudeB. wavelengthC. speedD.

Answers

Answer: frequency

Explanation:

amplitude is the max height at which the wave reaches
wavelength distance b/w two waves

the speed at which the wave is oscillating

frequency is no. of oscillations of  a wave per unit length

Study this model of a gravitational slingshot. then answer the questions. in this model, the velocity of the spacecraft at position 2 is the velocity of the craft at position 4. at position 1, the direction of the spacecraft changes because of . position 3 represents the .

Answers

In this model of a gravitational slingshot, the velocity of the spacecraft at position 2 is the same as the velocity of the craft at position 4.

At position 1, the direction of the spacecraft changes because of the gravitational pull of the planet. Position 3 represents the point of closest approach to the planet, where the gravitational force is the strongest. The gravitational slingshot effect increases the spacecraft's velocity as it passes the planet and moves away from it, thus allowing it to reach greater speeds than would be possible otherwise.

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A 1. 25 kg block is attached to a spring with spring constant 17. 5 N/m. While the block is sitting at rest, a student hits it with a hammer and almost instantaneously gives it a speed of 46. 0 cm/s. What are

Answers

The maximum displacement of the block from its equilibrium position is 0.063 meters.

To solve this problem, we can first find the initial potential energy stored in the spring by using the formula: PE = 0.5kx^2, where k is the spring constant and x is the initial displacement from equilibrium (which is zero). Thus, the initial potential energy is 0 J. Then, we can use the principle of conservation of energy to find the maximum displacement of the block from its equilibrium position. Since there is no external work done on the block-spring system, the initial kinetic energy of the block is converted entirely into potential energy stored in the spring when the block reaches its maximum displacement. Using the formula for kinetic energy, KE = 0.5mv^2, where m is the mass of the block and v is the initial velocity, we can find the initial kinetic energy to be 1.44 J. Setting the initial kinetic energy equal to the final potential energy, we can solve for x to find the maximum displacement of the block from its equilibrium position to be 0.063 meters.

It is important to note that the almost instantaneous hit with the hammer means that we can assume the time interval over which the force is applied to be very short and thus the impulse of the force can be treated as an instantaneous change in momentum of the block. Therefore, the conservation of momentum principle can be ignored in the problem.

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