Answers
The amplitude of the graph is 4. Option D.
What is amplitude?Amplitude refers to the maximum displacement or distance from the rest position of a vibrating object or wave. In other words, it measures the strength or intensity of the vibration or wave.
For sound waves, it determines the loudness of the sound, while for light waves, it affects the brightness of the light.
In the graph, the maximum amount of displacement of the wave is 4.
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Related Questions
The total distance between 4 consecutive Crust of travel wave is 6m.
what is wave length of wave
3/6m=2m
Answers
The wave's wavelength is 2 metres.
What does wavelength 1 translate into?1/ denotes the number of waves in a wave train that can be found in a length of one metre when wavelength is stated in metres, or the number in wavelength is stated in centimetres, then the length is one centimetre. This value is referred to as the spectrum line's wavenumber. The frequency equation is written as f = /, where is the wave speed and is the wavelength of the wave.
If the total distance between four consecutive crests of a wave is 6 meters, then the wavelength of the wave is equal to that distance divided by the number of crests, which is three.
So the wavelength of the wave is:
6 meters / 3 = 2 meters
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A proton (+1.6 × 10−19 C) moves 20 cm on a path in the direction of a uniform electric field of strength 2.4 N/C. How much work is done on the proton by the electrical field?
Answers
W=Fd
F=Eq
W=Eqd
E = 2.4 N/C
q = 1.6×10⁻¹⁹ C
d = 20 cm = 0.2 m
W = 2.4(1.6×10⁻¹⁹)(0.2)
W = 7.68×10⁻²⁰ J
If all of the dimensions of the block double (to become 20 cm wide, 8 cm tall, and 6 cm deep), what happens to the resistance of electric current along each axis?
Answers
Answer:
Assuming the block has uniform resistivity throughout, if all of the dimensions of the block double, then the resistance of electric current along each axis will increase by a factor of 8. This is because the resistance of a material is dependent on its dimensions, and specifically on its length, area, and resistivity. When the dimensions of the block double, its length, width, and height all double, which means that the overall length of the path the current must take through the material increases by a factor of 2+2+2=6. Since resistance is directly proportional to length, the overall resistance of the block increases by a factor of 6. Additionally, since the area of the block's cross-section increases by a factor of 4 (2 x 2), the overall resistance decreases by a factor of 4. Therefore, the overall effect is that the
What is one way that light waves differ from sound?
Answers
Answer:
The direction of vibration in the waves is at 90° to the direction that the light travels. Light travels in straight lines, so if you have to represent a ray of light in a drawing, always use a ruler. Unlike sound waves, light waves can travel through a vacuum (empty space).
Explanation:
In Part I, the independent variable, the one that is intentionally manipulated, is . In Part II, the independent variable changes to . The dependent variable, the one you measure the response in, is the same for Parts I and II. For both parts of the lab, the dependent variable is .
Answers
Kinetic energy is the dependent variable for both Parts, while mass is the independent variable for Part I and speed is the independent variable for Part II.
The independent variable is what, exactly?The variable in an experiment that is not altered by the experimental process is known as the independent variable. In contrast, the variable we must quantify and which is altered by the experimental circumstances is the dependent variable.
Is the experiment's manipulating the independent variable?An experiment's manipulated variable, also referred to as an independent variable, is a component that you can alter to observe how other factors react. The three categories of factors in an experiment are as follows: Variable that has been altered and controlled based on the trial.
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Question:
In Part I, the independent variable, the one that is intentionally manipulated, is
In Part II, the independent variable changes to
The dependent variable, the one you measure the response in, is the same for Parts I and II. For both parts of the
lab, the dependent variable is
A glass windowpane in a home is 0.62 cm thick and has dimensions of 1.5 m × 2.3 m. On a certain day, the indoor temperature is 26°C and the outdoor temperature is 0°C.
(a) What is the rate at which energy is transferred by heat through the glass?
W
(b) How much energy is lost through the window in one day, assuming the temperatures inside and outside remain constant?
J
Answers
lass windowpane in a home is 0.62 cm thick and has dimensions of 1.5 m × 2.3 m. On a certain day, the indoor temperature is 26°C and the outdoor temperature is 0°C.the amount of energy lost through the window in one day is approximately 37.9 MJ.
We can use the formula for heat transfer through a material, which is:
Q = k * A * (T1 - T2) / d
where Q is the rate of heat transfer, k is the thermal conductivity of the material, A is the surface area of the material, d is the thickness of the material, T1 is the temperature on one side of the material, and T2 is the temperature on the other side of the material.
(a) We first need to find the thermal conductivity of glass. According to engineeringtoolbox.com, the thermal conductivity of glass is approximately 1.05 W/(m*K). We convert the temperatures to Kelvin:
T1 = 26°C + 273.15 = 299.15 K
T2 = 0°C + 273.15 = 273.15 K
Plugging in the values:
Q = (1.05 W/(m*K)) * (1.5 m * 2.3 m) * (299.15 K - 273.15 K) / (0.62 cm / 100 cm/m)
Q = 438.37 W
So the rate at which energy is transferred by heat through the glass is 438.37 W.
(b) We can convert the rate of heat transfer to energy over time by using the formula:
E = Q * t
where E is the energy, Q is the rate of heat transfer, and t is the time. Assuming 24 hours in a day:
E = 438.37 W * 24 h * 3600 s/h
E = 37,910,899.2 J
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A student trying to calculate the
parameters of a satellite orbit obtained
a quantity Q which is related with the
orbital radius R., radius of the earth
R and acceleration due to gravity, g
½
2
by the formula Q
(SR²)
gR
dimensional analysis, find out what Q
represents.
Select one:
Tangential force
O Orbital speed
.
Centripetal acceleration
O Torque on the satellite
Using
Answers
Orbital speed is defined as Fg=GmM(R+h)2, where m is the satellite's mass and h is its height above the planet's surface.
How do you determine a satellite's orbital velocity?The orbital mobility is given by the formula g(R+h) = gr. Orbital velocity refers to the velocity needed to counteract the gravitational pull on the moon with its inertia, or propensity to continue moving.
What factors affect a satellite's orbital velocity?The planetary velocity of a satellite that orbits the Earth is determined by the height of the satellite above the planet. The needed orbital velocity increases with the distance from the Earth. At lower altitudes, a satellite encounters traces of Upper orbit, which causes drag.
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A marble rolls off a tabletop 1.1m high and hits the floor at a point 2.1m away from the tables edge in the horizontal direction.
A. How long (in seconds) is the marble (in m/s) in the air?
B. What is the speed of the marble (in m/s) when it leaves the tables edge?
C. What is the speed (in m/s) when it hits the floor?
Answers
y = vit + (1/2)gt^2 (Equation 1)
v = vi + gt (Equation 2)
where y is the vertical displacement, vi is the initial vertical velocity (which is zero when the marble leaves the table), t is the time, and v is the final velocity.
A. To find the time the marble is in the air, we can use Equation 1 with y = 1.1 m and vi = 0:
1.1 = (1/2)gt^2
Solving for t, we get:
t = sqrt(2*1.1/g) = 0.47 seconds
Therefore, the marble is in the air for 0.47 seconds.
B. To find the speed of the marble when it leaves the table, we can use Equation 2 with vi = 0 and t = 0.47 seconds:
v = gt = 9.810.47 = 4.61 m/s
Therefore, the speed of the marble when it leaves the table is 4.61 m/s.
C. To find the speed of the marble when it hits the floor, we need to find the horizontal and vertical components of its velocity. The horizontal component is constant, since there is no horizontal acceleration. The vertical component can be found using Equation 2 with vi = 0 and t = 0.47 seconds:
vy = gt = 9.810.47 = 4.61 m/s
The horizontal component of the velocity can be found from the distance traveled in the horizontal direction (2.1 m) and the time in the air (0.47 seconds):
vx = 2.1/0.47 = 4.47 m/s
The speed of the marble when it hits the floor is the magnitude of its velocity, which can be found using the Pythagorean theorem:
v = sqrt(vx^2 + vy^2) = sqrt(4.47^2 + 4.61^2) = 6.35 m/s
Therefore, the speed of the marble when it hits the floor is 6.35 m/s.
The thermal conductivities of human tissues vary greatly. Fat and skin have conductivities of about 0.20 W/m · K and 0.020 W/m · K respectively, while other tissues inside the body have conductivities of about 0.50 W/m · K. Assume that between the core region of the body and the skin surface lies a skin layer of 1.0 mm, fat layer of 0.50 cm, and 3.2 cm of other tissues.
(a) Find the R-factor for each of these layers, and the equivalent R-factor for all layers taken together, retaining two digits.
Rskin
m2 · K/W
Rfat
m2 · K/W
Rtissue
m2 · K/W
R
m2 · K/W
(b) Find the rate of energy loss when the core temperature is 37°C and the exterior temperature is 0°C. Assume that both a protective layer of clothing and an insulating layer of unmoving air are absent, and a body area of 2.0 m2.
Answers
Rounded to two digits, the equivalent R-factor for all layers is 0.36 m2·K/W. Rounded to two digits, the rate of energy loss is approximately 219 W.
Why do people use thermal conductivity?A crucial factor is thermal conductivity because it determines temperature gradients both during material development and inside of devices.
(a) The formula for the R-factor is:
R = thickness / thermal conductivity
For the skin layer:
Rskin = 0.001 m / 0.020 W/m·K = 0.05 m2·K/W
For the fat layer:
Rfat = 0.050 m / 0.20 W/m·K = 0.25 m2·K/W
For the other tissues:
Rtissue = 0.032 m / 0.50 W/m·K = 0.064 m2·K/W
To find the equivalent R-factor for all layers taken together, we need to add the individual R-factors together:
R = Rskin + Rfat + Rtissue
R = 0.05 m2·K/W + 0.25 m2·K/W + 0.064 m2·K/W
R = 0.364 m2·K/W
Rounded to two digits, the equivalent R-factor for all layers is 0.36 m2·K/W.
(b) The formula for the rate of energy loss is:
P = A * (Tcore - Texterior) / R
Converting the temperatures to kelvins:
Tcore = 37 + 273.15 = 310.15 K
Texterior = 0 + 273.15 = 273.15 K
Substituting the given values:
P = 2.0 m2 * (310.15 K - 273.15 K) / 0.36 m2·K/W
P = 219.44 W
Rounded to two digits, the rate of energy loss is approximately 219 W.
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A 75.0-kg man is riding an escalator in a shopping mall. The escalator moves the man at
a constant velocity from ground level to the floor above, a vertical height of 4.60 m. What
is the work done on the man by (a) the gravitational force and (b) the escalator?
Answers
The negative sign indicates that the work done by the escalator is in the opposite direction of the displacement, which is downward. So, the escalator is doing negative work on the man.
The gravitational force is doing positive work on the man because it is in the same direction as the displacement.
StepsWe need to use the formulas for work and gravitational potential energy:
work = force x distance x cos(theta)
gravitational potential energy = mgh
(a) The work done on the man by the gravitational force is given by:
work_gravity = mgh = (75.0 kg)(9.8 m/s^2)(4.60 m) = 3,301 J
The gravitational force is doing positive work on the man because it is in the same direction as the displacement.
(b) The work done on the man by the escalator is given by:
work_escalator = force_escalator x distance x cos(0) = force_escalator x distance
The escalator is moving the man at a constant velocity, so the net force on the man is zero (since the man is not accelerating). Therefore, the force of the escalator must be equal in magnitude and opposite in direction to the gravitational force:
force_escalator = -mg = -(75.0 kg)(9.8 m/s^2) = -735 N
Substituting this value and the distance (4.60 m) into the formula for work, we get:
work_escalator = (-735 N)(4.60 m) = -3,381 J
The negative sign indicates that the work done by the escalator is in the opposite direction of the displacement, which is downward. So, the escalator is doing negative work on the man.
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A stick is resting on a concrete step with 29
of its total length
hanging over the edge. A single ladybug lands on the end of the stick hanging over the edge, and the stick begins to tip. A moment later, a second, identical ladybug lands on the other end of the stick, which results in the stick coming momentarily to rest at =62.1∘
with respect to the horizontal, as shown in the figure.
If the mass of each bug is 3.09
times the mass of the stick and the stick is 15.1 cm
long, what is the magnitude
of the angular acceleration of the stick at the instant shown? Use =9.81 m/s2.
Answers
In physics, angular acceleration refers to the time rate of change of angular velocity. the magnitude of the angular acceleration of the stick at the instant shown results in tan(θ/2) = 0.010 and θ= 1.15.
Let stand in for the angle formed by the directions of the vectors A and B. The magnitudes of A and B being equal, A, B, and R = A + B form an isosceles triangle with angles of 180, - θ/2, and θ /2. R then equals 2A cos (θ/2) to determine its magnitude. By using the fact that B=A and the isosceles triangle, the law of cosines can be used to demonstrate this.
Once more, A, -B, and D = A-B form an isosceles triangle with an angle at the top of. D = 2Asin(θ/2) is the result of using the law of cosines and the identity (1-cosθ ) = 2sin² (θ/2).
R must equal 100D for the equation to hold, hence 2A cos(θ/2) = 200A sin(θ/2).
This results in tan(θ/2) = 0.010 and θ= 1.15.
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calculate the force exerted by air on a disk of radius 1.00m at the water's surface
Answers
The force exerted by air on a disk of radius 1.00m at the water's surface is approximately 318.3 N.
To calculate the force exerted by air on a disk of radius 1.00m at the water's surface, we need to know the air pressure and the surface area of the disk.
Assuming standard atmospheric pressure at sea level of 101.325 kPa and neglecting any effects due to wind, we can calculate the force exerted by air on the disk as follows:
Determine the surface area of the disk:
A = [tex]πr^2[/tex]
where r = 1.00m
A = [tex]π(1.00m)^2 = 3.14 m^2[/tex]
Calculate the force exerted by air on the disk using the formula:
F = PA
where P is the air pressure and A is the surface area of the disk.
F = [tex](101.325 kPa)(3.14 m^2)[/tex] = 318.3 N
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Microwaves travel at the speed of light 3.00x108 m/s. When the frequency of microwaves is 9.00x109Hz, what is their wavelength?
Answers
The wavelength of microwaves with a frequency of 9.00x10^9 Hz is approximately 0.0333 meters or 33.3 millimeters.
What is the speed of microwaves and what is their frequency?Microwaves are a type of electromagnetic radiation with a frequency range of around 300 MHz to 300 GHz. They are used for various applications, including communication, cooking, and medical imaging.
The speed of microwaves is the same as the speed of light, which is approximately 3.00x10^8 m/s. This means that microwaves travel at a very high speed and can cover long distances in a short amount of time.
How does the wavelength of microwaves change with their frequency?The wavelength of microwaves is inversely proportional to their frequency. This means that as the frequency of microwaves increases, their wavelength decreases.
In other words, higher frequency microwaves have shorter wavelengths, and vice versa. For example, the wavelength of microwaves with a frequency of 9.00x10^9 Hz is approximately 0.0333 meters or 33.3 millimeters.
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The compression ratio of a petrol engine is 20.0 to 1; that is, air in a cylinder is compressed adiabatically to 1/20.0 of its initial volume.
(a) If the initial pressure is 1.01× 10^5 and the initial temperature is 20℃, find the final pressure and the temperature after adiabatic compression.
(b) How much work does the gas do during the compression if the initial volume of the cylinder is 1.00 = 1.00 ×10^−3^3. Use the values = 20.8 /. and
= 1.400 for air.
(c) Hence, find the change in internal energy of the air.
Answers
The final temperature is 390 K and the final pressure is 6.46 x [tex]10^{6}[/tex] Pa. The work done by the petrol during compression is 7.20 x 10² J. The air's internal energy changed by -7.20 x 10² J.
Once adiabatic compression has occurred, determine the final pressure and temperature.The final pressure and temperature can be calculated using the adiabatic compression equation:
To start, here is the last volume:
Vf = Vi / 20.0 = 1.00 × [tex]10^{-3}[/tex] / 20.0 = 5.00 × [tex]10^{-5}[/tex] m³
We may then determine the final pressure by:
1.01 105 Pa * Pf = Pi * (V i / V f) (1.00 × [tex]10^{-3}[/tex] m³ / 5.00 × [tex]10^{-5}[/tex] m³)1.4 = 6.46 × [tex]10^{6}[/tex] Pa
Final temperature = (1 mol × 8.31 J/mol K) / (6.46 106 Pa × 5.00 × [tex]10^{-5}[/tex] m³) = 390 K
The final pressure is therefore 6.46 106 Pa, and the final temperature is 390 K.
How much effort is put forth by the petrol during compression?The equation: can be used to determine the work performed by the gas during compression.
W = (γ / (γ - 1)) × P i × V i × (1 - (1 / r(γ - 1)))
where P i and V i are the initial pressure and volume, r is the compression ratio (20.0), and is the adiabatic index (1.4 for air).
Inputting the values provided yields:
W = (1.4 / (1.4 - 1)) × 1.01 × [tex]10^{5}[/tex] Pa × 1.00 × [tex]10^{-3}[/tex] m³ × (1 - (1 / 20.0(1.4 - 1))) = 7.20 × 10² J
Calculate the change in internal energy.The first law of thermodynamics can be used to compute the change in internal energy:
ΔU = Q - W
where W is the work performed by the petrol and Q is the heat contributed to the system, which in this instance is adiabatic.
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Acceleration can be described as...
A. Change in velocity over time.
B. Change in position over time.
Answers
Answer:
A
Explanation:
because it is defined as the rate of change of velocity.
What is the difference between a subsurface and a surface event?
Answers
A subsurface is something that is below the layer that is on the surface, whereas a surface is the topside or upward side of a flat item like a table or a liquid.
What distinguishes the top from the subsurface?Surface mining takes place on the Earth's surface and involves moving unused materials out of the way. Subsurface mining, on the other hand, does not involve moving unused sediments or rocks out of the way.
What does the rock cycle's surface occurrence entail?processes on the surface that convert rock to sediment. deposition. sediment settles on the surface away from the breeze or water that is carrying it. melting. happens as rock sinks towards the mantle of the Earth.
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Suppose an alien civilization has a space station in circular orbit around its home planet. The station's orbital radius is four times the planet's radius.(a)if an alien astronaut has weight wsurface just before launch from the surface, will she be weightless when she reaches the station and floats inside of it?(b) If not, what will be the ratio of her weight in orbit to her weight on the planet's surface? (If she is weightless, enter 0.)
Answers
the astronaut's weight in orbit will be 1/16th of her weight on the planet's surface.
(a) Yes, the astronaut will be weightless when she reaches the station and floats inside it. This is because the space station is in freefall around the planet, and the astronaut will be in the same state of freefall as the station.
(b) The ratio of the astronaut's weight in orbit to her weight on the planet's surface can be found using the equation:
w_orbit/w_surface = [tex](R_surface / R_orbit)^2[/tex]
where w_surface is the astronaut's weight on the planet's surface, w_orbit is her weight in orbit, R_surface is the planet's radius, and R_orbit is the radius of the station's orbit.
Substituting R_orbit = 4R_surface and simplifying, we get:
w_orbit/w_surface = (1/16)
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Two iron nails hang from a bar magnet. Which diagram shows the magnetic poles induced in the nails?
Answers
Answer:
option A
Explanation:similar pole repel each other and opposite pole attract each other.other options (exceptA) shows that similar pole is attracting ,it is not podsible.
load=300,effort =80,load distance =4cm,effort distance =30cm,what mechanical advantage ?
Answers
ANSWER: the mechanical advantage is 3.75.
Explanation:
Given,
Load = 300
Effort = 80
Load distance = 4 cm
Effort distance = 30 cm
To calculate Load distance and Effort distance, we can use the formula:
Load x Load distance = Effort x Effort distance
300 x 4 = 80 x 30
1200 = 2400
Load distance = 4cm
Effort distance = 30cm
Now, we can calculate the mechanical advantage using the formula:
MA = Load / Effort
MA = 300 / 80
MA = 3.75
An object has a mass of 50kg. On earth, the weight of the object is almost 500 newtons but the object floats in space. Why does an object that is so difficult to lift on earth float on space ?
Answers
The object will continue to float in a stationary position until acted upon by a force, such as a push or pull.
What is Weight?
Weight is the force with which an object is attracted towards the Earth or any other celestial body due to gravity. The weight of an object can be calculated by multiplying its mass with the acceleration due to gravity. In the SI system of units, weight is measured in Newtons (N).
An object that has a mass of 50kg has a weight of nearly 500 newtons on Earth due to gravity. However, in space, where there is no significant gravity, the object will not experience any weight or force pushing it down. The object will float because there is no force acting upon it to cause it to move in a particular direction. This is due to the absence of gravity, which is the force responsible for the weight of an object.
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when light strikes a green opaque object the green wavelength of light is .....
1. reflected
2. absorbed
3. transmitted
while all other wavelengths of visible light are......
1. reflected
2. absorbed
3. transmitted
Answers
When light strikes a green opaque object, the green wavelength of light is absorbed, while all other wavelengths of visible light are reflected.
Why does a green object appear green to our eyes?A green object appears green to our eyes because it selectively absorbs all wavelengths of visible light except for the green wavelength of light, which is reflected back to our eyes.
When light strikes a green opaque object, the green wavelength of light is absorbed by the object. This means that the green light is not reflected or transmitted, but rather it is absorbed by the object.
What happens to the energy of the absorbed light when it is absorbed by an opaque object?When light is absorbed by an opaque object, the energy of the absorbed light is converted into other forms of energy, such as thermal energy. This is because the absorbed light energy causes the atoms in the object to vibrate, which in turn generates heat energy.
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10/10=x =35/56
x=?
help please
Answers
Mark as brainy please
If it takes a planet 8 years to orbit the sun, how long in years will it take the plantet to go all the way around our sky once?
Answers
it would take the planet approximately 9.14 years to go all the way around our sky once.
The time it takes for a planet to go all the way around our sky once is called its sidereal period. This is the time it takes for the planet to return to the same position in the sky relative to the fixed stars.
The sidereal period of a planet is related to its orbital period around the Sun, by the following formula:
Sidereal period = Orbital period / (1 - Earth's orbital period / Planet's orbital period)
The Earth's orbital period around the Sun is approximately 1 year. Substituting the given values, we get:
Sidereal period = 8 years / (1 - 1/8)
Sidereal period = 8 years / (7/8)
Sidereal period = 9.14 years (approx)
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How many Btus must be added to 34 lb. of ice at -32°F to change it to steam
at 416-F?
The answer should be like 48,500 something but I want to see the steps to get the answer
Answers
Based on the calculations, approximately 3,697,808 BTUs must be added to 34 lbs. of ice at -32°F to change it to steam at 416°F.
To solve this problem, we need to consider the three stages of the process:
Heating the ice from -32°F to 0°F
Melting the ice at 0°F
Heating the water from 0°F to 416°F
First, we need to calculate the amount of heat required to raise the temperature of 34 lb of ice from -32°F to 0°F. We can use the specific heat of ice, which is 0.5 Btu/lb°F:
Q1 = m * c * ΔT
Q1 = 34 lb * 0.5 Btu/lb°F * (0°F - (-32°F))
Q1 = 544 Btu
Next, we need to calculate the amount of heat required to melt the ice at 0°F. We can use the heat of fusion of ice, which is 144 Btu/lb:
Q2 = m * ΔHf
Q2 = 34 lb * 144 Btu/lb
Q2 = 4896 Btu
Finally, we need to calculate the amount of heat required to raise the temperature of the water from 0°F to 416°F. We can use the specific heat of water, which is 1.0 Btu/lb°F:
Q3 = m * c * ΔT
Q3 = 34 lb * 1.0 Btu/lb°F * (416°F - 0°F)
Q3 = 14,144 Btu
The total amount of heat required is the sum of Q1, Q2, and Q3:
Q total = Q1 + Q2 + Q3
Q total = 544 Btu + 4896 Btu + 14,144 Btu
Q total = 19,584 Btu
Therefore, 19,584 Btus must be added to 34 lb of ice at -32°F to change it to steam at 416°F.
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The escape speed from the surface of Planet Zoroaster is 12.0km/s. The planet has no atmosphere. A meteor far away from the planet moves at speed 5.0km/s on a collision course with Zoroaster. How fast is the meteor going when it hits the surface of the planet.
Answers
Answer:
The escape speed of a planet is the minimum speed that an object needs to attain to escape the gravitational pull of the planet and not fall back. Since the meteor's speed is less than the escape speed of Planet Zoroaster, it will not escape and will crash into the planet.
To find the final speed of the meteor when it hits the surface of the planet, we can use the principle of conservation of energy. At a great distance from the planet, the meteor has only kinetic energy. As it approaches the planet, its potential energy increases due to the planet's gravitational attraction, while its kinetic energy decreases due to the planet's gravitational deceleration.
At the moment of impact, all of the meteor's kinetic energy will be converted into other forms of energy (such as heat and sound) upon hitting the surface. Therefore, we can equate the initial kinetic energy of the meteor to the sum of its potential energy and its final kinetic energy just before impact.
Initial kinetic energy = 1/2 * m * v1^2
where m is the mass of the meteor and v1 is its initial speed.
Potential energy at the surface of the planet = -G * M * m / R
where G is the gravitational constant, M is the mass of the planet, m is the mass of the meteor, and R is the radius of the planet.
Final kinetic energy just before impact = 1/2 * m * v2^2
where v2 is the final speed of the meteor just before impact.
We can set these equal and solve for v2:
1/2 * m * v1^2 = -G * M * m / R + 1/2 * m * v2^2
Simplifying and solving for v2, we get:
v2 = sqrt(2 * G * M / R + v1^2)
Plugging in the given values, we get:
v2 = sqrt(2 * 6.6743 × 10^-11 m^3 kg^-1 s^-2 * M / 5 × 10^6 m + (5.0 km/s)^2)
where M is the mass of Planet Zoroaster.
Without knowing the mass of Planet Zoroaster, we cannot determine the exact value of v2. However, we can use the given escape speed to find the mass of the planet:
escape speed = sqrt(2 * G * M / R)
=> M = R * escape speed^2 / (2 * G)
Plugging in the given values, we get:
M = 5 × 10^6 m * (12.0 km/s)^2 / (2 * 6.6743 × 10^-11 m^3 kg^-1 s^-2) = 3.599 × 10^25 kg
Now we can calculate the final speed of the meteor:
v2 = sqrt(2 * 6.6743 × 10^-11 m^3 kg^-1 s^-2 * 3.599 × 10^25 kg / 5 × 10^6 m + (5.0 km/s)^2) ≈ 12.032 km/s
Therefore, the meteor will be moving at a speed of approximately 12.032 km/s when it hits the surface of Planet Zoroaster.
A runner is sprinting at 3 m/s. But 40 seconds later they are sprinting at 3.8 m/s. What is the runner’s acceleration?
Answers
A runner is sprinting at 3 m/s. But 40 seconds later they are sprinting at 3.8 m/s. What is the runner’s acceleration?
Answer:We can use the following formula to calculate the acceleration:
a = (vf - vi) / t
where:
a = acceleration
vf = final velocity
vi = initial velocity
t = time
In this case, the initial velocity (vi) is 3 m/s, the final velocity (vf) is 3.8 m/s, and the time (t) is 40 seconds.
So, we can plug these values into the formula and solve for the acceleration:
a = (3.8 m/s - 3 m/s) / 40 s
a = 0.8 m/s^2
Therefore, the runner's acceleration is 0.8 m/s__2__.
A standing wave formed on a rope that is 7.5 meters long. The fundamental harmonic forms at 14 Hz Speed
If the rope is being shaken to form a standing wave pattern displaying five "bumps", then the wave pattern would be called the harmonic. Complete the chart using the information from above.
Pic attached below
Answers
A standing wave formed on a rope that is 7.5 meters long. The fundamental harmonic forms at 14 Hz.
If the rope is being shaken to form a standing wave pattern displaying five "bumps", then the wave pattern would be called the fifth harmonic.
Complete the chart using the information from above:
( chart is attached below the answer )
To calculate the wavelength, we can use the formula: wavelength = speed / frequency.
For the fifth harmonic, the frequency is 70 Hz, and the speed is 7.5 m/s (given in the problem). Therefore, the wavelength is:
wavelength = speed / frequency = 7.5 / 70 = 0.107 meters.
We can also calculate the period using the formula: period = 1 / frequency. For the fifth harmonic, the period is:
period = 1 / frequency = 1 / 70 = 0.0143 seconds.
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A driver holds his hands on opposite sides of the 35-cm -diameter steering wheel in a modern sports car. A torque of 4.5 N⋅m is required to turn the wheel. If the driver applies an equal force on each side of the wheel, what is the minimum force each hand must supply?
Answers
Therefore, each hand must supply a minimum force of 12.86 N to turn the steering wheel.
How hard must you move the steering wheel?Although you can use any amount of power, modern cars all have assistance, so you don't need to use much force. You can add up to 200 N (20 kg), but any more weight may damage your steering rod ends, which could lead to increased steering vibration or even failure.
The formulas below provide the torque needed to move the steering wheel.
τ = Fr
where r is the steering wheel's radius and F is the power being applied to it.
Given that the steering wheel's diameter in this instance is 35 centimeters, the radius is as follows:
r = 35 cm / 2 = 17.5 cm = 0.175 m
The torque required is given as 4.5 N⋅m.
Therefore:
4.5 N⋅m = F * 0.175 m
Solving for F, we get:
F = 4.5 N⋅m / 0.175 m
F = 25.71 N
The minimal force that each hand must exert is as follows because the driver exerts equal force on each side of the wheel:
F/2 = 25.71 N / 2 = 12.86 N.
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What mass of water at 27.0°C must be allowed to come to thermal equilibrium with a 1.95-kg cube of aluminum initially at 150°C to lower the temperature of the aluminum to 60.0°C? Assume any water turned to steam subsequently recondenses.
kg
Answers
Q_aluminum = -Q_water
where Q_aluminum is the heat lost by the aluminum cube and Q_water is the heat gained by the water. We can also use the specific heat capacity of aluminum and water to calculate the heat lost or gained:
Q = m x c x ΔT
where Q is the heat, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
First, let's calculate the heat lost by the aluminum cube:
Q_aluminum = m_aluminum x c_aluminum x ΔT_aluminum
Q_aluminum = 1.95 kg x 0.91 J/g°C x (150°C - 60°C)
Q_aluminum = 311.22 kJ
Next, let's calculate the heat gained by the water:
Q_water = m_water x c_water x ΔT_water
Q_water = m_water x 4.18 J/g°C x (27.0°C - 60.0°C)
Q_water = -m_water x 4.18 J/g°C x 33.0°C
Q_water = -1381.14 m_water J
Since Q_aluminum = -Q_water, we can set these equations equal to each other and solve for the mass of water:
311.22 kJ = -1381.14 m_water J
m_water = -311.22 kJ / (-1381.14 J/g°C x 33.0°C)
m_water = 0.666 kg
Therefore, a mass of 0.666 kg of water at 27.0°C must be allowed to come to thermal equilibrium with the aluminum cube to lower its temperature to 60.0°C.
1. What is the horizontal distance of the center of gravity of the system from the point where the ladder touches the ground?
2. What is the torque about the axis of rotation (point B) by taking the total weight of the person + ladder acting at the center of gravity?
Answers
To answer the first question, we need to determine the location of the center of gravity of the system. Assuming the person and ladder can be treated as a uniform object, the center of gravity will be located at the midpoint of the ladder.
Let's say the ladder is 10 feet long, so the midpoint would be 5 feet from either end. If we assume the ladder is resting at a 60 degree angle against a vertical wall, we can use trigonometry to determine the horizontal distance of the center of gravity from the point where the ladder touches the ground.
Using the sine function, we know that sin(60) = opposite/hypotenuse, so the opposite side (which is the vertical height of the ladder) is 10*sin(60) = 8.66 feet. Therefore, the horizontal distance from the center of gravity to the point where the ladder touches the ground is also 8.66 feet.
To answer the second question :
We need to calculate the torque about the axis of rotation (point B) by taking the total weight of the person + ladder acting at the center of gravity. The formula for torque is torque = force x distance.
The force is equal to the weight of the person + ladder, which we'll assume is 300 pounds. The distance is the horizontal distance we just calculated, which is 8.66 feet.
So the torque about point B would be 300 pounds x 8.66 feet = 2,598 Newton-meters (Nm) or 2,598 pound-feet (lb-ft).
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