A raft is made of a plastic block with a density of 650 kg/m 3 , and its dimensions are 2.00 m à 3.00 m à 5.00 m. 1. what is the volume of the raft? _________________________________________________________________ 2. what is its mass? _________________________________________________________________ 3. what is its weight? _________________________________________________________________ 4. what is the raft's ap parent weight in water? (hint: density of water = 1.00 à 10 3 kg/m 3 ) _________________________________________________________________ 5. what is the buoyant force on the raft in water? _________________________________________________________________ 6. what is the mass of the displaced water? _________________________________________________________________ 7. what is the volume of the displaced water? _________________________________________________________________ 8. how much of the raft's volume is below water? how much is above? _________________________________________________________________ 9. answer items 5 â 8 using ethanol (density = 0.806 à 10 3 kg/m 3 ) instead of water.

Answers

Answer 1
1) The volume of the raft is the product between the lenghts of its three dimensions:
[tex]V = (2.00 m)(3.00m)(5.00m)=30 m^3[/tex]

2) The mass of the raft is the product between its density, d, and its volume, V:
[tex]m=dV=(650 kg/m^3)(30 m^3)=19500 kg[/tex]

3) The weight of the raft is the product between its mass m and the gravitational acceleration, [tex]g=9.81 m/s^2[/tex]:
[tex]W=mg=(19500 kg)(9.81 m/s^2)=1.91 \cdot 10^5 N[/tex]

4) The apparent weight is equal to the difference between the weight of the raft and the buoyancy (the weight of the displaced fluid):
[tex]W_a = W- \rho_W V_{disp} g[/tex]
where [tex]\rho _W = 1000 kg/m^3[/tex] is the water density and [tex]V_{disp}[/tex] is the volume of displaced fluid.
The density of the raft ([tex]650 kg/m^3[/tex]) is smaller than the water density ([tex]1000 kg/m^3[/tex]), this means that initially the buoyancy (which has upward direction) is larger than the weight (downward direction) and so the raft is pushed upward, until it reaches a condition of equilibrium and it floats. At equilibrium, the weight and the buoyancy are equal and opposite in sign:
[tex]W=B=\rho _W V_{disp} g[/tex]
and therefore, the apparent weight will be zero:
[tex]W_a = W-B=W-W=0[/tex]

5) The buoyant force B is the weight of the displaced fluid, as said in step 4):
[tex]B=\rho_W V_{disp} g[/tex]
When the raft is completely immersed in the water, the volume of fluid displaced [tex]V_{disp}[/tex] is equal to the volume of the raft, [tex]V_{disp}=V[/tex]. Therefore the buoyancy in this situation is
[tex]B= \rho_W V g = (1000 kg/m^3)(30 m^3)(9.81 m/s^2)=2.94 \cdot 10^5 N[/tex]
However, as we said in point 4), the raft is pushed upward until it reaches equilibrium and it floats. At equilibrium, the buoyancy will be equal to the weight of the raft (because the raft is in equilibrium), so:
[tex]B=W=1.91 \cdot 10^5 N[/tex]

6) At equilibrium, the mass of the displaced water is equal to the mass of the object. In fact, at equilibrium we have W=B, and this can be rewritten as
[tex]mg = m_{disp} g[/tex]
where [tex]m_{disp}= \rho_W V_{disp}[/tex] is the mass of the displaced water. From the previous equation, we obtain that [tex]m_{disp}=m=19500 kg[/tex].

7) Since we know that the mass of displaced water is equal to the mass of the raft, using the relationship [tex]m=dV[/tex] we can rewrite [tex]m=m_{disp}[/tex] as:
[tex]d V =d_W V_{disp}[/tex]
and so
[tex]V_{disp}= \frac{d V}{d_W}= \frac{(650 kg/m^3)(30m^3)}{1000kg/m^3}= 19.5 m^3 [/tex]

8) The volume of water displaced is (point 7) [tex]19.5 m^3[/tex]. This volume is now "filled" with part of the volume of the raft, therefore [tex]19.5 m^3[/tex] is also the volume of the raft below the water level. We can calculate the fraction of raft's volume below water level, with respect to the total volume of the raft, [tex]30 m^3[/tex]:
[tex] \frac{19.5 m^3}{30 m^3}\cdot 100= 65 \% [/tex]
Viceversa, the volume of raft above the water level is [tex]30 m^3-19.5 m^3 = 10.5 m^3[/tex]. Therefore, the fraction of volume of the raft above water level is
[tex] \frac{10.5 m^3}{30 m^3}\cdot 100 = 35 \% [/tex]

9) Let's repeat steps 5-8 replacing [tex]\rho _W[/tex], the water density, with [tex]\rho_E=806 kg/m^3[/tex], the ethanol density.

9-5) The buoyant force is given by:
[tex]B=\rho _E V_{disp} g = (806 kg/m^3)(30 m^3)(9.81 m/s^2)=2.37 \cdot 10^5 N[/tex]
when the raft is completely submerged. Then it goes upward until it reaches equilibrium and it floats: in this condition, B=W, so the buoyancy is equal to the weight of the raft.

9-6) Similarly as in point 6), the mass of the displaced ethanol is equal to the mass of the raft: 
[tex]m_E = m = 19500 kg[/tex]

9-7) Using the relationship [tex]d= \frac{m}{V} [/tex], we can find the volume of displaced ethanol:
[tex]V_E = \frac{m}{d_E} = \frac{19500 kg}{806 kg/m^3}=24.2 m^3 [/tex]

9-8) The volume of raft below the ethanol level is equal to the volume of ethanol displaced: [tex]24.2 m^3[/tex]. Therefore, the fraction of raft's volume below the ethanol level is 
[tex] \frac{24.2 m^3}{30 m^3}\cdot 100 = 81 \% [/tex]
Consequently, the raft's volume above the ethanol level is 
[tex]30 m^3 - 24.2 m^3 = 5.8 m^3[/tex]
and the fraction of volume above the ethanol level is
[tex] \frac{5.8 m^3}{30 m^3}\cdot 100 = 19 \% [/tex]

Related Questions

People are able to hear footsteps because the sound made by a foot hitting the floor travels through the air to reach their ears. is this absorption or transmission

Answers

The answer is transmission.

Answer: The correct answer is transmission.

Explanation:

Sound is a form of energy. The energy that survives the transfer is called the sound transmission. If the energy gets absorb then the sound is not heard to the listener. In this case, the absorption will occur.

People are able to hear footsteps because the sound made by a foot hitting the floor travels through the air to reach their ears.  In this case, the sound transmission will occur as the footsteps can be heard. It means that the energy is transferred here.    

A dam is a structure built across a river to hold back the river's water. The flow of water through a dam is controlled by gates. When the gates are closed, water is held at a greater height than it would otherwise occupy.

The water has_________ energy when the gates are closed due to its height. This energy is transformed into _______energy when the gates open and the water begins to flow downward.

Answers

Potential is the first blank and kinetic is the second blank. 

This should be correct

potential is the first one kinetic is the second

A 9cm diameter spherical ball whose surface is maintained at a temperature of 110c is

Answers

Final answer:

The question involves concepts of heat transfer and thermal equilibrium in physics, where two spheres reach thermal equilibrium through the transfer of heat, and how a spherical object equilibrates with its ambient temperature.

Explanation:

The question appears to be related to the concept of heat transfer and thermal equilibrium in Physics, specifically involving spherical objects and changes in their temperatures when placed in different environments or in contact with each other.

When considering two spheres of the same material but at different initial temperatures brought into thermal contact, the process involves the transfer of thermal energy from the hotter sphere to the cooler one until they reach a state of thermal equilibrium. This principle is grounded in the second law of thermodynamics, which states that heat energy flows from areas of high temperature to areas of low temperature until thermal equilibrium is achieved. The final temperature reached by both spheres depends on their masses and specific heat capacities, as well as their initial temperatures.

The phenomenon of thermal equilibrium is also apparent when exposing a spherical object to a different ambient temperature, as mentioned in parts of the question. The rate of heat transfer and the time taken for the sphere to reach the temperature of its surroundings can be analyzed using thermodynamics and heat transfer equations, including concepts like conduction, convection, and radiation.

A child sitting 1.20 m from the center of a merry-go-round moves with a speed of 1.35 m/s. (a) calculate the centripetal acceleration of the child.

Answers

The centripetal acceleration in an uniform circular motion is given by

a = V² / r

Where V is the speed and r the radius of the circle (distance to the center)

a = (1.35 m/s)² / 1.2m  = 1.519 m/s²

Which term is used to describe water that is evaporated, polluted, or used by crops? A. degenerated B. consumptive C. controlled D. processed

Answers

The correct answer is (B) Consumptive.

Explanation:
"Consumptive use" is the term used in the field of Water Science to define "the part of water withdrawn that is evaporated, given off by plants, used by crops, consumed by humans or livestock, or otherwise removed from the immediate water environment. It is also referred as water consumed." Hence the correct answer is (b) Consumptive.

Bats use ultrasound in echolocation. This sound is characterized by _____.

A. low frequency
B. low amplitude
C. high frequency
D. high amplitude

Answers

High frequency, as humans cannot hear the sound of the bats using echolocation because of it's such high frequency.
Hope this helps :)

Answer:

C. high frequency  

Explanation:

Bats use high frequency sound waves -ultra sound (20 to 200 kHz) to locate their prey via a technique -echolocation. The produce these sound waves and when the waves reflect from a prey nearby, they are able to estimate the size, position and speed of their prey. The human hearing range is up to 20 kHz, so we can hear the sound produced by some of the bats.

A tungsten wire is 4.5 m long and 0.55 mm in diameter. what is its resistance?

Answers

First you need to know the formula for resistance, which is:

[tex]R=[/tex] ρ  [tex]\frac{L}{A} [/tex]    --- (A)

Where,
ρ = Resistivity 
L = length 
A = Area

ρ = Resistivity of tungsten = 5.28 x [tex]10^{-8}[/tex] Ωm
L = Length = 4.5 m
A = Area = 0.55 * [tex]10^{-3}[/tex] * π

Plug-in the values in equation(A), you would get:

[tex]Resistance = \frac{5.28 *10^{-8} * 4.5}{0.55 * 10^{-3} * \pi } [/tex]

[tex]Resistance = 1.375 * 10^{-4} [/tex]Ω

A proton and an electron have the same kinetic energy upon entering a region of constant magnetic field. What is the ratio of the radii or their circular paths?

Answers

The Lorentz force on a particle of charge q produced by a magnetic field is
[tex]F=qvB[/tex]
where v is the velocity of the particle and B the intensity of the magnetic field.
Due to this force, the particle will acquire a circular motion, so this force will be the centripetal force of the motion:
[tex]m \frac{v^2}{r} = qvB[/tex]
where m is the mass of the particle, and [tex]r[/tex] the radius of the trajectory.
Re-arranging we have
[tex]r= \frac{mv}{qB} [/tex]

So, we have to find r for both the proton and the electron. We know that the two particles have same kinetic energy:
[tex]K_p = K_e[/tex]
and so
[tex] \frac{1}{2} m_p v_p^2 = \frac{1}{2}m_e v_e^2 [/tex]
The mass of the proton is 1833 times the mass of the electron ([tex]m_p = 1.67 \cdot 10^{-27} kg[/tex], [tex]m_e = 9.11 \cdot 10^{-31}kg[/tex]), i.e.
[tex]m_p = 1833 m_e[/tex]
and so from the relationship between the kinetic energies we find:
[tex]v_p = v_e \sqrt{ \frac{m_e}{m_p} }= v_e \sqrt{ \frac{m_e}{1833 m_e} } = \frac{v_e}{42.8} [/tex]

Now we can calculate the ratio between the radius of the proton and electron trajectories. Keeping in mind that q is the same for proton and electron, and the field B is the same, we have
[tex] \frac{r_p}{r_e} = \frac{m_p v_p}{m_e v_e}= \frac{(1833 m_e)( \frac{v_e}{42.8}) }{m_e v_e}=42.8 [/tex]
So, the radius of the proton trajectory is 42.8 times the radius of the electron trajectory.
Final answer:

The ratio of the radii of the circular paths of a proton and an electron with the same kinetic energy in a constant magnetic field can be determined using the formula for the radius of curvature of a charged particle in a magnetic field.

Explanation:

The ratio of the radii of the circular paths of a proton and an electron with the same kinetic energy in a constant magnetic field can be determined using the formula for the radius of curvature of a charged particle in a magnetic field. The formula is:

r = mv / (qB)

Where:

r is the radius of curvature m is the mass of the particle v is the velocity of the particle q is the charge of the particle B is the magnetic field strength

Since the kinetic energy of the proton and electron is the same, their velocities will be different due to their different masses. This means that the ratio of their radii of curvature will be different. To find the ratio, we can use the formula:

r_proton / r_electron = (m_electron / m_proton) * (v_proton / v_electron)

Where:

r_proton is the radius of curvature of the proton r_electron is the radius of curvature of the electron m_electron is the mass of the electron m_proton is the mass of the proton v_proton is the velocity of the proton v_electron is the velocity of the electron

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The chemical equation shown represents photosynthesis. Carbon dioxide plus A plus light with a right-pointing arrow towards B plus oxygen. The arrow has an x above it. What is the role of substance B in photosynthesis?

It stores chemical energy.
It converts light into chemical energy.
It traps light energy from the atmosphere.
It cools the atmosphere by changing into vapor.

Answers

I don't know the exact answer but I know it is NOT D or C, I am shooting for A but I may be wrong.    A
the answer is a. i think

Which law of motion accounts for the following statement?

"The gravity of the Sun causes the planets to move in a circular path."

first law
second law
third law

Answers

i know that its not the second law. I'm almost positive its the first one. Please let me know if I'm wrong. This sentence makes no sense when you put it with the third law. So, the first law is my guess...

Answer:

First law

Explanation:

The gravity of the Sun causes the planets to move in a circular path. This is due to first law of motion. The first law states that an object will be at rest and an object will be in motion until no external force acts on it.

It is possible due to sun's gravity pull that the planets move in a circular path. Without sun's gravity the planet would move in a straight line. Hence, the correct option is (a) " first law of motion".

In a hydraulic system, piston 1 has a surface area of 100 cm2, and piston 2 has a surface area of 900 cm2. A force of 150 N is exerted on piston 1 of the hydraulic lift. What force will be exerted on piston 2?

Answers

From Pascal's law, we can say that the pressure exerted by piston 1 on the fluid will be transmitted with equal intensity to piston 2:
[tex]p_1 = p_2[/tex] (1)

The relationship between the pressure applied p, the force applied F and the surface A is
[tex]p= \frac{F}{A} [/tex]

So we can rewrite (1) as
[tex] \frac{F_1}{A_1}= \frac{F_2}{A_2} [/tex]
And from this, we can find the magnitude of the force exerted on piston 2, F2:
[tex]F_2 = A_2 \frac{F_1}{A_1}=(900 cm^2) \frac{150 N}{100 cm^2}=1350 N [/tex]

response to an unconditioned stimulus that occurs naturally without learning is known as a(n) __________ response.

A.
neutral
B.
conditioned
C.
reconditioned
D.
unconditioned

Answers

The answer is D. Unconditioned
The response to an unconditioned stimulus that occurs naturally without learning and involuntarily triggers reaction is known as an unconditioned response. For example, you smell your favorite food while being cook may make you instantly feel hungry.  

Answer:

the answer is c

A switch that connects a battery to a 30μf capacitor is closed. several seconds later you find that the capacitor plates are charged to ±30μc. part a what is the emf of the battery?

Answers

You can find the emf of the battery by using:

Q = CV.

Q = Charge in capacitor plates = 30μC
C = Capacitance of the capacitor = 30μF

V = Q/C = 30/30 = 1V

Ans: The emf of the battery = 1V.
Final answer:

Using the formula for the voltage across a capacitor (V = Q/C), and given the charge on the capacitor (Q) and its capacitance (C), we find that the emf of the battery is 1 Volt.

Explanation:

The question is asking for the electromotive force (emf) of the battery. To determine this, we apply the formula for voltage across a capacitor: V = Q/C, where V is the voltage (or in this case, the emf of the battery), Q is the charge on the capacitor, and C is the capacitance of the capacitor.

Given Q = ±30µC (or 30x10^-6 C) and C = 30µF (or 30x10^-6 F), we substitute these values into the formula:  

V = (30x10^-6) / (30x10^-6)  

Therefore, the emf of the battery is 1 Volt.

This means that when the battery is fully charged, the voltage across the capacitor is also 1 Volt.

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Which resistor dissipates the most power, the one with the greatest resistance or the one with the least resistance? explain why this should be?

Answers

Final answer:

The resistor that dissipates the most power varies depending on the configuration of the circuit. In a series circuit, the resistor with the greatest resistance dissipates the most power due to the greater voltage drop across it. In a parallel circuit with a constant voltage source, the resistor with the smallest resistance dissipates the most power because it allows for the greatest current.

Explanation:

In a circuit, power dissipation is based on the formula, P = IV, also known as Joule's law. Substituting Ohm's law (V = IR) into this formula gives us a better understanding of how resistance affects power. This results in the formula P = I²R, meaning that power is directly proportional to the resistance when current is constant.

Therefore, a higher resistor value would, in theory, dissipate more power. However, in a series circuit where every resistor has the same current flowing through them, the resistor providing the greatest resistance will have the highest voltage (V) drop, hence dissipating more power.

Conversely, if the resistors are connected in parallel, the smallest resistor dissipates more power because it allows for the greatest current, provided the voltage source remains constant.

The discussion on power dissipation in resistors links to the P = V²/R equation, suggesting that lower resistance yields higher power when voltage is consistent. Therefore, your circuit configuration and the constants in the equation play crucial roles in determining which resistor dissipates the most power.

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The power dissipated by a resistor depends on whether the voltage or current is constant. With constant voltage, a lower resistance dissipates more power. With constant current, a higher resistance dissipates more power.

To determine which resistor dissipates the most power, we need to consider the power dissipation formulas. Power in a resistor can be calculated using two key formulas:

P = V² / R and P = I² R.

P = V² / R: When the voltage (V) across the resistor is constant, power decreases as resistance (R) increases. Therefore, with the same voltage applied, a resistor with a lower resistance will dissipate more power.

P = I² R: When the current (I) through the resistor is constant, power increases as resistance increases. Therefore, with the same current, a resistor with a higher resistance will dissipate more power.

These two formulas may seem contradictory at first, but they apply in different scenarios. In a circuit where voltage is constant, a lower resistance leads to higher power dissipation. In contrast, in a circuit where current is constant, a higher resistance leads to higher power dissipation.

Therefore, whether a resistor with the greatest or least resistance dissipates the most power depends on whether the voltage across the resistor or the current through the resistor is constant.

Explain how the lenses in refracting telescopes help scientists to see enlarged images of celestial objects

Answers

The objective lens makes a small real image of the object so that the eyepiece lens can act as a magnifying glass and produce an enlarged image of the objective lens's image. This is how

What is Refracting telescopes  ?

Refracting telescopes typically use two convex lenses one is objective lenses and the other is an eyepieces.

Enlargement is related to the magnification and magnification is directly proportional to the focal length of the objective lens. The objective have large focal length in order to see distant objects as enlarged .The objective  lens collects light from a distant object and brings that light to a focal point to create an image. Hence it ensures large magnification of the distant object

The refracting telescope works by bending light with lenses. The objective lens makes a small real image of the object so that the eyepiece lens can act as a magnifying glass and produce an enlarged image of the objective lens's image

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Use the diagram to answer the question. What happens at night?


Answers

The return flow goes to the right and instead of sea breeze, there's land breeze.

Answer:

Land breeze occurs at night

Explanation:

Land breeze is usually defined as the wind that blows from the land areas to the ocean surface. It occurs during the night time. It is because the land areas have the ability to release heat at a faster rate, in comparison to the ocean water bodies. When the land areas cools, the wind carries the cold and denser prevailing air and reaches the ocean surface in order to balance the warm rising air from the oceans. This is how the heat on earth is being balanced by the simultaneous occurrence of land and sea breeze.

Radioactive carbon, or C-14, is used to date fossil remains. When C-14 decays, as seen in the nuclear equation, it produces what nuclide of nitrogen? A) N-7 B) N-13 C) N-14 D) N-15

Answers

The reaction of radiodecay of carbon C-14 is
C-14 --> N-14 + e- + (ve)
where e- is an electron and (ve) is an electron-type antineutrino.
Basically, when the carbon nucleus (atomic number: 6, mass number: 14) decays, a neutron of the nucleus converts into a proton (therefore, the mass number remains the same, 14, but the atomic number increases by 1, therefore it becomes nitrogen) and releases an electron-antineutrino pair. 

So, the correct answer is C), N-14.

Answer:

the answer is c

Explanation:

i did it on usatestprep

A baby is born with an extra chromosome in each of its cells. Which of the following is responsible for this condition?

A.Albinism
B.Mutations
C.Segregation
D.Gene therapy

Answers

THE ANSWER YOU ARE LOOKING IS

(B) MUTATIONS ARE RESPONSIBLE FOR THIS

Answer:

Mutation is correct

Explanation:

A terrorist throws a grenade with a 6.00 second fuse off a building 150.0 m high at a speed of 10.0 m/s. If the angle at which the grenade is thrown is 30° below the horizontal, will the grenade explode before hitting the ground? What is the horizontal distance from the building at which the grenade will land.

Answers

Here we have a projectile motion. It is type of motion that is made of a vertical shot and a horizontal shot. This is how we will solve it.

Firste step is to find horizontal and vertical component of a speed.
[tex] v_{0x} =v_{0} * cos \alpha [/tex] \\ v_{0y} = v_{0} * sin \alpha [/tex]

We are given this information:
[tex]v_{0} = 10 m/s \\ h=150m \\ \alpha =-30°[/tex]
Angle is negative because it is below the horizontal.

VERTICAL SHOT
Time needed for a grenade to fall to the bottom of a building is given by a formula:
[tex]t= \frac{ v_{0y} }{g} \\ t= \frac{v_{0} * sin \alpha}{g} \\ t= \frac{-10*sin(-30)}{9.81} \\ t=0.51s[/tex]
We used negative value for a speed because it is considered that upwards shot has positive value and downwards shot has negative value.

The grenade will not explode before it hits the ground.


HORIZONTAL SHOT
The horizontal distance from the building at which the grenade will land is called range. The formula for a range is given by:
[tex]R= v_{0x} * \sqrt{ \frac{2h}{g} } \\ R=v_{0} * cos \alpha* \sqrt{ \frac{2h}{g} } \\ R=10*cos(-30)* \sqrt{ \frac{2*150}{9.81} } \\ R=47.89m[/tex] 

The grenade will hit the ground at distance of 47.89m.

A woman wearing snowshoes stands safely in the snow. If she removes her snowshoes, she quickly begins to sink. Explain what happens in terms of force and pressure.

Answers

The purpose of snowshoes is to widen the area pressure is applied on. When you wear plain shoes, the area of distribution of force is concentrated into a small area, namely the area of the shoes you are wearing. Now when pressure is applied on snow surface, it tends to crumble. The force of you standing is concentrated on the space your shoe occupies, increasing the pressure on that specific area. 

Now when you wear snowshoes, you widen the area and the pressure is then distributed over that area lessening the force on specific points. 


A thermometer is taken from an inside room to the outside, where the air temperature is 30° f. after 1 minute the thermometer reads 80° f, and after 5 minutes it reads 55° f. what is the initial temperature of the inside room? (round your answer to two decimal places.)

Answers

Final answer:

To determine the initial temperature of the inside room, we can convert the given temperatures from Fahrenheit to Celsius and calculate the temperature change. By using the temperature change and the final temperature in Celsius, we can find the initial temperature in Celsius. The initial temperature of the inside room is approximately 27.22°C.

Explanation:

To find out the initial temperature of the inside room, we can use the relationship between Fahrenheit and Celsius scales. We know that 30°F is equal to -1.11°C, and 80°F is equal to 26.67°C. By converting these temperatures to Celsius, we can determine the temperature change. Then, using the final temperature of 55°F, we can calculate the initial temperature using the temperature change.



To convert Fahrenheit to Celsius, we use the formula:



TC = (TF - 32) × (5/9)



By plugging in the given temperatures, we find:



TC1 = (30 - 32) × (5/9) ≈ -1.11°C



TC2 = (80 - 32) × (5/9) ≈ 26.67°C



Next, we calculate the temperature change:



ΔT = TC2 - TC1 = 26.67 - (-1.11) = 27.78°C



Finally, we use ΔT and the final temperature (TC=55°C) to find the initial temperature:



Initial temperature = final temperature - ΔT



Initial temperature ≈ 55 - 27.78 ≈ 27.22°C

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Find the Voltage drop (in mV) across an 46.6 m long copper wire with diameter of 1.11 mm and with 47.6 miliAmps of current running through it. (The resistivity of copper at room temperature is 1.68×10-8 Ohm×meter). Express the answer (only numerical value) to the nearest whole number.

Answers

First we need to calculate the resistance of this piece of wire. For a wire with resistivity [tex]\rho[/tex], length L and cross section A, the resistance is
[tex]R= \frac{\rho L}{A} [/tex]
The diameter d of the wire is [tex]d=1.11 mm=1.11 \cdot 10^{-3} m[/tex], so the cross sectional area is
[tex]A=\pi ( \frac{d}{2} )^2=9.7 \cdot 10^{-7} m^2[/tex]
Now, using [tex]L=46.6 m[/tex] and [tex]\rho=1.68 \cdot 10^{-8} \Omega m[/tex], we can calculate the resistance:
[tex]R= \frac{\rho L}{A}= \frac{(1.68 \cdot 10^{-8} \Omega m)(46.6 m)}{9.7 \cdot 10^{-7}m^2} =0.807 \Omega [/tex]

And now we can calculate the voltage drop across the resistor, by using Ohm's law, since we know the current flowing through it: [tex]I=47.6 mA=47.6 \cdot 10^{-3} A[/tex]
[tex]V=IR=(47.6 \cdot 10^{-3} A)(0.807 \Omega)=0.038 V=38 mV[/tex]

To grasp how weak this field is, if you wanted to produce it between two parallel metal plates by connecting an ordinary 1.5 v aa battery across these plates, how far apart would the plates have to be?

Answers

10 ft because the have to be connected

The distance between two parallel metal plates to create an electric field equivalent to that inside a 1.5V AA battery can be calculated using the formula E = V/d. Without a specific electric field strength value, the exact distance can't be provided. However, due to the low voltage of the battery, the necessary plate separation would be extremely small.

The question is asking how far apart two parallel metal plates must be to create an electric field equivalent to the electric field within a 1.5V AA battery, given that the electric field is uniform. To find out the distance between the plates, we need to use the formula for electric field strength, E = V/d, where E is the electric field strength, V is the potential difference, and d is the distance between the plates.

Since we know the voltage (V) from the AA battery is 1.5 V and we are looking for d, we can rearrange the formula to d = V/E. However, we don't have the value of the electric field strength E inside the battery. If we had a reference value, for example, electric field magnitude from another setup, we could use it to solve for d. For instance, if we knew that the electric field between two plates with a certain separation was, let's say, 4.50  imes 103 V/m for a 15.0 kV potential difference, we could find their distance and then extrapolate for the 1.5V scenario.

Without specific numbers, we cannot provide the exact distance for the plates. However, it's important to realize that the electric field strength would be very small compared to typical laboratory setups due to the low voltage of the AA battery. Hence, the plates separation would have to be extremely small to match the electric field inside the battery.

How fast (in rpm) must a centrifuge rotate if a particle 6.00 cm from the axis of rotation is to experience an acceleration of 113000 g's? if the answer has 4 digits or more, enter it without commas,
e.g. 13500?

Answers

The acceleration experienced by the particle is given by
[tex]a=113000 g=113000 \cdot 9.81 m/s^2[/tex]
This corresponds to the centripetal acceleration of the motion, which is related to the angular speed [tex]\omega[/tex] of the particle and its distance r from the axis by the relationship
[tex]a= \omega ^2 r [/tex]
In our problem, [tex]r=6 cm=0.06 m[/tex], so we can solve for [tex]\omega[/tex]:
[tex]\omega = \sqrt{ \frac{a}{r} } = \sqrt{ \frac{113000 \cdot 9.81 m/s^2}{0.06 m} }=4298 rad/s [/tex]
However, we must convert it into rpm (revolution per minute).
We know that 1 rad corresponds to [tex]( \frac{1}{2 \pi} )[/tex] revolutions, while [tex]1 s = \frac{1}{60} min[/tex]. So we the conversion is[tex]\omega = 4298 rad/s \cdot ( \frac{1}{2\pi} rev/rad )( 60 s/min)=41067 rpm[/tex]

A 0.450-kg hammer is moving horizontally at 7.00 m/s when it strikes a nail and comes to rest after driving the nail 1.00 cm into a board. (a) calculate the duration of the impact. (b) what was the average force exerted on the nail?

Answers

(a) The duration of impact of the hammer is [tex]\fbox{\begin\\1.43 \times {10^{ - 3}}\,{\text{s}}\end{minispace}}[/tex] .

(b) The average force exerted on the nail is [tex]\fbox{\begin\\2205\,{\text{N}}\end{minispace}}[/tex].

Further explanation:

When hammer hit the nail it got impacted by the hit and get into the board. This insertion in the board take time which is called duration of impact. The force exerted on the nail is directly proportional to the acceleration of the nail.

Given:

The speed of hammer is [tex]7\,{\text{m/s}}[/tex].

The distance of nail which is inserted in the board is [tex]1\,{\text{cm}}[/tex].

The mass of the hammer is [tex]0.450\,{\text{Kg}}[/tex].

Concept used:

The rate of change of displacement of a body in unit time is called speed of the body. It is a scalar quantity.

The expression for the speed of the body is given as.

[tex]v = \dfrac{s}{t}[/tex]

Rearrange the above expression for the time.

[tex]t=\dfrac{s}{v}[/tex]                                               …… (1)

Here, [tex]s[/tex]  is the distance covered, [tex]v[/tex]  is the speed of body and [tex]t[/tex]  is the time.

According to Newton’s second law of motion “the rate of change of momentum is equal to the force applied on the body.”

The expression for the newton’s law is given as.

[tex]F = ma[/tex]                                          ……. (2)

The expression for the acceleration of the body is given as.

[tex]\fbox{\begin\\a = \dfrac{{\left( {v - u} \right)}}{t}\end{minispace}}[/tex]                                           …… (3)

Here, [tex]u[/tex]  is the initial velocity and [tex]v[/tex]  is the final velocity.

Substitute [tex]1\,{\text{cm}}[/tex] for [tex]s[/tex] and [tex]7\,{\text{m/s}}[/tex]  for [tex]v[/tex] in equation (1).

[tex]\begin{aligned}t&=\frac{{1\,{\text{cm}}}}{{7\,{\text{m/s}}}}\\&=\frac{{1\,{\text{cm}}\left( {\frac{{1\,{\text{m}}}}{{100\,{\text{cm}}}}} \right)}}{{7\,{\text{m/s}}}}\\&=1.43 \times {10^{ - 3}}\,{\text{s}} \\ \end{aligned}[/tex]

Substitute [tex]1.43 \times {10^{ - 3}}\,{\text{s}}[/tex] for [tex]t[/tex], for[tex]0\,{\text{m/s}}[/tex]  and [tex]v[/tex]  for  in equation (3).

[tex]\begin{gathered}a= \frac{{\left( {0\,{\text{m/s}} - 7\,{\text{m/s}}} \right)}}{{\left( {1.43 \times {{10}^{ - 3}}\,{\text{s}}} \right)}} \\= \left( { - 4900\,{\text{m/}}{{\text{s}}^{\text{2}}}} \right) \\ \end{gathered}[/tex]

Substitute[tex]\left( { - 4900\,{\text{m/}}{{\text{s}}^{\text{2}}}} \right)[/tex] for [tex]a[/tex]  and [tex]0.450\,{\text{Kg}}[/tex]  for [tex]m[/tex]  in equation (2).

[tex]\begin{aligned}F&=\left( {0.450\,{\text{Kg}}} \right)\left( { - 4900\,{\text{m/}}{{\text{s}}^{\text{2}}}} \right)\\&=- 2209\,{\text{N}} \\ \end{aligned}[/tex]

Thus, the duration of impact is[tex]1.43 \times {10^{ - 3}}\,{\text{s}}[/tex]  and the force exerted on the nail is [tex]2209\,{\text{N}}[/tex]  in the opposite direction.

Learn more:

1.  Motion under friction https://brainly.com/question/7031524.

2.  Conservation of momentum https://brainly.com/question/9484203.

3. Force on a body https://brainly.com/question/6125929.

Answer Details:

Grade: College

Subject: Physics

Chapter: Kinematics

Keywords:

Acceleration, force, acceleration due to gravity, friction, normal, weight, mass, motion, impact, nail, hammer, acceleration, duration of impact, 0.450 kg, 7 m/s, 2205 N,1.429*10^-3 sec, 1.43*10^-3 sec.

The duration of the impact is 0.133 seconds.

The average force exerted on the nail was 5800 N.

(a) Let's use the following equations to solve this problem:

m = 0.450 kg

v_i = 7.00 m/s

v_f = 0 m/s

d = 0.01 m

where:

m is the mass of the hammer

v_i is the initial velocity of the hammer

v_f is the final velocity of the hammer (after it strikes the nail)

d is the distance that the nail is driven into the board

We know that the hammer comes to rest after it strikes the nail, so v_f = 0. We can also set the kinetic energy of the hammer before the impact equal to the work done by the force exerted by the nail on the hammer during the impact.

[tex]KE_i = W\dfrac{1}{2}mv_i^2 = Fd\dfrac{1}{2}(0.450 kg)(7.00 m/s)^2 = F(0.01 m)F = 5800 N[/tex]

The duration of the impact can be calculated using the following equation:

[tex]t = \dfrac{d}{v_i}t = \dfrac{0.01 m}{7.00 m/s}t = 0.0133 s[/tex]

(b) The average force exerted on the nail is equal to the force exerted by the hammer on the nail divided by the duration of the impact.

F_avg = F / t

F_avg = 5800 N / 0.0133 s

F_avg = 5800 N

Therefore, the average force exerted on the nail was 5800 N.

To know more about the Board, here

https://brainly.com/question/34682939

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When two notes are played simultaneously, creating a discordant sound, it is called _____.

A. Acoustics
B. Consonance
C. Timbre
D. Dissonance

Answers

Answer:

The correct answer is option D.

Explanation:

Acoustic : A branch of physics which study the properties of sound.

Consonance: Combination of notes occurring simultaneously due to relationship between their respective frequencies.

Timbre: A characteristic of a musical note which makes it distinct from another wave which also have same pitch and intensity.

Dissonance :When combination of two notes are played simultaneously with lack of harmony in between them.

Hence, the correct answer is option D.

Answer:

D. DISSONANCE

Explanation:

Anna is conducting an experiment to determine how weather affects cell phone reception. She is trying to decide the best way to conduct her experiment in order to collect meaningful data. Which of the following experiments would help Anna collect the best data? A. Test different cell phones in different locations on days with clear weather. B. Test different cell phones in different locations on days with rainy weather. C. Test a cell phone's reception in one location with clear weather and in another location with rainy weather. D. Test a cell phone's reception in the exact same location under various atmospheric conditions.

Answers

Answer:

D. Test a cell phone's reception in the exact same location under various atmospheric conditions

Explanation:

Components of an experiment:

Independent variable:

A manipulated variable, in an experiment or study, whose presence or degree incurs a change in the  dependent variable.

Dependent variable:

A variable which is being studied in the experiment and is supposed to change with respect to the independent variable.

Control variable:

Control variable includes the variables which are of no concern in the experiment and must be constant so that they do not interfere with the results of the experiment. Change in control variable might affect the results of an experiment.

In Anna's experiment, the independent variable is the atmospheric conditions. The dependent variable is cell phone reception that will change according to the atmospheric conditions. All other things related to the experiment are control variables like cellphone, location of the cell phone. Both of these must stay constant to collect the best data.

Hence, the best option is D.

Answer:

D. Test a cell phone's reception in the exact same location under various atmospheric conditions

Explanation:

An atomic nucleus has a charge of +40e. an electron is 10-9 m from the nucleus. what is the force on the electron?

Answers

The electron charge is equal to [tex]-e=-1.6\cdot 10^{-19}C[/tex]. The atomic nucleus of the problem has a charge of [tex]+40 e=40\cdot (1.6\cdot 10^{-19}C)=6.4\cdot 10^{-18}C[/tex]. The distance between the nucleus and the electron is [tex]r=10^{-9}m[/tex], so we can calculate the electrostatic (Coulomb) force between the two:
[tex]F=k_e \frac{(-e)(+40e) }{r^2} =8.99\cdot 10^9 Nm^2C^{-2} \frac{(-1.6\cdot 10^{-19}C)(6.4\cdot 10^{-18}C)}{(10^{-9}m)^2} =[/tex]
[tex]=-9.2 \cdot 10^{-9} N[/tex]
which is attractive, since the two charges have opposite sign.
Final answer:

The force on an electron placed 10-9 m away from a nucleus with a charge of +40e can be calculated using Coulomb's law, considering the charge of the electron and the proton, the distance between them, and Coulomb's constant.

Explanation:

The question pertains to the force experienced by an electron in the vicinity of an atomic nucleus with a charge of +40e. To calculate this force, we will use Coulomb's law, which states that the electric force (F) between two point charges is directly proportional to the product of the charges (q1 and q2) and inversely proportional to the square of the distance (r) between them. The formula is given by F = k * |q1 * q2| / r², where k is Coulomb's constant (8.9875 × 10⁹ N⋅m²/C²).

Given that the charge of a proton (and thus the atomic number Z) is +e and the charge of an electron is -e, the force will be attractive, and we can ignore the signs for magnitude calculation. The charge of a proton is e = 1.602 × 10⁻¹⁹ C. For a +40e charge, the total charge is 40 × e. Plug these values, along with the given distance of 10 × 10⁻¹ m into Coulomb's law to compute the force on the electron.

Therefore, the magnitude of the force on the electron by a nucleus with a charge of +40e located 10⁻¹ m away can be calculated using the steps above.

In a heat engine, if 500 j of heat enters the system, and the piston does 300 j of work, what is the final internal (thermal) energy of the system if the initial energy is 1500 j ?

Answers

The answer is 1,700 J.

A weight suspended from a spring is seen to bob up and down over a distance of 25 cm twice each second. what is its frequency? answer in units of hz.

Answers

For the frequency it is computed by 2 bobs/second which is equal to 2 Hz.Whereas the period is compute by 1/freq = 1/2 secondAnd lastly, the amplitude is the distance from the equilibrium position tot he maximum displacement so in this case, it is one half the 25 cm peak to peak distance, or 12.5 cm.
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