From largest to smallest, rank the gravitational force that each planet exerts on the star with mass M. Distances are as follows:_________.a) Planet A is 3d from M b) Planet B is 1d from M c) Planet C is 1d from M d) Planet D is 2d from M e) Planet E is 3d from M

Answer:

Explanation:

This exercise we will work using energy conservation, let's use two points

 lower. Ramp starting point

        Em₀ = K = ½ m v² + ½ I w²

more height. Point where e stops

        [tex]Em_{f}[/tex] = m g h

at the starting point the sphere is spinning let's look for the relationship between the angular and linear variables

        v = w r

the moment of inertia of a sphere is tabulated

         I = 2/5 M R2

let's use that energy is conserved

        Em₀ = Em_{f}

        ½ m v² + ½ (2/5 m r²) (v / r)² = m g h

        ½ v² + 1/5 v2 = g h

        h= 7/10 v² / g

In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the expression, x = 8.00 cos (5t + π / 8) where x is in centimeters and t is in seconds. (a) At t = 0, find the position of the piston. cm (b) At t = 0, find velocity of the piston. cm/s (c) At t = 0, find acceleration of the piston. cm/s2 (d) Find the period and amplitude of the motion. period s amplitude cm

(a) 7.392cm

(b) -15.32 cm/s

(c) -184cm/s²

(d) 0.4πs and 8.00cm

The general equation of a simple harmonic motion (SHM) is given by;

x(t) = A cos (wt + Φ)        --------------(i)

Where;

x(t) = position of the body at a given time t

A =  amplitude or maximum displacement during oscillation

w = angular velocity

t = time

Φ = phase constant.

Given from question:

x(t) = 8.00 cos (5t + π / 8)         ---------------(ii)

(a) At time t = 0;

The position, x(t), of the body (piston) is given by substituting the value of t = 0 into equation (ii) as follows;

x(0) = 8.00 cos (5(0) + π / 8)

x(0) = 8.00 cos (π /8)

x(0) = 8.00 x 0.924

x(0) = 7.392 cm

Therefore, the position of the piston at time t = 0 is 7.392cm

(b) To get the velocity, v(t), of the piston at t = 0, first differentiate equation (ii) with respect to t as follows;

v(t) = [tex]\frac{dx(t)}{dt}[/tex]

v(t) = [tex]\frac{d(8.00cos(5t + \pi / 8 ))}{dt}[/tex]

v(t) = 8 (-5 sin (5t + π / 8))

v(t) = -40sin(5t + π / 8)     --------------------(iii)

Now, substitute t=0 into the equation as follows;

v(0) = -40 sin(5(0) + π / 8)

v(0) = -40 sin(π / 8)

v(0) = -40 x 0.383

v(0) = -15.32 cm/s

Therefore, the velocity of the piston at time t = 0 is -15.32 cm/s

(c) To find the acceleration a(t) of the piston at t = 0, first differentiate equation (iii), which is the velocity equation, with respect to t as follows;

a(t) = [tex]\frac{dv(t)}{dt}[/tex]

a(t) = [tex]\frac{d(-40sin (5t + \pi /8))}{dt}[/tex]

a(t) = -200 cos (5t + π / 8)

Now, substitute t = 0 into the equation as follows;

a(0) = -200 cos (5(0) + π / 8)

a(0) = -200 cos (π / 8)

a(0) = -200 x 0.924

a(0) = -184.8 cm/s²

Therefore, the acceleration of the piston at time t = 0 is -184cm/s²

(d) To find the period, T, first, let's compare equations (i) and (ii) as follows;

x(t) = A cos (wt + Φ)                   --------------(i)

x(t) = 8.00 cos (5t + π / 8)         ---------------(ii)

From these equations it can be deduced that;

Amplitude, A = 8.00cm

Angular velocity, w = 5 rads/s

But;

w = [tex]\frac{2\pi }{T}[/tex]           [Where T = period of oscillation]

=> T = [tex]\frac{2\pi }{w}[/tex]

=> T = [tex]\frac{2\pi }{5}[/tex]

=> T = 0.4π s

Therefore, the period and amplitude of the piston's motion are respectively 0.4πs and 8.00cm

Answer:

C) It is either ferromagnetic or paramagnetic

Explanation:

The complete question is given below

We observe that a small sample of material placed in a non-uniform magnetic field accelerates toward a region of stronger field. What can we say about the material?

A) It must be ferromagnetic.

B) It must be paramagnetic.

C) It is either ferromagnetic or paramagnetic.

D) It must be diamagnetic.

A ferromagnetic material will respond towards a magnetic field. They are those materials that are attracted to a magnet. Ferromagnetism is associated with our everyday magnets and is the strongest form of magnetism in nature. Iron and its alloys is very good example of a material that readily demonstrate ferromagnetism.

Paramagnetic materials are weakly attracted to an externally applied magnetic field. They usually accelerate towards an electric field, and form internal induced magnetic field in the direction of the external magnetic field.

The difference is that ferromagnetic materials can retain their magnetization when the externally applied magnetic field is removed, unlike paramagnetic materials that do not retain their magnetization.

In contrast, a diamagnetic material is repelled away from an externally applied magnetic field.

Answer:

R = 1138.9 Ω

Explanation:

Hello,

In this case, for the given power (P) and current (I), we can compute the resistance (R) via:

R = P / I²

Thus, we obtain:

R = 1.64x10⁵ W / (12.0 A)²

R = 1138.9 Ω

Best regards.

Answer:

10.4 m/s

Explanation:

Given that

mass of the first snowball, m1 = 0.3 kg

mass of the second snowball, m2 = 0.7 kg

Magnitude of initial velocity for both masses, u = 10.4 m/s

To start with, we use the formula of conservation of linear momentum which states that

magnitude of initial momentum is equal to magnitude of final momentum.

m1u1 + m2u2 = V(m1 + m2)

0.3 * 10.4 + 0.7 * 10.4 = V(0.3 + 0.7)

3.12 + 7.28 = V(1)

10.4 = V

The 1 kg mass is an addition Of the 0.3 mass & 0.7 kg mass.

Thus, the speed of the 1 kg mass is 10.4 m/s

Answer:

Such limitations are given below.

Explanation:

Answer:

depending on how high it goes at 100m it has taken 2 secondes

Explanation:

At the highest point, the arrow is changing from moving up to moving down. At that exact point, its speed AND its velocity are both ZERO.

And air resistance actually makes no difference.

Answer:

ML²/6

Explanation:

Pls see attached file

The total mass is M = CL²/2, and the moment of inertia is I = ML²/2,

The length of the rod is L. It has a non-uniform distribution of mass given by:

dm/dx = Cx

where C has units kg/m²

dm = Cxdx

the total mass M of the rod can be calculated by integrating the above relation over the length:

[tex]M =\int\limits^L_0 {} \, dm\\\\M=\int\limits^L_0 {Cx} \, dx\\\\M=C[x^2/2]^L_0\\\\M=C[L^2/2]\\\\[/tex]

Thus,

C = 2M/L²

Now, the moment of inertia of the small element dx of the rod is given by:

dI = dm.x²

dI = Cx.x²dx

[tex]dI = \frac{2M}{L^2}x^3dx\\\\I= \frac{2M}{L^2}\int\limits^L_0 {x^3} \, dx \\\\I= \frac{2M}{L^2}[\frac{L^4}{4}][/tex]

I = ML²/2

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Answer:

3.6×10⁻⁶  Nm

Explanation:

From the question,

The expression for maximum torque is given as

τ = BANI.................Equation 1

where τ = maximum torque, B = magnetic field, A = Area of the coil, N = number of turns, I = current carried by the coil.

Given: B = 0.1 T, A = (5×12) = 60 cm² = 0.006 m², N = 600 turns, I = 10⁻⁵ A.

Substitute these values into equation 1

τ = 0.1(0.006)(600)(10⁻⁵)

τ = 3.6×10⁻⁶  Nm

Answer:

The period is [tex]T = 0.700 \ s[/tex]

Explanation:

From the question we are told that  

    The mass is [tex]m = 0.350 \ kg[/tex]

     The extension of the spring is  [tex]x = 12.0 \ cm = 0.12 \ m[/tex]

The spring constant for this is mathematically represented as

       [tex]k = \frac{F}{x}[/tex]

Where F is the force on the spring which is mathematically evaluated as

       [tex]F = mg = 0.350 * 9.8[/tex]

       [tex]F =3.43 \ N[/tex]

So  

    [tex]k = \frac{3.43 }{ 0.12}[/tex]

    [tex]k = 28.583 \ N/m[/tex]

The period of oscillation is mathematically evaluated as

      [tex]T = 2 \pi \sqrt{\frac{m}{k} }[/tex]

substituting values

     [tex]T = 2 * 3.142* \sqrt{\frac{0.35 }{28.583} }[/tex]

     [tex]T = 0.700 \ s[/tex]

Complete Question

A 10 gauge copper wire carries a current of 20 A. Assuming one free electron per copper atom, calculate the drift velocity of the electrons. (The cross-sectional area of a 10-gauge wire is 5.261 mm2.) mm/s

Answer:

The drift velocity is [tex]v = 0.0002808 \ m/s[/tex]

Explanation:

From the question we are told that

    The current on the copper is  [tex]I = 20 \ A[/tex]

     The cross-sectional area is  [tex]A = 5.261 \ mm^2 = 5.261 *10^{-6} \ m^2[/tex]

The number of copper atom in the wire is  mathematically evaluated

      [tex]n = \frac{\rho * N_a}Z}[/tex]

Where [tex]\rho[/tex] is the density of copper with a value [tex]\rho = 8.93 \ g/m^3[/tex]

          [tex]N_a[/tex] is the Avogadro's number with a value [tex]N_a = 6.02 *10^{23}\ atom/mol[/tex]

         Z  is the molar mass of copper with a value  [tex]Z = 63.55 \ g/mol[/tex]

So

     [tex]n = \frac{8.93 * 6.02 *10^{23}}{63.55}[/tex]

     [tex]n = 8.46 * 10^{28} \ atoms /m^3[/tex]

Given the 1 atom is equivalent to 1 free electron then the number of free electron is  

         [tex]N = 8.46 * 10^{28} \ electrons[/tex]

The current through the wire is mathematically represented as

         [tex]I = N * e * v * A[/tex]

substituting values

        [tex]20 = 8.46 *10^{28} * (1.60*10^{-19}) * v * 5.261 *10^{-6}[/tex]

=>     [tex]v = 0.0002808 \ m/s[/tex]

Answer:

The hydrostatic force on one end of the trough is 54994.464 N

Explanation:

Given;

liquid density, ρ = 810 kg/m³

side of the equilateral triangle, L = 8m

acceleration due to gravity, g =  9.8 m/s²

Hydrostatic force is given as;

H = ρgh

where;

h is the vertical height of the equilateral triangle

Draw a line to bisect upper end of the trough, to the vertex at the bottom, this line is the height of the equilateral triangle.

let the half side of the triangle = x

x = ⁸/₂ = 4m

The half section of the triangle forms a right angled triangle

h² = 8² - 4²

h² = 48

h = √48

h = 6.928m

F = ρgh

F = 810 x 9.8 x 6.928

F = 54994.464 N

Therefore, the hydrostatic force on one end of the trough is 54994.464 N

Answer:

20J

Explanation:

In a collision, whether elastic or inelastic, momentum is always conserved. Therefore, using the principle of conservation of momentum we can first get the final velocity of the two bodies after collision. This is given by;

m₁u₁ + m₂u₂ = (m₁ + m₂)v          ---------------(i)

Where;

m₁ and m₂ are the masses of first and second objects respectively

u₁ and u₂ are the initial velocities of the first and second objects respectively

v  is the final velocity of the two objects after collision;

From the question;

m₁ = 2.0kg

m₂ = 8.0kg

u₁ = 5.0m/s

u₂ = 0        (since the object is initially at rest)

Substitute these values into equation (i) as follows;

(2.0 x 5.0) + (8.0 x 0) = (2.0 + 8.0)v

(10.0) + (0) = (10.0)v

10.0 = 10.0v

v = 1m/s

The two bodies stick together and move off with a velocity of 1m/s after collision.

The kinetic energy(KE₁) of the objects before collision is given by

KE₁ = [tex]\frac{1}{2}[/tex]m₁u₁² +  [tex]\frac{1}{2}[/tex]m₂u₂²       ---------------(ii)

Substitute the appropriate values into equation (ii)

KE₁ = ([tex]\frac{1}{2}[/tex] x 2.0 x 5.0²) +  ([tex]\frac{1}{2}[/tex] x 8.0 x 0²)

KE₁ = 25.0J

Also, the kinetic energy(KE₂) of the objects after collision is given by

KE₂ = [tex]\frac{1}{2}[/tex](m₁ + m₂)v²      ---------------(iii)

Substitute the appropriate values into equation (iii)

KE₂ = [tex]\frac{1}{2}[/tex] ( 2.0 + 8.0) x 1²

KE₂ = 5J

The kinetic energy lost (K) by the system is therefore the difference between the kinetic energy before collision and kinetic energy after collision

K = KE₂ - KE₁

K = 5 - 25

K = -20J

The negative sign shows that energy was lost. The kinetic energy lost by the system is 20J

Answer:

Ratio of distance to displacement is pi/2

Explanation:

Pls see attached file for diagram and explanation

Answer:

b) During the turn, the door exerts a leftward force on you.

Explanation:

Although at the curve the car makes a turn without deceleration or accelerating, we must consider the fact that the direction of the instantaneous velocity of the car, which is always pointing tangentially away from the curve, is changing, producing a centripetal acceleration (acceleration is the rate of change of velocity) towards the center of the curve. The result is that a force inwards towards the center of the curve from the door, is exerted on you in the leftwards direction when your body collides with the door.

Complete Question

The complete question is shown on the first and second uploaded image

Answer:

The power created  is  [tex]P_{avg} = F * v_{avg}[/tex]

Explanation:

From the question we are told that

    The that the average power is  mathematically represented as

            [tex]P_{avg} = \frac{W }{\Delta t }[/tex]

Where W is  is the Workdone which is  mathematically represented as

         [tex]W = F * s[/tex]

      Where F is  the applies force and  s  is the displacement  due to the force  

        So  

                [tex]P_{avg} = \frac{F *s }{\Delta t }[/tex]

Now this  displacement can be represented mathematically as  

            [tex]s = v_{avg} * \Delta t[/tex]

Where [tex]v_{avg }[/tex] is the average  velocity and [tex]\Delta t[/tex] is the time  taken  

So  

            [tex]P_{avg} = \frac{F *v_{avg} * \Delta t }{\Delta t }[/tex]

=>         [tex]P_{avg} = F * v_{avg}[/tex]

Answer:

Pavg =  Fvavg

Explanation:

Since the P (power) done by the F (force) is:

P = Fs/t

and we are looking for the velocity, so then it would be:

P = Fv

with the average velocity the answer is:

Pavg =  Favg

If an object is moving at a constant speed, and the force F is also constant, this formula can be used to find the average power. If v  is changing, the formula can be used to find the instantaneous power at any given moment (with the quantity v in this case meaning the instantaneous velocity, of course).

Answer:

The total work done by the person is given as = m g h

= 4.5kg x 9.8m/s²x1.2m

= 52.92J

This is the work done in moving the block in a vertical distance

However there is no work done when the block is moved in a horizontal direction since ko work is done against gravity.

Explanation:

Answer:

Increasing the number of slits not only makes the diffraction maximum sharper, but also much more intense. If a 1 mm diameter laser beam strikes a 600 line/mm grating, then it covers 600 slits and the resulting line intensity is 90,000 x that of a double slit. Such a multiple-slit is called a diffraction grating.

Answer:

The area  of the water stream will be 1.74 cm^2

Explanation:

initial velocity of water u = 33.2 cm/s

initial area = 6.4 cm^2

height of fall = 7.05 cm

final area before hitting the sink = ?

as the water falls down the height, it accelerates under gravity; causing the speed to increase, and the area to decrease.

first we find the velocity before hitting the sink

using

[tex]v^{2} = u^{2} + 2gh[/tex]  -----Newton's equation of motion

where  v is the velocity of the water stream at the sink

u is the initial speed of the water at the spout

h is the height of fall

g is acceleration due to gravity, and it is positive downwards.

g = 981 cm/s^2

imputing relevant values, we have

[tex]v^{2} = 33.2^{2} + (2 * 981 * 7.05)[/tex]

[tex]v^{2} = 1102.24 + 13832.1 = 14934.34[/tex]

[tex]v = \sqrt{14934.34}[/tex] = 122.206 cm/s

according to continuity equation,

A1v1 = A2v2

where A1 is the initial area

V1 = initial velocity

A2 = final area

V2 = final velocity

6.4 x 33.2 = 122.206 x A2

212.48 = 122.206 x A2

A2 = 212.48 ÷ 122.206 ≅ 1.74 cm^2

Kinetic energy is the energy an object has due to its Motion.

Kinetic energy is a characteristic of a moving particle. It is a type of energy that a matter or particle possesses due to its motion.

It is expressed:

[tex]K_E = \frac{1}{2}mv^2[/tex]

Where m is the mass of the particle and v is velocity.

Hence, Kinetic energy is the energy an object has due to its Motion.

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Answer:

1.6 m/s west

Explanation:

The recoil velocity of the launcher is 1.6 m/s west.

When two bodies of different masses move together each other and have head on collision, they travel to same or different direction after collision.

A water-balloon launcher with mass 5 kg fires a 1 kg balloon with a velocity of 8 m/s to the east.

Final momentum will be zero, so

m₁u₁ +m₂u₂ =0

Substitute the values for m₁ = 5kg, m₂ =1kg and u₂ =8 m/s, then the recoil velocity will be

5 x v +1x8 = 0

v = - 1.6 m/s

Thus, the recoil velocity of the launcher is  1.6 m/s (West)

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Answer:

t = 0.029s

Explanation:

In order to calculate the interaction time at the moment of catching the ball, you take into account that the force exerted on an object is also given by the change, on time, of its linear momentum:

[tex]F=\frac{\Delta p}{\Delta t}=m\frac{\Delta v}{\Delta t}[/tex]       (1)

m: mass of the water balloon = 1.20kg

Δv: change in the speed of the balloon = v2 - v1

v2: final speed = 0m/s (the balloon stops in my hands)

v1: initial speed = 13.0m/s

Δt: interaction time = ?

The water balloon brakes if the force is more than 530N. You solve the equation (1) for Δt and replace the values of the other parameters:

[tex]|F|=|530N|= |m\frac{v_2-v_1}{\Delta t}|\\\\|530N|=| (1.20kg)\frac{0m/s-13.0m/s}{\Delta t}|\\\\\Delta t=0.029s[/tex]

The interaction time to avoid that the water balloon breaks is 0.029s

Answer:

ac = 3.92 m/s²

Explanation:

In this case the frictional force must balance the centripetal force for the car not to skid. Therefore,

Frictional Force = Centripetal Force

where,

Frictional Force = μ(Normal Force) = μ(weight) = μmg

Centripetal Force = (m)(ac)

Therefore,

μmg = (m)(ac)

ac = μg

where,

ac = magnitude of centripetal acceleration of car = ?

μ = coefficient of friction of tires (kinetic) = 0.4

g = 9.8 m/s²

Therefore,

ac = (0.4)(9.8 m/s²)

ac = 3.92 m/s²

Based on the data provided, the centripetal acceleration is 3.92 m/s²

Centripetal acceleration is the acceleration of a body moving in a circular path which is directed toward the center of the circle.

In the given question, the frictional force must balance the centripetal force for the car not to skid.

where,

Frictional Force = μR

R = mg

F = μmg

Centripetal Force = m

Then

μmg = ma

a = μg

ac = 0.4 * 9.8 m/s²

ac = 3.92 m/s²

Therefore, the centripetal acceleration is 3.92 m/s².

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Answer:

  m = 4

Explanation:

The expression that explains the constructive interference of a diffraction pattern is

         a sin θ = m λ

where a  is the width of the slit and λ the wavelength

         sin θ = m λ / a

The maximum value is for when the sine is 1, let's substitute

         1 = m λ/a  

         m = a /λ

let's reduce the magnitudes to the SI system

        a = 2.1 um = 2.1 10⁻⁶

        lam = 475 nm = 475 10⁻⁹ m

let's calculate

        m = 2.1  10⁻⁶ / 475 10⁻⁹

        m = 4.42

with m must be an integer the highest value is

         m = 4

Answer:

Explanation:

As a result of impact of time widening, a clock moving as for an observer seems to run all the more gradually than a clock that is very still in the observer's casing.  

At the point when observed from earth, the pendulum on the spaceship takes more time to finish one oscillation.  

Hence, the clock related with that pendulum will run more slow (gives fewer oscillations as observed from the earth)  than the clock related with the pendulum on earth.

Ans => B fewer oscillations

Answer:

54.6°

Explanation:

From law of reflection i=r.

So, construct the reflected ray at 55.7°degrees from the normal and let it fall on the other mirror.  

Now draw the second normal at the point of incidence and again measure the angle of incidence, and draw the angle of reflection.

If you consider triangle AOB, one angle is ∠AOB=90°

 and ∠OAB is 54.6°

From angle sum property third angle ie ∠ABO=180°-90°-54.6°=35.4°

So, the second incident angle will be 54.6°

Hence, the second reflected angle will be 54.6 degrees.

Answer: c. expansion coefficients.

Explanation: Bimetallic strips used as adjustable switches in electric appliances consist of metallic strips that must have different expansion coefficients.

I found the answer on Quizlet. :)

Bimetallic strips used as adjustable switches in electric appliances consist of metallic strips that must have different expansion coefficients. The correct option is c.

The coefficient of thermal expansion (CTE) is the rate at which a material expands as its temperature rises. This coefficient is determined at constant pressure and without a phase change, i.e. the material is expected to remain solid or fluid.

Bimetallic strips, which are utilized as adjustable switches in electric appliances, are made up of metallic strips with differing expansion coefficients. The coefficient of thermal expansion indicates how the size of an object varies as temperature changes.

Therefore, the correct option is c. expansion coefficients.

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Answer:

The centripetal acceleration changed by a factor of 0.5

Explanation:

Given;

first radius of the horizontal circle, r₁ = 500 m

speed of the airplane, v = 150 m/s

second radius of the airplane, r₂ = 1000 m

Centripetal acceleration is given as;

[tex]a = \frac{v^2}{r}[/tex]

At constant speed, we will have;

[tex]v^2 =ar\\\\v = \sqrt{ar}\\\\at \ constant\ v;\\\sqrt{a_1r_1} = \sqrt{a_2r_2}\\\\a_1r_1 = a_2r_2\\\\a_2 = \frac{a_1r_1}{r_2} \\\\a_2 = \frac{a_1*500}{1000}\\\\a_2 = \frac{a_1}{2} \\\\a_2 = \frac{1}{2} a_1[/tex]

a₂ = 0.5a₁

Therefore, the centripetal acceleration changed by a factor of 0.5

Answer:

2404 MPa

Explanation:

See attachment for solution

The maximum stress that exists at the tip of the internal crack is 3,400 Mpa.

The given parameters;

The maximum stress that exists at the tip of the internal crack is calculated as follows;

[tex]\sigma _{max} = 2\sigma \times \sqrt{(\frac{l}{r} )} \\\\\sigma _{max} = 2 \times 170 \times 10^6 \times \sqrt{(\frac{2.5\times 10^{-2}}{2.5 \times 10^{-4}})} \\\\\sigma _{max} = 3.4 \times 10^{9} \ Pa\\\\\sigma _{max} = 3,400\ Mpa[/tex]

Thus, the maximum stress that exists at the tip of the internal crack is 3,400 Mpa.

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Answer:

The angular acceleration of the tire is 0.454 rad/s²

Explanation:

Given;

initial velocity, u = 3.4 rev/s = 3.4 rev/s x 2π rad/rev

                        u = 21.3656 rad/sec

final velocity, v = 5.5 rev/s = 5.5 rev/s x 2π rad/rev

                      v = 34.562 rad/sec

Calculate the value of angular rotation, θ, of the tire

θ = Number of revolutions x 2π rad/rev

θ = [tex]\frac{260}{2 \pi r} *\frac{2 \pi \ rad}{rev}[/tex]

θ = (260 / r)

r is the radius of the tire = 64 / 2 = 32cm = 0.32 m

θ = (260 / 0.32)

θ = 812.5 rad

Apply the following kinematic equation, to determine angular acceleration of the tire;

[tex]v^2 = u^2 + 2 \alpha \theta\\\\2 \alpha \theta = v^2 - u^2\\\\\alpha = \frac{v^2-u^2}{2 \theta} \\\\\alpha = \frac{(34.562)^2-(21.3656)^2}{2 (812.5)}\\\\\alpha = \frac{738.043}{1625} \\\\\alpha = 0.454 \ rad/s^2[/tex]

Therefore, the angular acceleration of the tire is 0.454 rad/s²