According to the Traditional Square of Opposition: If "All S are P" is true, then is "Some S are P" true or false?

Answers

Answer 1

[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the concept of Logic.

Since in the above statement it is given that,

All S are P ==> True,

then obviously Some S are also P always, hence it is true.

Answer is True.


Related Questions

A negative charge of 2 C and a positive charge of 3 C are separated by 80 m. What is the force between the two charges?

Answers

Answer:

6

Explanation: i looked this up.

According to the Coloumb's law, the force is obtained from the charges and the distance between them is 8.4375×10⁶ N. This force results in the attractive force.

What is Coloumb's law?

Coloumb's law states the relation between the charges and the distance between the charges. Coloumb's law states that the Force is directly proportional to the product of charges and inversely proprotional to the square of distance between them.

The Coloumb's law gives the force of attraction or repulsion between the charged bodies. Two charges with positive or negative charges repels each other. One positive and one negative charge attract each other.

The force increases with the product of charges increases as product of charges and force are directly proprotional. The force decreases with the increase in distance of seperation and vice-versa. The SI unit of force is newton (N).

The Coloumb's law is:

          F = k (q₁×q₂ / r²)

k is the constant of proportionality and is equal to 9×10⁹ N.m²/C².

q₁, q₂ = charges

r² =  distance of seperation of charges.

From the given,

q₁ = -2C ( negative sign represents the negative charge)

q₂ = +3C ( + sign represents the positive charge)

r² = 80 m ( distance between the charges)

F = k (q₁×q₂ / r²)

  = 9×10⁹×2×3 / 80×80

 = 54×10⁹ / 6400

 = 8437500 N

F = 8.4375×10⁶ N

There is the presesnce of both positive and negative charges, hence it results in the attractive force. Hence, the force F between two charges separated by 80m is  8.4375×10⁶ N.

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What is surface tension ​

Answers

Answer:

Surface tension is,  the surface where the water meets the air, water molecules cling even more tightly to each other.

In Part 5.2.3 of the experiment, you will measure the index of refraction of yellow light using Lab Manual Equation 5.2. Suppose the minimum angle of deviation is 18 degrees. What is the index of refraction

Answers

Answer:

The answer is "1.26".

Explanation:

[tex]D=18^{\circ}[/tex]

The refractive index is:

[tex]\to \mu=2\sin(30^{\circ}+\frac{D}{2})\\\\[/tex]

       [tex]=2\sin(30^{\circ}+\frac{18^{\circ}}{2})\\\\=2\sin(30^{\circ}+9^{\circ})\\\\=2\sin(30^{\circ}+9^{\circ})\\\\=2\sin(39^{\circ})\\\\=2 \times 0.63\\\\=1.26[/tex]

15 points!

a. Calculate the electric potential energy stored in a 1.4 x 10-7 F capacitor
that stores 3.40 x 10-6 C of charge at 24.0 V.

Answers

Answer:

[tex]4.12\times 10^{-5}\ J[/tex].

Explanation:

Given that,

Capacitance, [tex]C=1.4\times 10^{-7}\ F[/tex]

Charge stored in the capacitor, [tex]Q=3.4\times 10^{-6}\ C[/tex]

We need to find the electric potential energy stored in the capacitor. The formula for the electric potential energy stored in the capacitor is given by :

[tex]E=\dfrac{Q^2}{2C}[/tex]

Put all the values,

[tex]E=\dfrac{(3.4\times 10^{-6})^2}{2\times 1.4\times 10^{-7}}\\\\=4.12\times 10^{-5}\ J[/tex]

So, the required electric potential eenergy is equal to [tex]4.12\times 10^{-5}\ J[/tex].

4. Speedy leaves the ground with an initial vertical velocity of 53 m/s and a horizontal velocity of 42 m/s.
How much time does he spend in the air?
How far (horizontally) does he travel during this time?
5. The Angry Bird is fired at an angle of 35 above the horizontal at a speed of 72 m/s.
Draw the initial velocity vector
Determine the initial horizontal velocity
Determine the initial vertical velocity
How much time does it spend in the air?
What horizontal distance does it go?

Answers

I know this answer I will be back

On Apollo Moon missions, the lunar module would blast off from the Moon's surface and dock with the command module in lunar orbit. After docking, the lunar module would be jettisoned and allowed to crash back onto the lunar surface. Seismometers placed on the Moon's surface by the astronauts would then pick up the resulting seismic waves.
Find the impact speed of the lunar module, given that it is jettisoned from an orbit 110 km above the lunar surface moving with a speed of 1600 m/s .
My Approach:
Ei = Ef
1/2*m*vi2 - (G*m*ME)/(radius of moon + orbital distance) = 1/2*m*vf2 ​- (G*m*ME)/r
=> (0.5 * m * 16002) - (6.67 * 10-11 * 7.35*1022 * m/(1737.4*103 +180*103) = (0.5*m*v^2) - (6.67*10-11 * 7.35*1022 * m/(1737.4*103 )

Answers

Answer:

Following are the solution to the given question:

Explanation:

For crashing speed, we can use energy conservation:

kinetic energy [tex]= \frac{1}{2}\times m \times v^2[/tex]  

potential energy [tex]= -\frac{GMm}{r}[/tex]

moon mass[tex]= 7.36\times 10^{22} \ kg[/tex]

Radius[tex]= 1738\ km[/tex]  

[tex]\to (K + U) \ orbit = (K + U)\ crash\\\\\to \frac{1}{2}\times m \times v_o^2 - \frac{GMm}{(1738000 + 110000)} \\\\ \to \frac{1}{2}\times m \times vc^2 - \frac{GMm}{1738000}[/tex]

Calculating the mass drop for the leave:

[tex]\to \frac{vo^2}{2} - \frac{GM}{1848000}\\\\ \to \frac{vc^2}{2} - \frac{GM}{1738000}[/tex]

Solve the value for

[tex]vc = \sqrt{(vo^2 +2\times GM \times(\frac{1}{1738000} - \frac{1}{1848000}))}\\\\vc = \sqrt{(1600^2 +2\times 6.67\times 10^{-11} \times 7.36 \times 10^{22}\times (\frac{1}{1738000} - \frac{1}{1848000}))}\\\\vc = 1701 \ \frac{m}{s}\\\\[/tex]  

The approach is correct but misrepresented in replacing 180 km instead of 110 km.

In a physics lab experiment for the determination of moment of inertia, a team weighs an object and finds a mass of 4.07 kg. They then hang the object on a pivot located 0.155 m from the object's center of mass and set it swinging at a small amplitude. As two of the team members carefully count 113 cycles of oscillation, the third member measures a duration of 247 s. What is the moment of inertia of the object with respect to its center of mass about an axis parallel to the pivot axis

Answers

Answer:

I = 0.65 kgm²

Explanation:

Since the mass is an inertial pendulum, we use the formula for the period, T of an inertial pendulum.

T = 2π√(I/mgh) where I = moment of inertia of object about pivot point, m = mass of object5 = 4.07 kg, g = acceleration due to gravity = 9.8 m/s² and h = distance of center of mass of object from pivot point = 0.155 m.

Given that the team measures 113 cycles of oscillation in 247 s, the period, T = time of oscillations/total number of oscillations = 247 s/113 oscillations = 2.186 s/oscillation

So, T = 2.186 s

We now find I by making it subject of the formula in the equation for T.

So,

T = 2π√(I/mgh)

dividing both sides by 2π, we have

T/2π = √(I/mgh)

squaring both sides, we have

(T/2π)² = [√(I/mgh)]²

T²/4π² = I/mgh

multiplying both sides by mgh, we have

T²mgh/4π² = I

I = T²mgh/4π²

substituting the values of the variables into the equation, we have

I = T²mgh/4π²

I = (2.186 s)² × 4.07 kg × 9.8 m/s² × 0.155 m/4π²

I = 4.778 s² × 4.07 kg × 9.8 m/s² × 0.155 m/4π²

I =  29.539 kgm²/4π²

I = 0.748 kgm²

Now I = I' + mh²  (parallel axis theorem) where I' = moment of inertia of object about its center of mass, m = mass of object = 4.07 kg and h = distance of center of mass object from pivot point.

So, I' = I - mh²

Substituting the values of the variables into the equation, we have

I' = I - mh²

I' = 0.748 kgm² - 4.07 kg × (0.155 m)²

I' = 0.748 kgm² - 4.07 kg × 0.02403 m²

I' = 0.748 kgm² - 0.098 kgm²

I = 0.65 kgm²

1. A train is moving north at 5 m/s on a straight track. The engine is causing it to accelerate northward at 2 m/s^2.
How far will it go before it is moving at 20 m/s?
A) 83
B) 43
C) 39
D) 94
E) 20

Answers

Answer:

(D) x = 93.8 m

Explanation:

v^2 = v0^2 + 2ax

(20 m/s)^2 = (5 m/s)^2 + 2(2 m/s^2)x

Solving for x,

x = 93.8 m

Consider the model of the energy transformation of this system. What can you say about N and M in the model?
A) M < N
B) N = M
C) N < M
D) N + M =

Answers

The correct answer is A

Model of the energy transformation of this system we can say about N and M in the model is M < N.

What is energy?

Energy is the ability or capability to do tasks, such as the ability to move an item (of a certain mass) by exerting force. Energy can exist in many different forms, including electrical, mechanical, chemical, thermal, or nuclear, and it can change its form.

The model shows the energy transformation in electrical appliance Fan the is lass of energy in form of heat so  M < N.

Model of the energy transformation of this system we can say about N and M in the model is M < N.

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A geologist notices that a river is eroding its valley at a constant rate. Knowing the height of the valley walls, how could the geologist figure out when the river started carving the valley?
A.
Count growth rings of trees growing on the valley floor.
B.
Divide the height of the valley walls by the rate of erosion.
C.
Fill up the river valley with rocks, and time how long it takes the rocks to wash out.
D.
Sit and observe the river for a few hours until the valley walls double in height.

Answers

Answer:

B.

Divide the height of the valley walls by the rate of erosion.

Explanation:

There is a relationship between the rate of erosion and the hieght at which it is eroded according to Newton's law of motion. In the case of the scenario above, the best way to determine the time the river started carving the valley would be the division of the height of the valley walls by the rate of erosion.

Suppose that a lion moves due EAST as to travel 25km in 4.2 hours. What is the average speed, and what is the average velocity. (2 answers separated by a comma)​

Answers

Answer:

5.95 km/h

Explanation:

Given that,

Distance moved, d = 25 km

Time taken by the lion, t = 4.2 hours

Average speed = distance/time

And

Average velocity = displacement/time

Here, distance = displacement

So,

[tex]v=s=\dfrac{25\ km}{4.2\ h}\\\\v=5.95\ km/h[/tex]

So, the average speed and the average speed of the lion is equal to 5.95 km/h.

Saved Which of the following is NOT an important function of facial display? Multinio Choic
A. emotion
B. attractiveness
c. Primacy
d. identity

Answers

Answer:

C

Explanation:

Primacy means being first or important so thats not an important facial display as the others.

Which of these will be the correct relationship between work input and work output?
A) Work input = Work output + Work against friction
B) Work input = Work output – Work against friction
C) Work input = Work output * Work against friction
D) Work input = Work output / Work against friction

Answers

Answer:

Work input = Work output * Work against friction is your answer so C

Explanation:

I hope this helps you :)

Answer:

A) Work input = Work output + Work against friction

Explanation:

How does the presence of a nucleus provide a method of basic cell
classification? *

Answers

Answer:

The nucleus-containing cells are called eukaryotic cells. Eukaryote means having membrane-bound organelles.

Explanation:

I hope this is what you were looking for?!

Hope this helps!

Have a great day!

-Hailey!

The cells which have a nucleus are called Eukaryotic cells. The cells which do not have a nucleus are called prokaryotic cells.

What is a nucleus?

The nucleus is the controlling center of the body. It performs all the major activities in the cell. The cell which possesses a nucleus is called a eukaryote. The cell which does not have a nucleus is called prokaryote.

A prokaryotic cell is a straightforward, one-celled (unicellular) organism that is devoid of a nucleus or any other organelle that is membrane-bound. The nucleoid, a dark area in the center of the cell, is where prokaryotic DNA is located.

Therefore, The cells which have a nucleus are called Eukaryotic cells. The cells which do not have a nucleus are called prokaryotic cells.

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The speed of surface waves in water decreases as the water becomes shallower. Suppose waves travel across the surface of a lake withn a speed of 2m/s and a wavelength of 1.5m. When these waves move into a shallower part of the lake, their speed decreases to 1.6m/s, though their frequency remains the same. Find the wavelength of the wave in the shallower water.

Answers

Answer:

The correct solution is "1.2 m".

Explanation:

The given values are:

Wavelength of waves,

λ = 1.5 m

Speed of waves on surface,

V = 2 m/sec

Speed of waves in water,

V₁ = 1.6 m/sec

As we know,

⇒  [tex]V=f\times \lambda[/tex]

or,

⇒  [tex]f=\frac{V}{\lambda}[/tex]

On substituting the values, we get

⇒      [tex]=\frac{2}{1.5}[/tex]

⇒      [tex]=1.33 \ Hz[/tex]

hence,

⇒  [tex]\lambda_1=\frac{V_1}{f}[/tex]

On substituting the values, we get

⇒       [tex]=\frac{1.6}{1.33}[/tex]

⇒       [tex]=1.2 \ m[/tex]

A bullet with mass m = 5.21 g is moving horizontally with a speed v = 443 m/s when it strikes a block of hardened steel with mass M = 14.8 kg (initially at rest). The bullet bounces off the block in a perfectly elastic collision. (a) What is the speed (m/s) of the block immediately after the collision?

Answers

[tex]V_{f2} =0.29 \dfrac{m}{s}[/tex] :Speed of the block immediately after the collision.

What is the elastic collision?

From elastic collision theory.

Momentum of a body is given as

[tex]P=m\times v[/tex]

where

p:Linear momentum

m: mass

v:velocity

There are 3 cases of collisions : elastic, inelastic and plastic.

For elastic collision the change in momentum remains constant

[tex]P_{i} =P_{f}[/tex]

Nomenclature and data

m₁: ball mass= 5.21 g= 5.21*10⁻³kg

V₀₁: initial ball speed,  =412 m/s

[tex]V_{f1}[/tex]: final ball speed

m₂: block mass =  14.8 kg  

V₀₂: initial block speed, = 0

[tex]V_{f2}[/tex]: final block speed

We apply furmula

[tex]P_{i} =P_{f}[/tex]

m₁[tex]\times[/tex]V₀₁+m₂[tex]\times[/tex]V₀₂=m₁[tex]\times[/tex]Vf₁+m₂[tex]\times[/tex]Vf₂

5.21[tex]\times[/tex]10⁻³[tex]\times[/tex]412+14.8[tex]\times[/tex]0= 5.21[tex]\times[/tex]10⁻³[tex]\times[/tex]Vf₁+14.8[tex]\times[/tex]Vf₂

2.15= 5.21*10⁻³[tex]\times[/tex]Vf₁+14.8[tex]\times[/tex]Vf₂ Equation (1)

For perfectly elastic collision the coefficient of elastic restitution (e) is equal to 1, and e is defined like this:

[tex]e=\dfrac{v_{f2-V_{f1} } }{v_{01-V_{ 02} } }[/tex]

1*(V₀₁-V₀₂) =Vf₂-Vf₁  , V₀₂=0, V₀₁ =412 m/s

412=Vf₂-Vf₁

Vf₁=Vf₂-412 Equation (2)

We replace Equation (2) in Equation (1)

2.15= 5.21[tex]\times[/tex]10⁻³(Vf₂-412)+14.8[tex]\times[/tex]Vf₂

2.15= 5.21[tex]\times[/tex]10⁻³*Vf₂-2.15+14.8*Vf₂

4.3=14.805Vf₂

[tex]Vf_{2} =\dfrac{4.3}{14.805} =0.29 \dfrac{m}{s}[/tex]: (+) ,with equal direction  of the movement of the ball before the collision.

Hence    [tex]V_{f2} =0.29 \dfrac{m}{s}[/tex]   Speed of the block immediately after the collision.

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Can someone take there time and answer this :)

Answers

Answer: I think B.)

Explanation:

the answer is D, because if there are the exact same organisms that are extinct in these two places, that means that they must have started at a similar place that no longer is connected.


People, animals, and all matter on Earth are

A. drawn toward the center of Earth by the planet's gravity

B. drawn toward other matter on Earth like the trees and the buildings, since all matter has gravity

C. not affected by Earth's gravity because people are so small in
comparison to the planet

D. held to Earth's surface by their own gravity

Answers

Answer:

A

Explanation:

To answer this, we can use process of elimination.

B: This question states that all matter has gravity. This is not correct. All matter is *effected* by gravity, but we do not have gravity inside of us.

C: If this were the case, we would all be floating off into space.

D: Same issue as question B.

In an elastic collision between a moving 10-kg mass and a stationary 10-kg mass half the momentum is transferred to the stationary mass. In this situation the total kinetic energy after the collision is less than it was before the collision. Where did the kinetic energy go?

A) The kinetic energy was destroyed during the collision.

B) Some of the kinetic energy was turned into momentum during the collision.

C) Some of the kinetic energy was turned into heat or used to deform the masses.

D) Some of the kinetic energy was turned into potential energy during the collision.

Answers

Answer: C

Explanation:

USAtestprep

In 2-3 complete sentences, analyze how scientists know dark matter and dark energy exist.

Answers

Answer:

It doesn't interact with baryonic matter and it's completely invisible to light and other forms of electromagnetic radiation, making dark matter impossible to detect with current instruments. But scientists are confident it exists because of the gravitational effects it appears to have on galaxies and galaxy clusters.

Explanation:

You and a friend are playing with a Coke can that you froze so it's solid to demonstrate some ideas of Rotational Physics. First, though, you want to calculate the Rotational Kinetic Energy of the can as it rolls down a sidewalk without slipping. This means it has both linear kinetic energy and rotational kinetic energy. [The freezing only matters because if there is liquid inside, the calculation for the Moment of inertia becomes more complicated]. A Coke can can be modeled as a solid cylinder rotating about its axis through the center of the cylinder. This can has a mass of 0.33 kg and a radius of 3.20 cm. You'll need to look up the equation for the Moment of Inertia in your textbook. It is rotating with a linear velocity of 6.00 meters / second in the counter-clockwise (or positive) direction. You can use this to determine the angular velocity of the can (since it is rolling without slipping). What is the Total Kinetic Energy of the Coke can

Answers

Answer:

  K_{total} = 8.91 J

Explanation:

In this exercise you are asked to find the kinetic energy of the can of coca-cola

         K_total = K_ {Translation} + K_ {rotation}

the translational kinetic energy is

         K_ {translation} = ½ m v²

the kinetic energy of rotation is

         K_ {rotation} = ½ I w²

The moment of inertia of a cylinder is

           I = ½ m r²

we substitute

          K_ {total} = ½ m v² + ½ (½ m r²) w²

angular and linear velocity are related

          v = w r

we substitute

          K_ {total} = ½ m v² + ¼ m r² v² / r²

          K_ {total} = m v² (½ + ¼)

          K_ {total} = ¾ m v²

let's calculate

          K_ {total} = ¾ 0.33 6.00²

           K_{total} = 8.91 J

How does the wave period relate to the frequency of a wave?

Answers

Answer:

its in the picture hope it helps make brainlliest ty

A car is moving with speed 30 m/s and acceleration 4 m/s2 at a given instant. (a) Using a second-degree Taylor polynomial, estimate how far the car moves in the next second.

Answers

Answer:

68 meters moved in the next seconds

Explanation:

Given

[tex]u= 30m/s[/tex]

[tex]a = 4m/s^2[/tex]

Required

Distance covered by the car in the next second

At a point in time t, the current distance is calculated as:

[tex]s(t) = ut + \frac{1}{2}at^2[/tex]

Substitute values for a and u in the above equation.

[tex]s(t) =30 * t + \frac{1}{2} * 4 * t^2[/tex]

[tex]s(t) =30t + 2t^2[/tex]

Next, we generate the second degree Taylor polynomial as follows;

Calculate velocity (s'(t))

Differentiate s(t) to get velocity

[tex]s(t) =30t + 2t^2[/tex]

[tex]s'(t) =30 + 4t[/tex]

Calculate acceleration (s"(t))

Differentiate s'(t) to get acceleration

[tex]s'(t) =30 + 4t[/tex]

[tex]s"(t) =4[/tex]

When t = 0

We have:

[tex]s(0) = 30 * 0 + 2 * 0^2 = 0[/tex]

[tex]s'(0) =30 + 4*0 = 30[/tex]

[tex]s"(0) = 4[/tex]

So, the second degree tailor series is:

[tex]T_2(t) = s(t) * t^0 + s'(t) * \frac{t^1}{1!} + s"(t) * \frac{t^2}{2!}[/tex]

To see the distance moved in the next second, we set t to 1

So, we have:

[tex]T_2(1) = s(1) * 1^0 + s'(1) * \frac{1^1}{1!} + s"(2) * \frac{1^2}{2!}[/tex]

[tex]T_2(1) = s(1) * + s'(1) * \frac{1}{1} + s"(1) * \frac{1}{2}[/tex]

[tex]T_2(1) = s(1) * + s'(1) * 1 + s"(1) * \frac{1}{2}[/tex]

[tex]T_2(1) = s(1) * + s'(1) + \frac{s"(1)}{2}[/tex]

Solving s(1), s'(1) and s"(1)

We have:

[tex]s(1) =30*1 + 2*1^2 = 32[/tex]

[tex]s'(1) =30 + 4*1 = 34[/tex]

[tex]s"(1) =4[/tex]

Hence:

[tex]T_2(1) = 32 + 34 + \frac{4}{2}[/tex]

[tex]T_2(1) = 32 + 34 + 2[/tex]

[tex]T_2(1) = 68[/tex]

A student must analyze data collected from an experiment in which a block of mass 2M traveling with a speed v0 collides with a block of mass M that is initially at rest. After the collision, the two blocks stick together. What applications of the equation for the conservation of momentum represent the initial and final momentum of the system for a completely inelastic collision between the blocks?

Answers

Solution :

In the question, it is given that the collision is inelastic and the blocks stick together.

In an inelastic collision, the linear momentum is conserved but the kinetic energy is not conserved.

The linear momentum is given by :

[tex]$\vec p = m \vec v$[/tex] (mass x velocity)

So according to the conservation of linear momentum,

[tex]$\vec p_{(\text{before collision})}=\vec p_{(\text{after collision})}$[/tex]

Let the velocity after the collision is [tex]$v_F$[/tex]

[tex]$m_1v_0+m_2 \times 0 = m_1v_F+m_2v_F$[/tex]

Putting the values of [tex]$m_1 \text{ and}\ m_2$[/tex]

[tex]$m_1=2M \text{ and}\ m_2=M$[/tex]

∴ [tex]$2Mv_0=2Mv_F+Mv_F$[/tex], as the blocks stick together after the collision.

and  [tex]$2MV_0=3Mv_F$[/tex], as the blocks stick together after the collision.

The diagram shows a charge moving into an electric field. The charge will most likely leave the electric field near which letter? OW OX OY OZ ​

Answers

you haven't attached the diagram, but i assume that this diagram is what you were talking about

Answer:

near Y

Explanation:

the electric field lines goes from a positive charge to a negative charge. This means that a positive charge would move in the same direction of the field lines, while a negative charge would move in the opposite direction of the field lines. the field lines are created from +vely charged plate to -vely charged plate so the negative charged particles moves towards the lower plate which is positively charged, and opposite to the direction of field lines.

The charge will most likely leave the electric field near Y letter. Hence option C is correct.

What is electric charge ?

Electric charge is the physical property of matter that experiences force when it is placed in electric field. F = qE where q is amount of charge, E = electric field and F = is force experienced by the charge. there are two types of charges, positive charge and negative charge which are generally carried by proton and electron resp. like charges repel each other and unlike charges attract each other. the flow charges is called as current. Elementary charge is amount of charge a electron is having, whose value is 1.602 x 10⁻¹⁹ C

The charge on the electron is negative, and the force is directed in the opposite direction as the electric field. When an electron is projected perpendicular to a uniform electric field, it experiences an electric force in the opposite direction of the field.

the trajectory of the charged particle in the electric filed is parabolic and in magnetic field it is circular. when this electron moves perpendicular to the electric field, electron experience force in opposite direction to the electric field and due to parabolic nature, it will leave at Y.

Hence option C is correct.

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Which is a property of bases?

A.
highly metal reactive

B.
sour to the taste

C.
slippery feel

D.
low pH

Answers

Answer:

C. Slippery feel

Explanation:

Slippery feel would be the correct answer (:

5. A 6.0-kilogram mass is moving with a speed of 2.0 m/s. What is the kinetic energy of the mass?

Answers

Answer:

K.E. = ½ × mv²

= ½ × 6 × (2)²

= ½ × 6 × 4

= 3 × 4

= 12 J

An infant's toy has a 120 g wooden animal hanging from a spring. If pulled down gently, the animal oscillates up and down with a period of 0.54 s . His older sister pulls the spring a bit more than intended. She pulls the animal 32 cm below its equilibrium position, then lets go. The animal flies upward and detaches from the spring right at the animal's equilibrium position. Part A If the animal does not hit anything on the way up, how far above its equilibrium position will it go

Answers

Answer:

the wooden animal will go 0.7068 m above its equilibrium

Explanation:

Given the data in the question;

mass of wooden animal m = 120 g = 0.12 kg

the animal oscillates up and down, T = 0.54 s

older sister pulls the animal 32 cm below its equilibrium position;

x = 32 cm = 0.32 m

g = 9.81 m/s²

We know that

k = mω²

where ω = 2π/T

So, k = m( 2π/T )²

we substitute

k = 0.12( 2π / 0.54 )²

k = 0.12 × (11.6355)²

k = 0.12 × 135.38486

k = 16.25 N/c

so Also,

kx²/2 = mgh

we solve for h

h = kx² / 2mg

we substitute

h = ( 16.25 × (0.32)²) / ( 2 × 0.12 × 9.81 )

h = 1.664 / 2.3544

h = 0.7068 m

Therefore, the wooden animal will go 0.7068 m above its equilibrium

g 1. Water flows through a 30.0 cm diameter water pipe at a speed of 3.00 m/s. All of the water in the pipe flows into a smaller pipe that is 10.0 cm in diameter. Determine: a) The speed of the water flowing through the 10.0 cm diameter pipe. b) The mass of water that flows through the larger pipe in 1.00 minute. c) The mass of water that flows through the smaller pipe in 1.00 minute.

Answers

Answer:

a) v₂ = 30 m/s

b) m₁ = 12600 kg

c) m₂ = 12600 kg

Explanation:

a)

Using the continuity equation:

[tex]A_1v_1 = A_2v_2[/tex]

where,

A₁ = Area of inlet = π(0.15 m)² = 0.07 m²

A₂ = Area of outlet = π(0.05 m)² = 0.007 m²

v₁ = speed at inlet = 3 m/s

v₂ = speed at outlet = ?

Therefore,

[tex](0.07\ m^2)(3\ m/s)=(0.007\ m^2)v_2\\\\v_2 = \frac{0.21\ m^3/s}{0.007\ m^2}[/tex]

v₂ = 30 m/s

b)

[tex]m_1 = \rho A_1v_1t[/tex]

where,

m₁ = mass of water flowing in = ?

ρ = density of water = 1000 kg/m³

t = time = 1 min = 60 s

Therefore,

[tex]m_1 = (1000\ kg/m^3)(0.07\ m^2)(3\ m/s)(60\ s)\\[/tex]

m₁ = 12600 kg

c)

[tex]m_1 = \rho A_1v_1t[/tex]

where,

m₂ = mass of water flowing out = ?

ρ = density of water = 1000 kg/m³

t = time = 1 min = 60 s

Therefore,

[tex]m_2 = (1000\ kg/m^3)(0.007\ m^2)(30\ m/s)(60\ s)\\[/tex]

m₂ = 12600 kg

The fictional rocket ship Adventure is measured to be 65 m long by the ship's captain inside the rocket.When the rocket moves past a space dock at 0.5c. As rocket ship Adventure passes by the space dock, the ship's captain flashes a flashlight at 1.20-s intervals as measured by space-dock personnel.

Required:
How often does the flashlight flash relative to the captain?

Answers

Answer:

1.04 s

Explanation:

The computation is shown below:

As we know that

t = t' × 1 ÷ (√(1 - (v/c)^2)

here

v = 0.5c

t = 1.20 -s

So,

1.20 = t' × 1 ÷ (√(1 - (0.5/c)^2)

1.20 = t' × 1 ÷ (√(1 - (0.5)^2)

1.20 = t' ÷ √0.75

1.20 = t' ÷ 0.866

t' = 0.866 × 1.20

= 1.04 s

The above formula should be applied

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