The net work done in accelerating a solid cylindrical wheel from rest to an angular speed of 5050 rev/ min is W=590. J. If the radius of the wheel is 1.10m, what is its mass?

Answers

Answer 1

The mass of the solid cylindrical wheel is 71.14 kg .

What is mass?

Measuring inertia, a property of all stuff that cannot be changed. What a body of matter is in essence is the resistance it provides to a change in its speed or position brought about by the application of a force.

What is acceleration ?

Acceleration is the term for the rate of change in speed. In most cases, but not always, acceleration denotes a shift in speed. An object is still moving in a circular path, but the direction of its velocity is changing, thus it is still gaining speed.

final angular speed of wheel is

w = 50 rev/m/n = 50 * 2π/ 60 = 1rev/ min = 2π/ 60 rad/s

w = 10π/6 rad/s

work done w = 590 J

radius of wheel is r = 1.10 m

as we know that work done in rotating of wheel is

W = 1/2 I W²,

Where I is moment of inertia of the wheel

moment of inertia of a solid cylindrical wheel is

I = 1/2 mr², where m is mass

∴ W = Hw/ r²w²

m= 4*590/ (1.10)² ( 10π/6) ² = 4* 590* 36/ 1.21* 100 π²

m= 71.14 kg

Therefore, mass of the solid cylindrical wheel is 71.14 kg .

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Related Questions

A piece of wood 350 mm × 350 mm and 15 mm thick conducts heat through its thickness under steady state conditions. The rate of heat flow is measured to be 14.0 watts when the temperature difference is 28 C°. Determine the coefficient of thermal conductivity for this wood

Answers

The coefficient of thermal conductivity (k) is related to the rate of heat flow (Q), the cross-sectional area (A), the length (L), the temperature difference (ΔT), and the thermal resistance (Rth) by the following equation:

k = Q / (A * ΔT * L) = Rth * (A * ΔT)

Reorganizing this equation gives:

Rth = k / (A * ΔT)

The given information in the problem is:

Rate of heat flow (Q) = 14.0 watts

Thermal resistance (Rth) = (350 mm × 350 mm × 15 mm) / (14.0 watts) = 31.5 mm⁴/C

Temperature difference (ΔT) = 28°C

Substituting these values into the equation, we have:

k = Q / (A * ΔT) = 14.0 W / (0.35 m² * 28°C) = 1.94 W/mK

So the coefficient of thermal conductivity (k) for this wood is approximately 1.94 W/mK.

2 An electric kettle is marked "230V, 1.5 kW.
a Explain what these numbers mean.
b Calculate the correct fuse that should be used.
c Explain why a 230V, 100 W bulb glows more brightly than a 230 V, 60 W
bulb when both are connected to the mains supply.

Answers

The power needed to boil the water is divided by the element's power output, and the result is multiplied by 100 to get the efficiency of the kettle as a percentage. The answer is 79 %.

To Find the efficiency of electric kettle ?

We are informed that

Electric kettle power is 1 kW.

Electric kettle voltage is 230 V.

The time it takes the kettle to bring the water to boiling point is 7.5 minutes.

1 kg = mass of water.

Heat generated equals V x I x t + Pt.

generated heat = 1000 W x 7.5 x 60

Heat absorbed equals (100 - 15) x 1 x 4200 = 4200 x 85

Efficiency is determined by multiplying the heat produced by the heat absorbed by 100.

= 4.2 x 85 x 10^3 / 4.5 x 10^5 x 100

= 357 / 4.5 = 79 %

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Does oil or water expand more? Will give brainliest!

Answers

Answer:

Heat, which is the exchange of energy between a system and its surroundings, occurs in three major ways: conduction, convection and radiation.

Which has higher heat capacity oil or water?

For both the hot plate and the microwave, olive oil will heat up faster than water because the heat capacity of oil is lower than the heat capacity of water. Water requires more energy per gram of liquid to change its temperature.

when I search I found this answer I hope it can help you answer your question.

Water expands more .

Fish can adjust their buoyancy with an organ called a swim bladder. The swim bladder is a flexible gas-filled sac; a fish can increase or decrease the amount of gas in its swim bladder so that it stays neutrally buoyant, neither sinking nor floating. Suppose a fish is neutrally buoyant at some depth and then goes deeper. What needs to happen to the volume of air in the swim bladder

Answers

As the fish goes deeper, the volume of air in the swim bladder increases.

What is Buoyant force?Buoyant force is the upward force a fluid exerts on an object.

Buoyant force is calculated using the following formula;

F = ρVg

where;

ρ is the density of the fluid.V is the volume of the fluid displaced.g is acceleration due to gravity.

The volume of the fluid displaced is calculated as follows;

V = Ah

where;

A is the area of the object.h is the depth of the fluid.

Thus, we can conclude that as the fish goes deeper, the volume of air in the swim bladder increases.

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A thin rod of length 2.15 m and mass 13.1 kg is rotated at an angular speed of 3.95 rad/s around an axis perpendicular to the rod and through its center of mass. Find the magnitude of the rod's angular momentum.

Answers

Answer:

L = 239.2 J.s

Explanation:

The angular momentum of the rod is given by the following formula:

L = mvr

where,

L = Angular Momentum = ?

m = mass = 13.1 kg

r = radius of circle of rotation = length of rod = 2.15 m

v = linear speed of rod = r(angular speed of rod) = (2.15 m)(3.95 rad/s)

v = 8.5 m/s

Therefore,

L = (13.1 kg)(8.5 m/s)(2.15 m)

L = 239.2 J.s

The angular momentum of the thin rod will be L = 239.2 J.s

What is angular momentum?

Whenever any object has rotational motion then its angular momentum will be the product of the linear velocity of the object and the radius of the circle of rotation of the object.

The angular momentum of the rod is given by the following formula:

\(L= MVr\)

where,

L = Angular Momentum = ?

m = mass = 13.1 kg

r = radius of circle of rotation = length of rod = 2.15 m

w=3.95 rad/s

Now the angular momentum will be calculated as:

\(L= MVr\)

The linear velocity will be

\(V=wr=3.95\times 2.15=8.5\ \frac{m}{s}\)

Now put the value in the formula we get:

\(L=13.1\times 8.5\times 2.15=239.2\ J\)

\(L=239.2\ J\)

Hence the angular momentum of the thin rod will be L = 239.2 J.s

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Jupiter's Great Red Spot is
1.slowly shrinking
2.a large storm
3.smaller than Saturn's spot
4.a large area of liquid hydrogen

Answers

Answer:    

2 : A large storm

Explanation: I hope this helps

Electromagnetic waves used in cell phones are called

a. radio waves
b.microwaves
c. Gamma rays
d. Ultraviolet rays

Answers

Answer:

A.Radio waves

Explanation:

If vector A represents displacement from point O(x1, y1,z1) and P(x2, Yz, Z2) ؟

If vector A represents displacement from point O(x1, y1,z1) and P(x2, Yz, Z2)

Answers

The magnitude of the displacement of the vector A is determined as 6.2 units.

What is the magnitude of displacement of the vector?

The magnitude of the displacement of the vector is calculated as follows;

| A | = √[ (x₂ - x₁ )²  +  (y₂ - y₁ )² +  (z₂ - z₁ )²]

where;

| A | is the magnitude of vector Ax₂  and x₁ are the final and initial position on  x - coordinate respectively.y₂ and y₁ are the final and initial position on  y - coordinate respectively.z₂ and z₁ are the final and initial position on  z- coordinate respectively.

The magnitude of vector A is calculated as;

| A | = √[ (2 - 0 )²  +  (3 - 0 )² +  (5 - 0 )²]

| A | = √ (4 + 9 + 25)

| A | = √ ( 38)

| A | = 6.2 units

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The complete question is below;

If vector A represents displacement from point O(x1, y1,z1) and P(x2, Yz, Z2). find the magnitude of the displacement of vector A.

shows a map of Olivia's trip to a coffee shop. She gets on her bike at Loomis and then rides south 0.9mi to Broadway. She turns east onto Broadway, rides 0.8 mi to where Broadway turns, and then continues another 1.2mi to the shop. What is the magnitude of the total displacement of her trip?

Answers

The  magnitude of the total displacement of her trip is 2.2 miles.

Total displacement of Olivia's trip

The magnitude of the total displacement of her trip is calculated as follows;

Total east journey = 0.8 mi + 1.2 mi = 2 mi

Resultant displacement = √(y² + x²)

Resultant displacement = √(0.9² + 2²)

Resultant displacement = 2.2 mi

Thus, the  magnitude of the total displacement of her trip is 2.2 miles.

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A student conducts an experiment to determine how the temperature of water affects the time for sugar to di solve. In each trial, the
student uses a different amount of sugar and a different temperature of water.
What is wrong with this experimental design?
The student changed too many variables
The student did not change enough variables
The student needs to perform more trials
The student does not have a dependent variable

Answers

Answer:

I think it's A

Explanation:

he shouldn't have changed the amount of sugar, because the whole point is to see which temperature dissolves sugar more quickly.

A physics student rolls a ball down a hill with an initial velocity of 2.5m/s. If it accelerates down the hill at a rate of 6.3m/s^2, How long will it take to reach the bottom of the hill, 150 meters away?

Please help!!!

Answers

I'll assume you mean the hill is 150 m along its slope, since that's the direction the ball rolls.

The distance x it rolls after time t is

x = (2.5 m/s) t + 1/2 (6.3 m/s²) t²

Set x = 150 m and solve for t :

150 m = (2.5 m/s) t + 1/2 (6.3 m/s²) t²

(3.15 m/s²) t² + (2.5 m/s) t - 150 m = 0

t = 1/2 [(-2.5 m/s) + √((2.5 m/s)² - 4 * (3.15 m/s²) * (-150 m))]

(Use the quadratic formula, and take the positive root)

t ≈ 6.52 s

Which one of the following is the longest length?
(a) 100 m
(b) 104 µm
(c) 107 nm
(d) 102 mm​

Answers

Okay, let's convert all the lengths to the same unit to compare:

(a) 100 m = 100 meters

(b) 104 μm = 104 micrometers = 104 × 10^-6 meters = 0.000104 meters

(c) 107 nm = 107 nanometers = 107 × 10^-9 meters = 0.000000000997 meters

(d) 102 mm = 102 millimeters = 102 × 10^-3 meters = 0.0102 meters

The longest length is:

(a) 100 m = 100 meters

The answer is option (a).

Answer: 100 m

Explanation:

1 μm = \(10^{-6}\) m = 0,000001 m

1 nm = \(10^{-9}\) m = 0,000000001 m

1 mm = \(10^{-3}\) m = 0,001 m

∴ 100 m es la mayor longitud

a charged cloud system produces an electric field in the air near the earth surface. When a particle (q=-2.0x10-9)is acted on by a downward electrostatic force of 3.0x10^-6 N when placed in this field, determine the magnitude of the electric field

Answers

The magnitude of the electrical field would be 1.5x10^3 N/C.

Electrical field calculation

The electrostatic force experienced by a charged particle in an electric field is given by the formula:

F = qE

Where F is the electrostatic force, q is the charge of the particle, and E is the electric field strength.

In this case, the electrostatic force acting on the particle is 3.0x10^-6 N and the charge of the particle is -2.0x10^-9 C. So we have:

3.0x10^-6 N = (-2.0x10^-9 C)E

Solving for E, we get:

E = (3.0x10^-6 N) / (-2.0x10^-9 C)

E = -1.5x10^3 N/C

Since the electric field is a vector quantity, its magnitude is always positive. Therefore, the magnitude of the electric field in this case is:

|E| = 1.5x10^3 N/C

So the magnitude of the electric field is 1.5x10^3 N/C, directed downward.

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A car travels at a constant speed up a ramp making an angle of 28 degrees with the horizontal component of velocity is 40 kmh^-1, find the vertical and horizontal component of velocity.

Answers

Answer:

Vx = 35.31 [km/h]

Vy = 18.77 [km/h]

Explanation:

In order to solve this problem, we must decompose the velocity component by means of the angle of 28° using the cosine function of the angle.

\(v_{x} = 40*cos(28)\\V_{x} = 35.31 [km/h]\)

In order to find the vertical component, we must use the sine function of the angle.

\(V_{y}=40*sin(28)\\V_{y} = 18.77 [km/h]\)

A bag contains 2 orange balls and 3 blue balls. Two balls are selected without putting the first one back. What is the probability they are both orange?.

Answers

Overall probability of this particular event happening are 2/5 and 1/4, respectively. You get 2/20 when you add them all together. Justify with 1/10.

What are examples and probability?

The justification for probability serves as the basic foundation for density of a reference substance. For instance, this same theoretically chance of receiving a head while tossing a coin is 12.

The probability formula is what?

The possibility is typically defined as the proportion of positive outcomes to all alternatives in the sample space. Probability and plausibility, as well as its homophones in these other language skills, are words that have their roots in medieval knowledge and Cicero. They are typically used to denote opinions that are plausible or widely accepted.

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A bullet traveling at 5.0 x10^2 meters per is brought to rest by an impulse of 50 Newton*seconds. Find the mass of the bullet.

Answers

The bullet stops moving on hitting on a surface. Hence, the impulse here is equal to the momentum. Therefore, the mass of the bullet is 0.1 Kg.

What is impulse?

Impulse in physics is the change in momentum. It is the product of the force and change in time.

hence, impulse = f. dt

When the bullet is travelling with  a velocity of 500 m/s it has a momentum. When it brought to rest, momentum become zero. Thus, the momentum is equal to the impulse here.

Therefore, f.dt = m. v

f.dt = 50 N s

v = 500 m/s

m = 50 N s/500 m/s = 0.1 Kg

Therefore, the mass of the bullet is 0.1 Kg.

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help pls!!

Fig above shows a wave traveling through a medium. Use the fig to answer the questions below.

A) What is the amplitude of the wave ? Include correct units.
B) Use the graph to determine the time of one wave. Use it to find the frequency.
C) If the speed of the wave is 25 cm/s, what is the wavelength of the wave ? Show data listing, equation , substitution leading to the answer for full credit.

help pls!!Fig above shows a wave traveling through a medium. Use the fig to answer the questions below.A)

Answers

(a) The amplitude of the wave is determined as 8 cm.

(b) The period of the wave motion is  20 s and the frequency of the wave is 0.05 Hz

(c) The wavelength of the wave is 500 cm.

What is the amplitude of the wave ?

(a) The amplitude of the wave is the maximum displacement of the wave.

from the graph, amplitude of the wave = 8 cm

(b) The period of the wave motion is calculated as;

T = 20 s

The frequency of the wave = 1/T = 1/20 s = 0.05 Hz

(c) The wavelength of the wave is calculated by applying the following wave formula.

λ = v / f

λ = 25 cm/s / 0.05 Hz

λ = 500 cm

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Two blocks, 1 and 2, are connected by a massless string that passes over a massless pulley. 1 has a mass of 2.25 kg and is on an incline of angle 1=42.5∘ that has a coefficient of kinetic friction 1=0.205. 2 has a mass of 5.55 kg and is on an incline of angle 2=33.5∘ that has a coefficient of kinetic friction 2=0.105

. The figure illustrates the configuration.

A system of two blocks connected by a rope passing over a pulley. The system sits atop a scalene triangle whose long edge forms the base. The pulley is attached to the apex of the triangle. Box M subscript 1 rests on the triangle edge to the left of the pulley, which makes an angle of theta subscript 1 with the base of the triangle. The coefficient of friction between box M sub 1 and the surface is mu subscript 1. Box M subscript 2 rests on the triangle edge to the right of the pulley, which makes an angle of theta subscript 2 with the base of the triangle. The coefficient of friction between box M sub 2 and the surface is mu subscript 2.

Answers

The force acting on the system of two blocks connected by a rope passing over a pulley is -13.26 N.

The system of two blocks connected by a rope passing over a pulley are M1 and M2, where M1 rests on the triangle edge to the left of the pulley, which makes an angle of theta subscript 1 with the base of the triangle. The coefficient of friction between box M1 and the surface is mu subscript 1. M2 rests on the triangle edge to the right of the pulley, which makes an angle of theta subscript 2 with the base of the triangle.

The coefficient of friction between box M2 and the surface is mu subscript 2. The system sits atop a scalene triangle whose long edge forms the base. The pulley is attached to the apex of the triangle.M1 has a mass of 2.25 kg and is on an incline of angle 1=42.5∘ that has a coefficient of kinetic friction 1=0.205. M2 has a mass of 5.55 kg and is on an incline of angle 2=33.5∘ that has a coefficient of kinetic friction 2=0.105.The free-body diagram of M1 shows that the weight of M1 acts straight downwards (vertically) and the normal force acts perpendicular to the slope.

The force of friction opposes the motion and acts opposite to the direction of motion.M1 = 2.25 kgTheta subscript 1 = 42.5 degreesMu subscript 1 = 0.205g = 9.81 m/s²In the free-body diagram of M2, the normal force acts perpendicular to the incline of the slope, the weight of the object acts vertically downwards and parallel to the incline, and the force of friction opposes the motion and acts opposite to the direction of motion.M2 = 5.55 kgTheta subscript 2 = 33.5 degreesMu subscript 2 = 0.105g = 9.81 m/s²The tension in the string is the same throughout the rope. Since the masses are being pulled by the same rope, the acceleration of the objects is the same as the acceleration of the rope.

The tension in the string is directly proportional to the acceleration of the objects and the rope.A system of two blocks connected by a rope passing over a pulley has a total mass of M. The acceleration of the system is given by the formula below:a = [(m1-m2)gsin(θ1) - μ1(m1+m2)gcos(θ1)] / (m1 + m2)Where, μ1 = 0.205 is the coefficient of friction of block M1θ1 = 42.5 degrees is the angle of the incline of block M1M1 = 2.25 kg is the mass of block M1M2 = 5.55 kg is the mass of block M2g = 9.81 m/s² is the acceleration due to gravitysinθ1 = sin 42.5 = 0.67cosθ1 = cos 42.5 = 0.75The acceleration of the system is:a = [(2.25-5.55)(9.81)(0.67) - (0.205)(2.25+5.55)(9.81)(0.75)] / (2.25 + 5.55)a = -1.7 m/s² (the negative sign indicates that the system is accelerating in the opposite direction).

The force acting on the system is given by:F = MaWhere M is the total mass of the system and a is the acceleration of the system. The total mass of the system is:M = m1 + m2M = 2.25 + 5.55M = 7.8 kgThe force acting on the system is:F = 7.8(-1.7)F = -13.26 N (the negative sign indicates that the force is acting in the opposite direction).

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Explain how the Earth, Moon, and Sun all cause the moon phases.

Answers

Answer:The sun provides the light to see the moon, while the earth casts a shadow on the moon but on full moons there is no shadow from the earth on the moon, and the moon is the thing affected by all of this

Explanation:

20 POINTS NEED ANSWER ASAP Is this a scientific model? Use complete sentences to explain why or why not.

A map showing the winter outlook for the United States
Public Domain

Answers

umm actually is 10 points

If moving charges create magnetic fields and all materials are made up of atoms that have moving charges, why are most things NOT magnetic?

Answers

Magnetism is the result of the "spin" of the electron and most of these cancel each other out in larger bodies thus most things not being magnetic.

the period of a simple pendulum increases by 50% when the length of the pendulum is increased by 0.6 m.
The intial length of the pendulum is
a) 1.2m
b) 0.48m
c) 0.24m
d) 0.12m.

Answers

Answer:

b) 0.48m is the right answer.

The correct answer is (b) 0.48m.
This can be determined by using the formula for the period of a simple pendulum, which is: T = 2π√(l/g), where T is the period, l is the length of the pendulum, and g is the acceleration due to gravity. Since the period is increased by 50%, and the length of the pendulum is increased by 0.6m, the initial length of the pendulum can be found by solving for l in the equation: (T + T/2) = 2π√((l+0.6m)/g).

Consider the circuit in Figure 5 with e(t) = 12sin(120pit) V. When S1 and S2 are
open, i leads e by 30°. When SI is closed and S2 is open, i lags e by 30°. When S1 and S2 are closed, i has an amplitude 0.5A. What are R, L, and C?

Consider the circuit in Figure 5 with e(t) = 12sin(120pit) V. When S1 and S2 areopen, i leads e by 30.

Answers

Based on the information, it should be noted that the resistance R is 0.5 Ω.

How to calculate the resistance

When S1 and S2 are open, i leads e by 30°. In this case, the circuit consists of only the inductor (L) and the capacitor (C) in series. Therefore, the impedance of the circuit can be written as:

Z = jωL - 1/(jωC)

Since i leads e by 30°, we can express the phasor relationship as:

I = k * e^(j(ωt + θ))

Z = jωL - 1/(jωC) = j(120π)L - 1/(j(120π)C)

Re(Z) = 0

By equating the real parts, we get:

0 = 0 - 1/(120πC)

Let's assume that there is a resistance (R) in series with the inductor and capacitor. The impedance equation becomes:

Z = R + jωL - 1/(jωC)

Z = R + jωL

Im(Z) = ωL > 0

Substituting the angular frequency and rearranging the inequality, we have:

120πL > 0

L > 0

This condition implies that the inductance L must be greater than zero.

When S1 and S2 are closed, i has an amplitude of 0.5 A. In this case, the impedance is:

Z = R + jωL - 1/(jωC)

Since the amplitude of i is given as 0.5 A, we can express the phasor relationship as:

I = 0.5 * e^(j(ωt + θ))

By substituting this phasor relationship into the impedance equation, we can determine the value of R. The real part of the impedance must be equal to R:

Re(Z) = R

Since the amplitude of i is 0.5 A, the real part of the impedance must be equal to 0.5 A: 0.5 = R

Therefore, the resistance R is 0.5 Ω.

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Can anyone please help me with this question i am struggling!!! the picture is above

Can anyone please help me with this question i am struggling!!! the picture is above

Answers

Answer:

proportional tax is.the answer.

Explanation:

because both girls tax is equal.

A laser positioned on a ship is used to communicate with a small two man research submarine resting on the bottom of a lake. The laser is positioned 12 m above the surface of the water, and it strikes the water 20 m from the side of the ship. The water is 76 m deep and has an index of refraction of 1.33. How far is the submarine from the side of the ship

Answers

Answer:

84.1 m

Explanation:

Given :

The distance from the ship to submarine :

20 + y

Using Pythagoras :

Tan θ = opposite / Adjacent

Tan θ = 20 / 12

12 tan θ = 20

θ = tan^-1(20/12)

20

θ = 59.036°

The angle phi;

n1sinθ1 = n2sin θ

Sin 59.036 = 1.33 * sin phi

Sin phi = sinsin(59.04) ÷1.33

0.8574907 = 1.33 * sin phi

Sin phi = 0.8574907 / 1.33

Sin phi = 0.6447298

phi = sin(0.6447298

Phi = 40.15°

From Pythagoras :

y = 76tan40.15°

y = 76 * 0.8435707

y = 64.11

20 + y

20 + 64.11 = 84.11

A laser positioned on a ship is used to communicate with a small two man research submarine resting on

Calculate the magnitude of force, is the vertica Component of force is 10N and its horizontal apre to 60º​.

Answers

I’m not sure sorry could you give another answer I’m sure I can help ,

What are the action and linking verb in: are you a spoiled child?

Answers

All of the sense verbs; look, smell, touch, appear, sound, taste, and feel can be linking verbs. Other examples of verbs that can be linking verbs and action verbs include turn, remain, prove, and grow.



An electron starts from rest and falls through a potential rise of 100V. What is its final
speed?​

Answers

Answer:

The final speed of electron=\(5.93\times 10^6m/s\)

Explanation:

We are given that

Initial velocity, u=0

Potential, V=100 V

We have to find the final speed.

Mass of electron, \(m=9.1\times 10^{-31} kg\)

Charge on electron, q=\(1.6\times 10^{-19}C\)

We know that

\(qV=\frac{1}{2}mv^2-\frac{1}{2}mu^2\)

Using the formula

\(1.6\times 10^{-19}\times 100=\frac{1}{2}\times 9.1\times 10^{-31} v^2-0\)

\(v^2=\frac{2\times 1.6\times 10^{-19}\times 100}{9.1\times 10^{-31}}\)

\(v=\sqrt{\frac{2\times 1.6\times 10^{-19}\times 100}{9.1\times 10^{-31}}}\)

\(v=5.93\times 10^6m/s\)

Hence, the final speed of electron=\(5.93\times 10^6m/s\)

4. Four objects are situated along the y axis as follows: a 2.00kg object is at +3.00m, a 3.00kg object is at +2.50m, a 2.50kg object is at the origin, and a 4.00kg object is at -0.500m. Where is the center of mass of these objects?​

Answers

Answer: 1.348 meters

Explanation: Although the sign is missing from the location of the 4.00 kg object, it is assumed to be positive. The net moment of all the objects about the center of mass must be zero. Let the center of mass be on the y axis at a point  c . Adding the four moments together, we get:

(2.00)(3.00−c)+(3.00)(2.50−c)+(2.50)(0−c)+(4.00)(0.500−c)=0

6.00−2.00c+7.50−3.00c+0−2.50c+2.00−4.00c=0

11.5c=15.50

c=  1.348 metres

The center of mass is on the y axis at  y  = 1.348 metres.

A 24.4kg dog is running northward at 2.14m/s, while a 5.53kg cat is running eastward at 3.56m/s. Their 78.5kg owner has the same momentum as the two pets taken together. Find the direction of the owner's velocity. Find the magnitude of the owner's velocity.

Answers

The owner's velocity is in the opposite direction of the combined velocity of the dog and the cat, and its magnitude is approximately 0.916 m/s.

To solve the given problem, we can use the principle of conservation of momentum to find the direction and magnitude of the owner's velocity.

Let's denote the velocity of the dog as v1 (northward), the velocity of the cat as v2 (eastward), and the velocity of the owner as v (unknown).

According to the conservation of momentum, the total momentum before the interaction is equal to the total momentum after the interaction.

The total momentum before the interaction is given by:

Total momentum before = (mass of the dog * velocity of the dog) + (mass of the cat * velocity of the cat) + (mass of the owner * velocity of the owner)

Mass of the dog (m1) = 24.4 kg

Velocity of the dog (v1) = 2.14 m/s

Mass of the cat (m2) = 5.53 kg

Velocity of the cat (v2) = 3.56 m/s

Mass of the owner (m3) = 78.5 kg

Velocity of the owner (v) = unknown

Total momentum before = (24.4 kg * 2.14 m/s) + (5.53 kg * 3.56 m/s) + (78.5 kg * v)

The total momentum after the interaction is zero since the owner has the same momentum as the pets taken together.

Total momentum after = 0

Equating the two expressions:

(24.4 kg * 2.14 m/s) + (5.53 kg * 3.56 m/s) + (78.5 kg * v) = 0

Simplifying the equation:

(52.216 kg·m/s) + (19.6488 kg·m/s) + (78.5 kg * v) = 0

71.8648 kg·m/s + (78.5 kg * v) = 0

Solving for v:

78.5 kg * v = -71.8648 kg·m/s

v = -71.8648 kg·m/s / 78.5 kg

v ≈ -0.916 m/s

Therefore, the direction of the owner's velocity is opposite to the combined velocity of the dog and the cat, and the magnitude of the owner's velocity is approximately 0.916 m/s.

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