The free-fall acceleration at the surface of planet 1 is 22 m/s^2. The radius and the mass of planet 2 are twice those of planet 1. What is the free-fall acceleration on planet 2?

Answers

Answer 1

Answer:

g₂ = 11 m/s²

Explanation:

The value of free-fall acceleration on the surface of a planet is given by the following formula:

[tex]g = \frac{Gm}{r^2}[/tex]

where,

g = free-fall acceleration

G = Universal Gravitational Constant

m = mass of the planet

r = radius of planet

FOR PLANET 1:

[tex]g_1 = \frac{Gm_1}{r_1^2}\\\\\frac{Gm_1}{r_1^2} = 22 m/s^2[/tex] --------------------- equation (1)

FOR PLANET 2:

[tex]g_2 = \frac{Gm_2}{r_2^2}\\\\g_2 = \frac{G(2m_1)}{(2r_1)^2}\\\\g_2 = \frac{1}{2}\frac{Gm_1}{r_1^2}\\\\[/tex]

using equation (1):

[tex]g_2 = \frac{g_1}{2}\\\\g_2 = \frac{22\ m/s^2}{2}[/tex]

g₂ = 11 m/s²


Related Questions

A source emits sound at a fixed constant frequency f. If you run towards the source, the frequency you hear is

Answers

Answer:

increased because as you run into each sound wave the time between each sound decreases meaning the period of each wave decreases to your years and since f=1/T and T is decreasing by greater than 0, f must increase.

Explanation:

You simultaneously release two balls: one you throw horizontally, and the other you drop straight down. Which one will reach the ground first? Why?
(a) The ball dropped straight down lands first, since it travels a shorter distance.
(b) Neither. Their vertical motion is the same, so they will reach the ground at the same time.
(c) It depends on the mass of the balls—the heavier ball falls faster so lands first

Answers

Answer:

Option B.

Explanation:

Remember that we can think on any movement as a sum of a movement in the y-axis, the movement in the x-axis, and the movement in the z-axis. And these are not related, this means that, for example, the movement in x does not affect the movement in y.

So, when we analyze the problem of "how long takes an object to hit the ground"

We do not care for the horizontal motion of the object, we only care for the vertical motion of the object.

So, if an object is dropped, and another has a given initial velocity in the x-axis, in both cases the initial velocity in the y-axis will zero.

And in both cases, the only vertical force acting on the balls will be the gravitational force (so both objects will have the same vertical acceleration and the same vertical initial velocity) with this, we already know that the vertical motion of both objects will be exactly the same.

So, both objects will hit the ground at the same time.

(notice that here we are ignoring things like air resistance and other complex forces)

So here the correct option is b:  Neither. Their vertical motion is the same, so they will reach the ground at the same time.

Find the coefficient of kinetic friction between a 3.80-kg block and the horizontal surface on which it rests if an 87.0-N/m spring must be stretched by 6.50 cm to pull it with constant speed. Assume that the spring pulls in the horizontal direction.

Answers

Answer:

 μ = 0.15

Explanation:

Let's start by using Hooke's law to find the force applied to the block

          F = k x

          F = 87.0 0.065

          F = 5.655 N

Now we use the translational equilibrium relation since the block has no acceleration

          ∑ F = 0

          F -fr = 0

          F = fr

           

the expression for the friction force is

          fr = μ N

if we write Newton's second law for the y-axis

          N -W = 0

          N = W = mg

we substitute

          F = μ mg

          μ = F / mg

          μ = [tex]\frac{5.655}{3.8 \ 9.8}[/tex]

          μ = 0.15

Why is the melting of ice a physical change?
A. It changes the chemical composition of water.
B. It does not change the chemical composition of water.
C. It creates new chemical bonds.
D. It forms new products.
E. It is an irreversible change that forms new products.

Answers

It does not change the chemical composition of water.

A 2.90 m segment of wire supplying current to the motor of a submerged submarine carries 1400 A and feels a 2.00 N repulsive force from a parallel wire 4.50 cm away. What is the direction and magnitude (in A) of the current in the other wire? magnitude A direction

Answers

Answer:

[tex]I_2=30.9A[/tex]

Explanation:

From the question we are told that:

Wire segment [tex]l_s=2.9m[/tex]

Initial Current [tex]I_1=1400A[/tex]

Force [tex]F=2.00N[/tex]

Distance of Wire [tex]d=4.50cm=>0.0450m[/tex]

Generally the equation for Force is mathematically given by

 [tex]F=\frac{\mu_0 * I_1*I_2*l_s}{2 \pi *r}[/tex]

 [tex]F=\frac{4 \pi*10^{-7} *1400 I*I_2*2.9}{2 \pi *0.0450}[/tex]

 [tex]I_2=\frac{22.5*10^-2}{2*10^{-7}*1400*2.6}[/tex]

 [tex]I_2=30.9A[/tex]

How do the magnitude and direction of the electric field on the left side of the dipole compare to the right side for the same distance

Answers

Answer:

The magnitude of the electric field is same while the direction at the left and at the right is opposite to each other.

Explanation:

The direction of the electric field due to the dipole on the axial line is same as  the direction of dipole moment.

The magnitude of the electric field due to an electric dipole on its axial line is

[tex]E=\frac{2kp}{r^3}[/tex]

where, k is the constant, p is the electric dipole moment and r is the distance from the center of dipole.

The magnitude of the electric field is same while the direction at the left and at the right is opposite to each other.  

A chimpanzee sitting against his favorite tree gets up and walks 51 m due east and 39 m due south to reach a termite mound, where he eats lunch. (a) What is the shortest distance between the tree and the termite mound

Answers

Answer:

64.20m

Explanation:

As we can see from the image I have attached below, the route that the chipanzee makes forms a right triangle. In this case, the shortest distance is represented by x in the image, which is the hypotenuse. To find this value we use the Pythagorean theorem which is the following.

[tex]a^{2} +b^{2} = c^{2}[/tex]

where a and b are the length of the two sides and c is the length of the hypotenuse (x). Therefore, we can plug in the values of the image and solve for x

[tex]51^{2} +39^{2} =x^{2}[/tex]

2,601 + 1,521 = [tex]x^{2}[/tex]

4,122 = [tex]x^{2}[/tex]   ... square root both sides

64.20 = x

Finally, we see that the shortest distance is 64.20m

Receptor elétrico 5 pontos Dispositivo que converte energia elétrica em outra forma de energia, não exclusivamente térmica. Exemplos: motores elétricos, ventiladores, liquidificadores, geladeiras, aparelhos de sons, vídeos, celulares, computadores?

Answers

Answer:

Electromechanical transducer and Electrical receiver.

Explanation:

Electromechanical transducer is the part of a communication system which converted electrical waves or electrical energy into sound waves. The most common example loudspeaker while on the other hand, Electrical receiver is a device that converts electrical energy into another form of energy, except thermal. Examples are cell phones, computers and television.

A metre rule is used to measure the length of a piece of string in a certain experiment. It is found to be 20 cm long to the nearest millimeter. How should thisresult be recorded in a table of results? a. 0.2000m b. 0.200m c. 0.20m d. 0.2m​

Answers

Answer:

C

Explanation:

20 cm = 0.2m

since uncertainty is 0.1 cm (0.001 m), should be recorded to same number of decimal place as uncertainty

therefore it's 0.200m

Which is a mixture?
'a' sodium metal
'b' chlorine gas
'c' sodium metal and chlorine gas
'd' sodium chloride (salt) and water

Answers

Answer:

d. Sodium chloride (salt) + water

Explanation:

A mixture is made up of two or more substance combined together (combined chemically).NaCl (salt) can completely dissolve in water and sodium chlorine (aqueous) is a homogeneous mixture.sodium metal when extracted is a soft, silvery white solid.chlorine gas is a pure gas.sodium metal and chlorine gas are at pure state hence they are not mixture.

learn more: https://brainly.com/question/2331419

Answer:D. Sodium chloride (salt) and water

Explanation:

I got it right on edge 2023


hope this is helpful!

Light of intensity I0 and polarized horizontally passes through three polarizes. The first and third polarizing axes are horizontal, but the second one is oriented 20.0� to the horizontal. In terms of I0, what is the intensity of the light that passes through the set of polarizers?
A) 0.442 I0
B) 0.180 I0
C) 0.780 I0
D) 0.883 I0

Answers

Answer:

Option C.

Explanation:

Suppose that we have light polarized in some given direction with an intensity I0, and it passes through a polarizer that has an angle θ with respect to the polarization of the light, the intensity that comes out of the polarizer will be:

I(θ) = I0*cos^2(θ)

Ok, we know that the light is polarized horizontally and comes with an intensity I0

The first polarizer axis is horizontal, then the intensity after this polarizer is:

then θ = 0°

I(0°) = I0*cos^2(0°) = I0

The intensity does not change. The axis of polarization does not change.

The second polarizer is oriented at 20° from the horizontal, then the intensity that comes out of this polarizer is:

I(20°) =  I0*cos^2(20°) = I0*0.88

And the axis of polarization of the light that comes out is now 20° from the horizontal

Now the light passes through the last polarizer, which has an axis oriented horizontally, so the final intensity of the light will be:

note that here the initial polarization is  I0*0.88

and the angle between the axis is 20° again.

Then the final intensity is:

I(20°) =  I0*0.88*cos^2(20°) = I0*0.78

Then the correct option is C.

A coin and feather are dropped in a moon. what will fall earlier on ground.give reasons.if they are dropped in the earth,which one will fall faster

Answers

Answer:

on the moon, they will fall at the timeon earth, the coin will fall faster to the ground

Explanation:

A coin and feather dropped in a moon experience the same acceleration due to gravity as small as 1.625 m/s², and because of the absence of air resistance both will fall at the same rate to the ground.

If the same coin and feather are dropped in the earth, they will experience the same acceleration due to gravity of 9.81 m/s² and because of the presence of air resistance, the heavier object (coin) will be pulled faster to the ground by gravity than the lighter object (feather).

After a laser beam passes through two thin parallel slits, the first completely dark fringes occur at 19.0 with the original direction of the beam, as viewed on a screen far from the slits. (a) What is the ratio of the distance between the slits to the wavelength of the light illuminating the slits

Answers

Answer:

[tex]$\frac{d}{\lambda} = 1.54$[/tex]

Explanation:

Given :

The first dark fringe is for m = 0

[tex]$\theta_1 = \pm 19^\circ$[/tex]

Now we know for a double slit experiments , the position of the dark fringes is give by :

[tex]$d \sin \theta=\left(m+\frac{1}{2}\right) \lambda$[/tex]

The ratio of distance between the two slits, d to the light's wavelength that illuminates the slits, λ :

[tex]$d \sin \theta=\left(\frac{1}{2}\right) \lambda$[/tex]     (since, m = 0)

[tex]$d \sin \theta=\frac{\lambda}{2}$[/tex]

[tex]$\frac{d}{\lambda} = \frac{1}{2 \sin \theta}$[/tex]

[tex]$\frac{d}{\lambda} = \frac{1}{2 \sin 19^\circ}$[/tex]

[tex]$\frac{d}{\lambda} = 1.54$[/tex]

Therefore, the ratio is [tex]$\frac{1}{1.54}$[/tex]  or 1 : 1.54

Find a parametric representation for the surface. The plane through the origin that contains the vectors i - j and j - k

Answers

Answer:

parametric representation: x = u, y = v - u ,  z = - v

Explanation:

Given vectors :

i - j ,  j - k

represent the vector equation of the plane as:

r ( u, v ) = r₀ + ua + vb

where:  r₀ = position vector

            u and v = real numbers

             a and b = nonparallel vectors

expressing the nonparallel vectors as :

a = i -j , b = j - k , r = ( x,y,z ) and r₀ = ( x₀, y₀, z₀ )

hence we can express vector equation of the plane as

r(u,v) = ( x₀ + u, y₀ - u + v,  z₀ - v )

Finally the parametric representation of the surface through (0,0,0) i.e. origin = 0

( x, y , z ) = ( x₀ + u,  y₀ - u + v,   z₀ - v )

x = 0 + u ,

y = 0 - u + v

z = 0 - v

parametric representation: x = u, y = v - u ,  z = - v

For waves moving through the atmosphere at a constant velocity, higher frequency waves must have proportionally longer wavelengths.
a) true
b) false

Answers

Answer:

false.

Explanation:

We know that for a wave that moves with velocity V, with a wavelength λ, and a frequency f, we have the relation:

V = λ*f

So, if the velocity is constant and we increase the frequency to:

f' > f

we will have a new wavelength λ'

Such that:

V = f'*λ'

And V = f*λ

Then we have:

f'*λ' = f*λ

Solvinf for λ', we get:

λ' =(f/f')*λ

And because:

f' > f

then:

(f/f') < 1

Then:

λ' =(f/f')*λ < λ

So, if we increase the frequency, we need to decrease the wavelength.

So, for higher frequency waves, we must have proportionally shorter wavelengths.

Then we can conclude that the given statement:

"or waves moving through the atmosphere at a constant velocity, higher frequency waves must have proportionally longer wavelengths"

is false.

•. What is called the error due to the procedure and used apparatuses?
a. Random error
b. Index error
c. Systematic error
d. Parallax error.​

Answers

Answer:

[tex]c.) \: systematic \: error \\ \\ = > it \: is \: the \: error \: caused \: \\ \\ due \: to \: the \: procedure \\ \\ \: and \: used \: apparatuses \\ \\ \huge\mathfrak\red{Hope \: it \: helps}[/tex]

If you buy an amateur-sized reflecting telescope, say around 10 inches (25cm) aperture, it'll have something in it that sends the gathered starlight out the side of the telescope tube. What do we call this thing

Answers

Answer: objective lens

Explanation:

Light enters a refra

Light enters a telescope through a lens at the upper end, which focuses the light near the bottom of the telescope. An eyepiece then magnifies the image so that it can be viewed by the eye, or a detector like a photographic plate can be placed at the focus. The upper end of a reflecting telescope is open, and the light passes through to the mirror located at the bottom of the telescope. The mirror then focuses the light at the top end, where it can be detected. Alternatively, a second mirror may reflect the light to a position outside the telescope structure, where an observer can have easier access to it.

A proton is released from rest at the positive plate of a parallel-plate capacitor. It crosses the capacitor and reaches the negative plate with a speed of 54000 m/s. The experiment is repeated with a He+ ion (charge e, mass 4 u).What is the ion's speed at the negative plate?

Answers

4058 m longest serving

When an object is in free fall, ____________________.

Answers

Answer:

Objects that are said to be undergoing free fall, are not encountering a significant force of air resistance; they are falling under the sole influence of gravity.

Explanation:

Under such conditions, all objects will fall with the same rate of acceleration, regardless of their mass.

Consider a tall building of height 200.0 m. A stone A is dropped from the top (from the cornice of the building). One second later another stone B is thrown vertically up from the point on the ground just below the point from where stone A is dropped.Birthstones meet at half the height of the tower. (a) Find the initial velocity of vertical throw of stone B.(b) Find the velocities of A and B, just before they meet.

Answers

Answer:

a)  v₀ = 44.27 m / s, b) stone A  v = 44.276 m / s,  stone B   v = 0.006 m / s

Explanation:

a) This is a kinematics exercise, let's start by finding the time it takes for stone A to reach half the height of the building y = 100 m

          y = y₀ + v₀ t - ½ gt²

as the stone is released its initial velocity is zero

         y- y₀ = 0 - ½ g t²

         t = [tex]\sqrt{ -2(y-y_o)/g}[/tex]

         t = [tex]\sqrt{ -2(100-200)/9.8}[/tex]

         t = 4.518 s

now we can find the initial velocity of stone B to reach this height at the same time

         y = y₀ + v₀ t - ½ g t²

stone B leaves the floor so its initial height is zero

         100 = 0 + v₀ 4.518 - ½ 9.8 4.518²

         100 = 4.518 v₀ - 100.02

         v₀ = [tex]\frac{100-100.02}{4.518}[/tex]

         v₀ = 44.27 m / s

   

b) the speed of the two stones at the meeting point

stone A

          v = v₀ - gt

          v = 0 - 9.8 4.518

          v = 44.276 m / s

stone B

          v = v₀ -g t

          v = 44.27 - 9.8 4.518

          v = 0.006 m / s

Why is the temperature constant during the melting of water?​

Answers

[tex] \orange{\underline{\huge{\bold{\textit{\green{\bf{QUESTION}}}}}}}[/tex]

Why is the temperature constant during the melting of water?

[tex] \huge\mathbb{\red A \pink{N}\purple{S} \blue{W} \orange{ER}}[/tex]

[tex] \orange{\underline{\huge{\bold{\textit{\green{\bf{ REASON}}}}}}}[/tex]

THE HEAT WE R SUPPLYING TO THE WATER TO RAISE THE TEMP OF THE WATER IS USED BY THE MOLECULES TO BREAK INTERMOLECULAR BONDS WHICH HELP IN THE CHANGING OF THE LATTICE (STRUCTURE) OF THE WATER .

ICE HAS A HEXAGONAL RING LIKE STRUCTURE WHICH IS CONVERTED INTO REGULAR CRYSTALLINE STRUCTURE WHICH CAN ONLY BE FORMED WITH THE HELP OF FORMATION OF NEW BONDS AND BREAKDOWN OF OLDER ONES

THE AMOUNT OF ENERGY WHICH IS USED IN CONVERSATION OF THE STATE OF FROM SOLID TO LIQUID IS KNOWN AS LATENT HEAT OF FUSION.

SO TEMP REMAIN CONSTANT DURING CHANGE IN STATE .

[tex] \red \star{Thanks \: And \: Brainlist} \blue\star \\ \green\star If \: U \: Liked \: My \: Answer \purple \star[/tex]

A block of mass M is connected by a string and pulley to a hanging mass m.
The coefficient of kinetic friction between block M and the table is 0.2, and also, M = 20 kg, m = 10 kg.
b. Find the acceleration of the system and tensions on the string.
c. How far will block m drop in the first seconds after the system is released?
d. How long will block M move during the above time?
e. At the time, calculate the velocity of block M
f. Find out the deceleration of block M if the connection string is removal by cutting after the first second. Then, calculate the time taken to contact block M and pulley
How far will block m drop in the first seconds after the system is released?

Answers

(b) Use Newton's second law. The net forces on block M are

• ∑ F (horizontal) = T - f = Ma … … … [1]

• ∑ F (vertical) = n - Mg = 0 … … … [2]

where T is the magnitude of the tension, f is the mag. of kinetic friction between block M and the table, a is the acceleration of block M (but since both blocks are moving together, the smaller block m also shares this acceleration), and n is the mag. of the normal force between the block and the table.

Right away, we see n = Mg, and so f = µn = 0.2Mg.

The net force on block m is

• ∑ F = mg - T = ma … … … [3]

You can eliminate T and solve for a by adding [1] to [3] :

(T - 0.2Mg) + (mg - T ) = Ma + ma

(m - 0.2M) g = (M + m) a

a = (10 kg - 0.2 (20 kg)) (9.8 m/s²) / (10 kg + 20 kg)

a = 1.96 m/s²

We can get the tension from [3] :

T = m (g - a)

T = (10 kg) (9.8 m/s² - 1.96 m/s²)

T = 78.4 N

(c/d) No time duration seems to be specified, so I'll just assume some time t before block M reaches the edge of the table (whatever that time might be), after which either block would move the same distance of

1/2 (1.96 m/s²) t

(e) Assuming block M starts from rest, its velocity at time t is

(1.96 m/s²) t

(f) After t = 1 s, block M reaches a speed of 1.96 m/s. When the string is cut, the tension force vanishes and the block slows down due to friction. By Newton's second law, we have

F = -f = Ma

The effect of friction is constant, so that f = 0.2Mg as before, and

-0.2Mg = Ma

a = -0.2g

a = -1.96 m/s²

Then block M slides a distance x such that

0² - (1.96 m/s²) = 2 (-1.96 m/s²) x

x = (1.96 m/s²) /  (2 (1.96 m/s²))

x = 0.5 m

(I don't quite understand what is being asked by the part that says "calculate the time taken to contact block M and pulley" …)

Meanwhile, block m would be in free fall, so after 1 s it would fall a distance

x = 1/2 (-9.8 m/s²) (1 s)

x = 4.9 m

A bullet with mass 5.35 g is fired horizontally into a 2.174-kg block attached to a horizontal spring. The spring has a constant 6.17 102 N/m and reaches a maximum compression of 6.34 cm.
(a) Find the initial speed of the bullet-block system.
(b) Find the speed of the bullet.

Answers

Answer:

a)[tex]V=1.067\: m/s[/tex]

b)[tex]v=434.65\: m/s [/tex]  

Explanation:

a)

Using the conservation of energy between the moment when the bullet hit the block and the maximum compression of the spring.

[tex]\frac{1}{2}MV^{2}=\frac{1}{2}k\Delta x^{2}[/tex]

Where:

M is the bullet-block mass (0.00535 kg + 2.174 kg = 2.17935 kg)V is the speed of the systemk is the spring constant (6.17*10² N/m)Δx is the compression of the spring (0.0634 m)

Then, let's find the initial speed of the bullet-block system.

[tex]V^{2}=\frac{k\Delta x^{2}}{M}[/tex]

[tex]V=\sqrt{\frac{6.17*10^{2}*0.0634^{2}}{2.17935}}[/tex]

[tex]V=1.067\: m/s[/tex]

b)

Using the conservation of momentum we can find the velocity of the bullet.

[tex]mv=MV[/tex]

[tex]v=\frac{MV}{m}[/tex]

[tex]v=\frac{2.17935*1.067}{0.00535}[/tex]

[tex]v=434.65\: m/s [/tex]  

I hope it helps you!

             

 

A 100-m long transmission cable is suspended between two towers. If the mass density is 18.2 g/cm and the tension in the cable is 6543 N, what is the speed (m/s2) of transverse waves on the cable

Answers

It’s 20 m longest 24me the song

If an object travels on a circular path is an acceleration? What is changing to cause an acceleration?

Answers

For this reason, it can be safely concluded that an object moving in a circle at constant speed is indeed accelerating. It is accelerating because the direction of the velocity vector is changing.

~~~NEED HELP ASAP~~~
Please solve each section and show all work for each section.

Answers

Explanation:

Forces on Block A:

Let the x-axis be (+) towards the right and y-axis be (+) in the upward direction. We can write the net forces on mass [tex]m_A[/tex] as

[tex]x:\:\:(F_{net})_x = f_N - T = -m_Aa\:\:\:\:\:\:\:(1)[/tex]

[tex]y:\:\:(F_{net})_y = N - m_Ag = 0 \:\:\:\:\:\:\:\:\:(2)[/tex]

Substituting (2) into (1), we get

[tex]\mu_km_Ag - T = -m_Aa \:\:\:\:\:\:\:\:\:(3)[/tex]

where [tex]f_N= \mu_kN[/tex], the frictional force on [tex]m_A.[/tex] Set this aside for now and let's look at the forces on [tex]m_B[/tex]

Forces on Block B:

Let the x-axis be (+) up along the inclined plane. We can write the forces on [tex]m_B[/tex] as

[tex]x:\:\:(F_{net})_x = T - m_B\sin30= -m_Ba\:\:\:\:\:\:\:(4)[/tex]

[tex]y:\:\:(F_{net})_y = N - m_Bg\cos30 = 0 \:\:\:\:\:\:\:\:\:(5)[/tex]

From (5), we can solve for N as

[tex]N = m_B\cos30 \:\:\:\:\:\:\:\:\:(6)[/tex]

Set (6) aside for now. We will use this expression later. From (3), we can see that the tension T is given by

[tex]T = m_A( \mu_kg + a)\:\:\:\:\:\:\:\:\:(7)[/tex]

Substituting (7) into (4) we get

[tex]m_A(\mu_kg + a) - m_Bg\sin 30 = -m_Ba[/tex]

Collecting similar terms together, we get

[tex](m_A + m_B)a = m_Bg\sin30 - \mu_km_Ag[/tex]

or

[tex]a = \left[ \dfrac{m_B\sin30 - \mu_km_A}{(m_A + m_B)} \right]g\:\:\:\:\:\:\:\:\:(8)[/tex]

Putting in the numbers, we find that [tex]a = 1.4\:\text{m/s}[/tex]. To find the tension T, put the value for the acceleration into (7) and we'll get [tex]T = 21.3\:\text{N}[/tex]. To find the force exerted by the inclined plane on block B, put the numbers into (6) and you'll get [tex]N = 50.9\:\text{N}[/tex]

93 cm3 liquid has a mass of 77 g. When calculating its density what is the appropriate number of significant figures

Answers

Answer:

828 kg/m³ or 0.828 g/cm³

Explanation:

Applying,

D = m/V............. Equation 1

Where D = density of the liquid, m = mass of the liquid, V = volume of the liquid.

From the question,

Given: m = 77 g , V = 93 cm³

Substitute these values into equation 1

D = 77/93

D = 0.828 g/cm³

Converting to kg/m³

D = 828 kg/m³

A wheel accelerates so that it's angular speed increases uniformly from 150 rads/s to 580 rads/s in 16 revolutions.Cakcjlate its angular acceleration. ​

Answers

Answer:

A = 26.875 rad/s²

Explanation:

Given the following data;

Initial angular speed, Uw = 150 rads/s.

Final angular speed, Vw = 580 rads/s.

Time = 16 seconds.

To calculate the angular acceleration;

From kinematics equation;

At = Vw - Uw

Where;

A is the angular acceleration.t is the timeVw is the final angular speed.Uw is the initial angular speed.

Substituting into the formula, we have;

A*16 = 580 - 150

16A = 430

A = 430/16

A = 26.875 rad/s²

Two metal spheres are made of the same material and have the same diameter, but one is solid and the other is hollow. If their temperature is increased by the same amount:_______.
A) the solid sphere becomes heavier and the hollow one lighter.
B) the solid sphere becomes bigger than the hollow one.
C) the hollow sphere becomes bigger than the solid one.
D) the two spheres remain of equal size.
E) the solid sphere becomes lighter and the hollow one heavier.

Answers

Answer:

D) the two spheres remain of equal size.

Explanation:

Since the body of the sphere is made up of both the same material. Thus the orientation will not affect the expansion. That is solid upon solid and hollow upon the hollow sphere. Hence it can be said that both the sphere expands and is due to the material used for making both of them is the same.

A ball is launched from the ground with a horizontal speed of 30 m/s and a vertical speed of 30 m/s. How long will it take to get to the top of its trajectory? A. 3 seconds B. 4 seconds C. 2 seconds D. 6 seconds

Answers

Answer:

A (3 seconds)

Explanation:

Well here we have a type of motion called projectile motion and it is pretty similar to an upside down parabola. The top of the trajectory is the vertex of the parabola and is also when v=0.

Lets identify our givens.

Givens:

Horizontal speed= 30m/s

Vertical Speed= 30 m/s

Since the ball is in freefall after being launched ay=-g(take up to be positive) and ax=0

The ball is launched from the ground so y0=0

Final vertical velocity= 0

This problem is now relatively easy because we only need to find the vertical distance so we can ignore horizontal speed and use

vy=vy0+ayt

Plug in our givens

0=30-10t

solve for t

t=3 seconds

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