A 91-kg astronaut and a 1300-kg satellite are at rest relative to the space shuttle. The astronaut pushes on the satellite, giving it a speed of 0.17 m/s directly away from the shuttle. Seven-and-a-half seconds later the astronaut comes into contact with the shuttle.

Required:
What was the initial distance from the shuttle to the astronaut?

Answer:

use voltage=current*resistance

v=i*r

50=i*10

50/10=i

i=5

hope it's clear

Given the following data:

Voltage = 50 Volt

Resistance = 10 Ohm

To determine the current flowing through the circuit, we would apply Ohm's law:

Mathematically, Ohm's law is given by the formula;

[tex]V = IR[/tex]

Where;

V is voltage measured in voltage.

I is current measured in amperes.

R is resistance measured in ohms.

Making I the subject of formula, we have:

[tex]I = \frac{V}{R}[/tex]

Substituting the given parameters into the formula, we have;

[tex]I = \frac{50}{10}[/tex]

Current, I = 5 Ampere.

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. . . is carrying more energy than a wave in the same medium with a lower amplitude.

Answer:

Fermat's principle states that the path taken by a ray between two given points is the path that can be traversed in the least time.

Thus this least distance being the same as least time will only apply to reflection alone because in reflection light travels In the same direction so least distance will also mean least time. But for refraction light travels in different mediums at different speeds so least distance and least time paths will definately not be the same

Answer:

149.05J

Explanation:

Hello,

Data;

Weight = 12N

x = 80miles

Radius of the moon = 1079.4mi

W = mg

But gravity at moon = ⅙ the gravity on earth

12 = ⅙ × m

M = 2kg

Mass of the module = 2kg

K = F.x

F(x) = k / x²

2 = k / (1079.4)²

k = 2.33×10⁶

Work = ∫f.dx

work = ∫₁₀₇₉.₄¹¹⁵⁹ . (2.33×10⁶/x²).dx

Work = (-2.33×10⁶) ×(¹/₁₁₅₉ - ¹/₁₀₇₉)

work = 149.05J

Answer:

Explanation:

For sound level in decibel scale the relation is

dB = 10 log I / I₀ where I₀ = 10⁻¹² and I is intensity of sound whose decibel scale is to be calculated .

Putting the given values

61 = 10 log I / 10⁻¹²

log I / 10⁻¹² = 6.1

I = 10⁻¹² x 10⁶°¹

[tex]=10^{-5.9}[/tex]

intensity of sound of 5 persons

[tex]I=5\times 10^{-5.9}[/tex]

[tex]dB=10log\frac{5 X 10^{-5.9}}{10^{-12}}[/tex]

= 10log 5 x 10⁶°¹

= 10( 6.1 + log 5 )

= 67.98

sound level will be 67.98 dB .

Answer:

1. A

2. B or C

Explanation:

1.

F=ma, meaning that if you use two times more force on a constant mass, the acceleration must double. Acceleration is change in velocity, which means that if you are aiming for the same final velocity the change must happen in half of the time. Therefore, the correct answer is choice A.

2.

By Newton's first law, an object in motion will stay in motion unless an external force acts on it. Since there is nothing pushing the puck in the other direction, the puck will either keep on going for at a constant velocity or will reduce its speed gradually, depending on whether or not this ice is considered to be frictionless. Hope this helps!

(1) You must exert the force for a time interval that is  shorter than the time interval of your first attempt.

(2) The hockey puck reduces speed abruptly.

According to Newton's second law of motion; the force applied to an object is directly proportional to the mass and acceleration of the object.

F = ma

[tex]F = \frac{mv}{t}[/tex]

Thus, to apply a force that is twice as large as the first while maintaining the same velocity, you must exert the force for a time interval that is  shorter than the time interval of your first attempt.

(2) The force applied to an object is direct directly proportional to the velocity of the object. Once you stop applying force to the hockey puck, it moves for a short with initial momentum gained before it will stop.

Thus, the magnitude of the velocity (speed) will drop sharply once the force on the object is removed.

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Answer:

The current in the coil is 4.086 A

Explanation:

Given;

radius of the circular coil, R = 2.5 cm = 0.025 m

number of turns of the circular coil, N = 740 turns

magnetic field at the center of the coil, B = 0.076 T

The magnetic field at the center of the coil is given by;

[tex]B = \frac{N\mu_o I}{2R}[/tex]

where;

μ₀ is permeability of free space = 4 x 10⁻⁷ m/A

I is the current in the coil

R is radius of the coil

N is the number of turns of the coil

The current in the circular coil is given by

[tex]B = \frac{N\mu_o I}{2R} \\\\I = \frac{2BR}{N\mu_o} \\\\I =\frac{2*0.076*0.025}{740*4\pi*10^{-7}} \\\\I = 4.086 \ A[/tex]

Therefore, the current in the coil is 4.086 A

Answer:

The magnitude of the current in the wire is 5.5A, and the direction of the current is in the positive y direction.

Explanation:

- To find the direction of the conventional current in the wire you use the following formula:

[tex]\vec{F}=i\vec{l}\ X\ \vec{B}[/tex]       (1)

i: current in the wire = ?

F: magnitude of the magnetic force on the wire = 15.1N

B: magnitude of the magnetic field = 6.1T

l: length of the wire that is affected by the magnetic field = 0.45m

The direction of the magnetic force is in the x direction (+^i) and the direction of the magnetic field is in the +z direction (+^k).

The direction of the current must be in the +y direction (+^j). In fact, you have:

^j X ^k = ^i

The current and the magnetic field are perpendicular between them, then, you solve for i in the equation (1):

[tex]F=ilBsin90\°\\\\i=\frac{F}{lB}=\frac{15.1N}{(0.45m)(6.1T)}=5.5A[/tex]

The magnitude of the current in the wire is 5.5A, and the direction of the current is in the positive y direction.

Answer:

375 and 450

Explanation:

The computation of the initial and the final temperature is shown below:

In condition 1:

The efficiency of a Carnot cycle is [tex]\frac{1}{6}[/tex]

So, the equation is

[tex]\frac{1}{6} = 1 - \frac{T_2}{T_1}[/tex]

For condition 2:

Now if the temperature is reduced by 75 degrees So, the efficiency is [tex]\frac{1}{3}[/tex]

Therefore the next equation is

[tex]\frac{1}{3} = 1 - \frac{T_2 - 75}{T_1}[/tex]

Now solve both the equations

solve equations (1) and (2)

[tex]2(1 - T_2/T_1) = 1 - (T_2 - 75)/T_1\\\\2 - 1 = 2T_2/T_1 - (T_2 - 75)/T_1\\\\ = (T_2 + 75)/T_1T_1 = T_2 + 75\\\Now\ we\ will\ Put\ the\ values\ into\ equation (1)\\\\1/6 = 1 - T_2/(T_2 + 75)\\\\1/6 = (75)/(T_2 + 75)[/tex]

T_2 + 450 = 75

T_2 = 375

Now put the T_2 value in any of the above equation

i.e

T_1 = T_2 + 75

T_1 = 375 + 75

= 450

Answer:

The charge stored in the capacitor will stay the same. However, the electric potential across the two plates will increase. (Assuming that the permittivity of the space between the two plates stays the same.)

Explanation:

The two plates of this capacitor are no longer connected to each other. As a result, there's no way for the charge on one plate to move to the other. [tex]Q[/tex], the amount of charge stored in this capacitor, will stay the same.

The formula [tex]\displaystyle Q = C\, V[/tex] relates the electric potential across a capacitor to:

While [tex]Q[/tex] stays the same, moving the two plates apart could affect the potential [tex]V[/tex] by changing the capacitance [tex]C[/tex] of this capacitor. The formula for the capacitance of a parallel-plate capacitor is:

[tex]\displaystyle C = \frac{\epsilon\, A}{d}[/tex],

where

Assume that the two plates are separated with vacuum. Moving the two plates apart will not affect the value of [tex]\epsilon[/tex]. Neither will that change the area of the two plates.

However, as [tex]d[/tex] (the distance between the two plates) increases, the value of [tex]\displaystyle C = \frac{\epsilon\, A}{d}[/tex] will become smaller. In other words, moving the two plates of a parallel-plate capacitor apart would reduce its capacitance.

On the other hand, the formula [tex]\displaystyle Q = C\, V[/tex] can be rewritten as:

[tex]V = \displaystyle \frac{Q}{C}[/tex].

The value of [tex]Q[/tex] (charge stored in this capacitor) stays the same. As the value of [tex]C[/tex] becomes smaller, the value of the fraction will become larger. Hence, the electric potential across this capacitor will become larger as the two plates are moved away from one another.  

Answer:

Final pressure 0.105atm

Explanation:

Let V1 represent the initial volume of dry air at NTP.

under adiabatic condition: no heat is lost or  gained by the system. This does not implies that the constant temperature throughout the system , but rather that no heat gained or loss by the system.

Adiabatic expansion:

[tex]\frac{T_1}{T_2} =(\frac{V_1}{V_2} )^{\gamma -1}[/tex]

273/T2=(5V1/V1)^(1.4−1)

273/T2=5^0.4

Final temperature  T2=143.41 K

Also

P1/P2=(V2/V1)^γ

1/P2=(5V1/V1)^1.4

Final pressure P2=0.105atm

Answer:

the angular momentum is 1015.52 kg m²/s

Explanation:

given data

mass of each flywheel, m = 65 kg

radius of flywheel, r = 1.47 m

ω1 = 8.94 rad/s

ω2 = - 3.42 rad/s

to find out

magnitude of the net angular momentum

solution

we get here Moment of inertia that is express as

I = 0.5 m r²    .................1

put here value and we get

I = 0.5 × 65 × 1.47 × 1.47

I = 70.23 kg m²

and

now we get here Angular momentum that is express as

L = I × ω    ...........................2

and Net angular momentum will be

L = 2 × I x ω1 - I × ω2

put here value and we get

L = 2 × 70.23 × 8.94 - 70.23 × 3.42

L = 1015.52 kg m²/s

so

the angular momentum is 1015.52 kg m²/s

The magnitude of the net angular momentum of the system will be "1015.52 kg.m²/s".

According to the question,

Flywheel's mass, m = 65 kg

Flywheel's radius, r = 1.47 m

ω₁ = 8.94 rad/s

ω₂ = 3.42 rad/s

We know,

The moment of inertia (I),

= 0.5 m r²

By substituting the values,

= 0.5 × 65 × 1.47 × 1.47

= 70.23 kg.m²

hence, The angular momentum be:

→ L = I × ω or,

     = 2 × I × ω₁ - l × ω₂

     = 2 × 70.23 × 8.94 - 70.23 × 3.42

     = 1015.52 kg.m²/s

Thus the above answer is correct.

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The position of a particle is r(t)= (4.0t²i+ 2.4j- 5.6tk) m. (Express your answers in vector form.)

(a) Determine its velocity (in m/s) and acceleration (in m/s²) as functions of time. (Use the following as necessary: t. Assume t is seconds, r is in meters, and v is in m/s, Do not include units in your answer.)

v(t)= ________m/s

a(t)= ________m/s²

(b) What are its velocity (in m/s) and acceleration (in m/s²) at time t 0?

v(0) =_______ m/s

a(0)=_______ m/s²

(a)

v(t)= [tex]8ti - 5.6k[/tex] m/s

a(t)= 8i m/s²

(b)

v(0) = -5.6k m/s

a(0)= 8i m/s²

From the question, the position of the particle is given by;

r(t)= (4.0t²i+ 2.4j- 5.6tk)        -----------------(i)

(a)

(i)To get the velocity, v(t), of the particle, we'll take the first derivative of the position of the particle (given by equation (i)) with respect to time, t, as follows;

v(t) = [tex]\frac{dr(t)}{dt}[/tex] = [tex]\frac{d(4.0t^2i + 2.4j - 5.6tk)}{dt}[/tex]

v(t) = [tex]\frac{dr(t)}{dt}[/tex] = [tex]8ti +0j - 5.6k[/tex]

v(t) = [tex]8ti - 5.6k[/tex]          --------------------(ii)

(ii) To get the acceleration, a(t), of the particle, we'll take the first derivative of the velocity of the particle (given by equation (ii)) with respect to time, t, as follows;

a(t) = [tex]\frac{dv(t)}{dt}[/tex]  = [tex]\frac{d(8ti - 5.6k)}{dt}[/tex]

a(t) = 8i                    --------------------(iii)

(b)

(i) To get the velocity of the particle at time t = 0, substitute the value of t = 0 into equation (ii) as follows;

v(t) = [tex]8ti - 5.6k[/tex]  

v(0) = 8(0)i - 5.6k

v(0) = 0 - 5.6k

v(0) = -5.6k

(ii) To get the acceleration of the particle at time t = 0, substitute the value of t = 0 into equation (iii) as follows;

a(t) = 8i

a(0) = 8i

Answer:

Charge density on the sphere = 2.2 × 10⁻⁸ C/m²

Explanation:

Given:

Radius of sphere (r) = 12 cm = 0.12 m

Distance from the electric field R = 24 cm = 0.24 m

Magnitude (E) = 640 N/C

Find:

Charge density on the sphere

Computation:

Charge on the sphere (q) = (1/K)ER²            (K = 9 × 10⁹)

Charge on the sphere (q) = [1/(9 × 10⁹)](640)(0.24)²

Charge on the sphere (q) = 4 × 10⁻⁹ C

Charge density on the sphere = q / [4πr²]

Charge density on the sphere = [4 × 10⁻⁹] / [4(3.14)(0.12)²]

Charge density on the sphere = [4 × 10⁻⁹] / [0.18]

Charge density on the sphere = 2.2 × 10⁻⁸ C/m²

Answer:

100% efficiency

Explanation:

the machine has _100%_ efficiency.

(fill in the blank)

Answer:

100%

Explanation: A p e x

Complete question:

Two cars start moving from the same point. One travels south at 28 mi/h and the other travels west at 21 mi/h. At what rate is the distance between the cars increasing four hours later.

Answer:

The rate at which the distance between the cars is increasing four hours later is 35 mi/h.

Explanation:

Given;

speed of one car, dx/dt = 28 mi/h South

speed of the second car, dy/dt = 21 mi/h West

The distance between the cars is the line joining west to south, which forms a right angled triangle with the two positions.

Apply Pythagoras theorem to evaluate this distance;

let the distance between the cars = z

x² + y² = z² -------- equation (1)

Differentiate with respect to time (t)

[tex]2x\frac{dx}{dt} + 2y\frac{dy}{dt} = 2z\frac{dz}{dt}[/tex] ----- equation (2)

Since the speed of the cars is constant, after 4 hours their different distance will be;

x: 28(4) = 112 mi

y: 21(4) = 84 mi

[tex]z = \sqrt{x^2 + y^2} \\\\z = \sqrt{112^2 + 84^2} \\\\z = 140 \ mi[/tex]

Substitute in the value of x, y, z, dx/dt, dy /dt into equation (2) and solve for dz/dt

[tex]2x\frac{dx}{dt} + 2y\frac{dy}{dt} = 2z\frac{dz}{dt} \\\\2(112)(28) + 2(84)(21) = 2(140)\frac{dz}{dt} \\\\9800 = 280\frac{dz}{dt} \\\\\frac{dz}{dt} = \frac{9800}{280} \\\\\frac{dz}{dt} = 35 \ mi/h[/tex]

Therefore, the rate at which the distance between the cars is increasing four hours later is 35 mi/h

Answer:

a) q = 4.47 10⁻⁵ C

b)     ΔV = 4.47 10⁴ V

Explanation:

A Leyden bottle works as a condenser that accumulates electrical charge, so we can use the formula of the energy stored in a capacitor

           U = Q² / 2C

         Q = √ (2UC)

let's reduce the magnitudes to the SI system

   c = 1 nF = 1 10⁻⁹ F

let's calculate

         q = √ (2 1 10⁻⁹-9)

         q = 0.447 10⁻⁴ C

         q = 4.47 10⁻⁵ C

b) for the potential difference we use

             C = Q / ΔV

            ΔV = Q / C

            ΔV = 4.47 10⁻⁵ / 1 10⁻⁹

            ΔV = 4.47 10⁴ V

Answer:

r = 0.405m = 40.5cm

Explanation:

In order to calculate the length of the string between Wanda and the ball, you take into account that the tension force is equal to the centripetal force over the ball. So, you can use the following formula:

[tex]F_c=ma_c=m\frac{v^2}{r}[/tex]       (1)

Fc: centripetal acceleration (tension force on the string) = 12N

m: mass of the ball = 60g = 0.06kg

r: length of the string = ?

v: linear speed of the ball = 9.0m/s

You solve for r in the equation (1) and replace the values of the other parameters:

[tex]r=\frac{mv^2}{F_c}=\frac{(0.06kg)(9.0m/s)^2}{12N}=0.405m[/tex]

The length of the string between Wanda and the ball is 0.405m = 40.5cm

Answer:

Surface tension is the tendency of liquid surfaces to shrink into the minimum surface area possible. Surface tension allows insects (e.g. water striders), usually denser than water, to float and slide on a water surface.

Explanation:

Answer:

It is the tension of the surface film of a liquid caused by the attraction of the particles in the surface layer by the bulk of the liquid, which tends to minimize surface area.

Answer:

  315,000 ft·lb

Explanation:

At 300 ft and 5 lb/ft, the weight of the cable is (300 f)(5 lb/ft) = 1500 lb. The work done to raise it is equivalent to the work done to raise the cable's center of mass. Since the cable is of uniform density, its center of mass is half the cable length below the winch.

  total work done = work to raise cable + work to raise load

  = (1500 lb)(150 ft) +(300 lb)(300 ft) = 315,000 ft·lb

Explanation:

Ohms law states that the electrical current present in a metallic conductor is directly proportional to the potential difference between the metallic conductor and inversely proportional to the resistance therefore if the voltage is increased resistance also increases provided that temperature and other physical properties remains constant V=IR

Answer:

The tension in the cable is 18371.9 newtons.

Explanation:

Physically speaking, the tension can be calculated with the help of the Second Newton's Law. The upward acceleration means that magnitude of tension must be greater than weight of elevator, whose equation of equilibrium is described below:

[tex]\Sigma F = T - m\cdot g = m \cdot a[/tex]

Where:

[tex]T[/tex] - Tension in the cable, measured in newtons.

[tex]m[/tex] - Mass of the elevator, measured in kilograms.

[tex]g[/tex] - Gravity constant, measured in meters per square second.

[tex]a[/tex] - Net acceleration of the elevator, measured in meters in square second.

Now, tension is cleared and resultant expression is also simplified:

[tex]T = m \cdot (a + g)[/tex]

If [tex]m = 1700\,kg[/tex], [tex]a = 1\,\frac{m}{s^{2}}[/tex] and [tex]g = 9.807\,\frac{m}{s^{2}}[/tex], the tension in the cable is:

[tex]T = (1700\,kg)\cdot \left(1\,\frac{m}{s^{2}}+9.807\,\frac{m}{s^{2}} \right)[/tex]

[tex]T = 18371.9\,N[/tex]

The tension in the cable is 18371.9 newtons.

Answer:

a) The final angular velocity of the system is 4 radians per second, b) The amount of mechanical energy lost due to friction is 5.25 joules.

Explanation:

a) The problem is a clear representation of the Principle of the Angular Momentum Conservation, where moment of inertia of the system is increased by the adding of the uniform rod and there are no external forces exerted on the system. This system is represented by the following model:

[tex]I_{d} \cdot \omega_{o} = (I_{d} + I_{r})\cdot \omega_{f}[/tex]

Where:

[tex]\omega_{o}[/tex], [tex]\omega_{f}[/tex] - Initial and final angular velocities, measured in radians per second.

[tex]I_{d}[/tex], [tex]I_{r}[/tex] - Moments of inertia of the uniform solid disk and uniform rod, measured in [tex]kg\cdot m^{2}[/tex].

Now, the final angular speed is cleared:

[tex]\omega_{f} = \frac{I_{d}}{I_{d}+I_{r}}\cdot \omega_{o}[/tex]

The moments of inertia of the uniform solid disk and uniform rod are modelled by these formulas:

Solid Disk

[tex]I_{d} = \frac{1}{2}\cdot m_{d}\cdot r_{d}^{2}[/tex]

Where:

[tex]m_{d}[/tex] - Mass of the disk, measured in kilograms.

[tex]r_{d}[/tex] - Radius of the disk, measured in meters.

Given that [tex]m_{d} = 1\,kg[/tex] and [tex]r_{d} = 1\,m[/tex], the moment of inertia of the disk is:

[tex]I_{d} = \frac{1}{2}\cdot (1\,kg)\cdot (1\,m)^{2}[/tex]

[tex]I_{d} = 0.5\,kg\cdot m^{2}[/tex]

Rod (rotating about its center)

[tex]I_{r} = \frac{1}{12}\cdot m_{r}\cdot l_{r}^{2}[/tex]

Where:

[tex]m_{r}[/tex] - Mass of the rod, measured in kilograms.

[tex]l_{r}[/tex] - Length of the rod, measured in meters.

Given that [tex]m_{r} = 0.5\,kg[/tex] and [tex]l_{r} = 3\,m[/tex], the moment of inertia of the rod is:

[tex]I_{r} = \frac{1}{12}\cdot (0.5\,kg)\cdot (3\,m)^{2}[/tex]

[tex]I_{r} = 0.375\,kg\cdot m^{2}[/tex]

Now, knowing that [tex]\omega_{o} = 7\,\frac{rad}{s}[/tex], the final angular velocity is:

[tex]\omega_{f} = \left(\frac{0.5\,kg\cdot m^{2}}{0.5\,kg\cdot m^{2}+0.375\,kg\cdot m^{2}}\right)\cdot \left(7\,\frac{rad}{s} \right)[/tex]

[tex]\omega_{f} = 4\,\frac{rad}{s}[/tex]

The final angular velocity of the system is 4 radians per second.

b) According to the Principle of Energy Conservation, the inclusion of the uniform rod on the turntable is represented by the following expression:

[tex]K_{1} = K_{2} + \Delta E_{loss}[/tex]

Where:

[tex]K_{1}[/tex] - Rotational kinetic energy of the uniform disk, measured in joules.

[tex]K_{2}[/tex] - Rotational kinetic energy of the system (uniform disk + uniform rod), measured in joules.

[tex]\Delta E_{loss}[/tex] - Mechanical energy lost due to friction, measured in joules.

The mechanical energy lost due to friction is cleared:

[tex]\Delta E_{loss} = K_{1} - K_{2}[/tex]

Now, the expression is expanded and mechanical energy losses is calculated:

[tex]\Delta E_{loss} = \frac{1}{2}\cdot I_{d}\cdot \omega_{o}^{2} - \frac{1}{2}\cdot (I_{d}+I_{r})\cdot \omega_{f}^{2}[/tex]

[tex]\Delta E_{loss} = \frac{1}{2}\cdot (0.5\,kg\cdot m^{2})\cdot \left(7\,\frac{rad}{s} \right)^{2} - \frac{1}{2}\cdot (0.5\,kg\cdot m^{2} + 0.375\,kg\cdot m^{2})\cdot \left(4\,\frac{rad}{s} \right)^{2}[/tex]

[tex]\Delta E_{loss} = 5.25\,J[/tex]

The amount of mechanical energy lost due to friction is 5.25 joules.

Answer:

t = 1.098*RC

Explanation:

In order to calculate the time that the capacitor takes to reach 2/3 of its maximum charge, you use the following formula for the charge of the capacitor:

[tex]Q=Q_{max}[1-e^{-\frac{t}{RC}}][/tex]         (1)

Qmax: maximum charge capacity of the capacitor

t: time

R: resistor of the circuit

C: capacitance of the circuit

When the capacitor has 2/3 of its maximum charge, you have that

Q=(2/3)Qmax    

You replace the previous expression for Q in the equation (1), and use properties of logarithms to solve for t:

[tex]Q=\frac{2}{3}Q_{max}=Q_{max}[1-e^{-\frac{t}{RC}}]\\\\\frac{2}{3}=1-e^{-\frac{t}{RC}}\\\\e^{-\frac{t}{RC}}=\frac{1}{3}\\\\-\frac{t}{RC}=ln(\frac{1}{3})\\\\t=-RCln(\frac{1}{3})=1.098RC[/tex]

The charge in the capacitor reaches 2/3 of its maximum charge in a time equal to 1.098RC

Answer:

E= 71dB

Explanation:

See attached file for step by step calculation

Explanation:

As per Rayleigh criterion, the angular resolution is given as follows:

[tex]\theta=\frac{1.22 \lambda}{D}[/tex]

From this expression larger the size of aperture, smaller will be the value of angular resolution and hence, better will be the device i.e. precision for distinguishing two points at very high angular difference is higher.

Answer:

Due to flipping of polarity

Explanation:

During the changing of polarity, the current on the one side is maximum as the polarity change then the current is gradually reducing toget from another end.

Answer:

the kinetic energy lost in the collison is a) 30 J

Explanation:

given data

mass of door m1 = 35 kg

width a = 90 cm = 0.9 m

the mass of ball  m2 = 500 g = 0.5 kg

initial speed of ball  u = 20 m/s

final speed of ball  v = 16 m/s

r = 60 cm = 0.6 m

soluion

we will consider here final angular speed of the door = w

so now we use conservation of angular momentum  that is

Li = Lf    ........................1

that is express as

m2 × u × r = I × w + m2 × v × r

put here value and we get  

0.5 × 20 × 0.6 = [tex](m1 \times \frac{a^2}{12})[/tex] × w + 0.5 × 16 × 0.6

solve it we get

w = 0.508 rad/s

so that here

the kinetic energy lost in the collison,

KE = KE initial - KE final     ..................2

put here value

KE = 0.5 × m2 × u² - (0.5 × I × w² + 0.5 × m2 × v²)

KE = 0.5 × (0.5 × 20² - (35 × 0.9² ÷ 12) × 0.508² - 0.5 × 16²) J

KE = 30 J

the kinetic energy lost in the collison is a) 30 J

Answer:

(a) The value of the ratio m₁/m₂ is 0.581

(b)  the acceleration of the combined masses is 1.139 m/s²

Explanation:

Given;

The acceleration of force applied to M₁, a₁ = 3.10 m/s²

The same force applied to M₂ has acceleration, a₂ = 1.80 m/s²

Let this force = F

According Newton's second law of motion;

F = ma

(a) the value of the ratio m₁/m₂

since the applied force is same in both cases,  M₁a₁ = M₂a₂

[tex]\frac{m_1}{m_2} = \frac{a_2}{a_1} \\\\\frac{m_1}{m_2} = \frac{1.8}{3.1} \\\\\frac{m_1}{m_2} = 0.581[/tex]

(b) the acceleration of m₁ and m₂ combined as one object under the action force F

F = ma

[tex]a = \frac{F}{M} \\\\a = \frac{F}{m_1 + m_2} \\\\a = \frac{F}{0.581m_2 + m_2}\\\\a = \frac{F}{1.581m_2}[/tex]

[tex]But, m_2 = \frac{F}{a_2} \\\\a = \frac{F}{1.581m_2} = \frac{F*a_2}{1.581F} \\\\a = \frac{a_2}{1.581} \\\\a = \frac{1.8}{1.581} = 1.139 \ m/s^2[/tex]

Therefore, the acceleration of the combined masses is 1.139 m/s²

a. The value of the ratio is 0.581.

b. The acceleration should be [tex]1.139 m/s^2[/tex]

Since

The acceleration of force applied to [tex]M_1,a_1 = 3.10 m/s^2[/tex]

The same force applied to[tex]M_2[/tex] has acceleration, [tex]a_2 = 1.80 m/s^2[/tex]

Here we assume force be F

Now we know that

F = ma

a. The ratio should be

[tex]m_1\div m_2 = a_2\div a_1\\\\m_1\div m_2 = 1.8\div 3.1[/tex]

= 0.581

b.  The acceleration should be

f = ma

a = F/m

[tex]a = f/m_1+m_2\\\\= F/0.581 + m_2\\\\=F/1.581m_2[/tex]

However [tex]m_2 = F/a_2[/tex]

So,

[tex]a = F\div 1.581m_2\\\\= f\times a_2/1.581F\\\\= a_2/1.581\\\\= 1.8/1.581\\\\= 1.139 m/s^2[/tex]

Learn more about acceleration here: https://brainly.com/question/24815335

Answer:

Wmax = 63.65 ≈ 64 lb

Explanation: