Okay, here are the steps:
1) Density of water: 1.00 x 103 kg/m3
Density of mercury: 1.36 x 104 kg/m3
2) Volume of cylindrical tube: 0.250 m tall
Area of base = pi * r^2 (where r = 0.05 m)
So volume (V) = pi * r^2 * h = 0.005pi * 0.25 = 0.05pi m^3
3) Volume occupied by mercury = 0.05pi * (0.75) = 0.0375pi m^3
Volume occupied by water = 0.05pi * (0.25) = 0.0125pi m^3
4) Mass of mercury = 0.0375pi * 1.36 x 104 kg/m3 = 5 x 10^3 kg
Mass of water = 0.0125pi * 1.00 x 103 kg/m3 = 1.25 x 10^2 kg
5) Total mass (m) = 5 x 10^3 + 1.25 x 10^2 = 7.125 x 10^3 kg
6) Absolute pressure (p) = mg/A = (7.125 x 10^3 kg) * (9.8 m/s^2) / (0.005pi m^2)
= 283750 Pa
So the absolute pressure (p) at the bottom of the graduated cylinder is 283750 Pa.
Let me know if you have any other questions!
A surface at 27 °C emits radiation at a rate of 100 W. At what rate does an identical surface at 54 °C emit radiation
The rate of radiation emitted by an identical surface at 54°C is 2,170,812.96 W. This is significantly higher than the rate of radiation emitted by the surface at 27°C, which was 100 W.
What is Stefan-Boltzmann Law?The Stefan-Boltzmann Law states that the rate of radiation emitted by a blackbody is proportional to the fourth power of its absolute temperature.
The rate of radiation emitted by an identical surface at 54°C can be found using the Stefan-Boltzmann Law.
Therefore, we can calculate the rate of radiation emitted by the surface at 54°C using the following equation:
Power emitted = σ x (Temperature)⁴
Where σ is the Stefan-Boltzmann constant, which is equal to 5.67 x 10⁻⁸ Wm⁻²K⁻⁴.
Plugging in the given values, we have:
Power emitted = 5.67 x 10⁻⁸ Wm⁻²K⁻⁴ x (54 + 273)⁴
Power emitted = 2,170,812.96 W
Therefore, the rate of radiation emitted by an identical surface at 54°C is 2,170,812.96 W. This is significantly higher than the rate of radiation emitted by the surface at 27°C, which was 100 W. This is due to the fact that the fourth power of the absolute temperature of the surface is much higher at 54°C than at 27°C.
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The rate of radiation emitted by an identical surface at 54°C is 2,170,812.96 W. This is significantly higher than the rate of radiation emitted by the surface at 27°C, which was 100 W.
What is Stefan-Boltzmann Law?The Stefan-Boltzmann Law states that the rate of radiation emitted by a blackbody is proportional to the fourth power of its absolute temperature.
The rate of radiation emitted by an identical surface at 54°C can be found using the Stefan-Boltzmann Law.
Therefore, we can calculate the rate of radiation emitted by the surface at 54°C using the following equation:
Power emitted = σ x (Temperature)⁴
Where σ is the Stefan-Boltzmann constant, which is equal to 5.67 x 10⁻⁸ Wm⁻²K⁻⁴.
Plugging in the given values, we have:
Power emitted = 5.67 x 10⁻⁸ Wm⁻²K⁻⁴ x (54 + 273)⁴
Power emitted = 2,170,812.96 W
Therefore, the rate of radiation emitted by an identical surface at 54°C is 2,170,812.96 W. This is significantly higher than the rate of radiation emitted by the surface at 27°C, which was 100 W. This is due to the fact that the fourth power of the absolute temperature of the surface is much higher at 54°C than at 27°C.
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A loop of area 0.100 m² is oriented at
a 15.5 degree angle to a 0.500 T
magnetic field. It rotates until it is at a
45.0 degree angle with the field. What
is the resulting CHANGE in the
magnetic flux?
[?] Wb
Answer:
-0.0122 Wb
Explanation:
The magnetic flux through a loop of area A and with an angle θ between the magnetic field and the loop's normal is given by:
Φ = BAcos(θ)
The initial magnetic flux is:
Φ1 = BAcos(θ1) = 0.500 T * 0.100 m² * cos(15.5°) = 0.0476 Wb
The final magnetic flux is:
Φ2 = BAcos(θ2) = 0.500 T * 0.100 m² * cos(45.0°) = 0.0354 Wb
The change in magnetic flux is:
ΔΦ = Φ2 - Φ1 = 0.0354 Wb - 0.0476 Wb = -0.0122 Wb
Therefore, the resulting change in magnetic flux is -0.0122 Wb.
In mirror 1 of two 110° superimposed mirrors
If the rays of the sun fall at an angle of a = 60°, 2nd
What is the difference between thinking in the mirror?
In the case of two superimposed mirrors, the virtual image will be a reflection of the original object, with the angle between the object and its virtual image depending on the angle between the mirrors.
How to solveIf you are referring to two superimposed mirrors with an angle of 110° between them, and sunlight is striking the first mirror at an angle of 60°, then you might be looking to calculate the angle of reflection.
The angle of incidence is equal to the angle of reflection. In this case, the angle of incidence, a, is 60°, so the angle of reflection will also be 60°. However, this angle is measured with respect to the normal (a perpendicular line to the mirror's surface), not with respect to the mirror itself.
The difference between thinking in the mirror might refer to the virtual image created by the mirror. In the case of two superimposed mirrors, the virtual image will be a reflection of the original object, with the angle between the object and its virtual image depending on the angle between the mirrors.
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An impulse of 200 N.s is applied horizontally by a soccer player of mass 74 kg at the start of a sprint (initial velocity= 0). What is the player’s change in momentum and velocity reached
The velocity reached by the soccer player is 2.7 m/s.
Impulse applied by the soccer player = 200 Ns
Mass of the soccer player = 74 kg
According to impulse-momentum theorem, the average net external force multiplied by the time it takes for that force to take effect equals the impulse, which is equal to the change in momentum.
Impulse = Fnet × t
Fnet x t = ma × t = m × v
mv = ΔP
where ΔP is the change in momentum.
So,
The change in momentum of the player, ΔP = 200 Kgm/s
So, velocity reached, v = 200/74
v = 2.7 m/s
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What is mass? Write two differences between fundament .
Mass is a measure of the amount of matter in an object and is a fundamental property of matter. Fundamental forces refer to the interactions between particles, whereas fundamental particles are the building blocks of matter.
Mass is a measure of the amount of matter in an object, usually measured in kilograms (kg). It is a fundamental property of matter that does not change with location or gravitational forces.
Two differences between fundamental forces and fundamental particles are:
1. Fundamental forces refer to the interactions between particles, whereas fundamental particles are the building blocks of matter that makeup everything in the universe.
2. There are four fundamental forces - gravitational, electromagnetic, weak nuclear, and strong nuclear - while there are six types of fundamental particles - quarks, leptons, bosons, neutrinos, antimatter particles, and Higgs bosons.
Therefore,A fundamental characteristic of matter is mass, which is a measurement of how much matter there is in an item. Fundamental particles are the building components of matter, whereas fundamental forces relate to the interactions between particles.
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A narrow white light ray is incident on a block of fused quartz at an angle of 39.1°. Find the angular width of the light ray inside the quartz. (The refraction index is 1.47 at 400nm and 1.458 at 700nm). Answer in units of °.
The angular width of the light ray inside the fused quartz is 52.4°.
What is angular width?
Angular width is the measure of the size or extent of an object or phenomenon as it appears to an observer, expressed in angular units (such as degrees). It is the angle subtended by the object or phenomenon at the observer's eye. In optics, angular width is often used to describe the apparent size of an object or image viewed through a lens or other optical instrument.
The angular width of the light ray inside the fused quartz can be found using the formula:
θ2 = [tex]Sin^{-1}(n2/n1 * sin(θ1))[/tex]
where θ1 is the angle of incidence, n1 is the refractive index of the medium outside the quartz (assumed to be air, which has a refractive index of 1), n2 is the refractive index of the quartz, and θ2 is the angle of refraction.
To find θ2, we need to first find the average refractive index of the quartz for the narrow white light ray. We can use the formula:
[tex]n_{avg}[/tex] = ([tex]n_{blue}[/tex] + [tex]n_{red}[/tex]) / 2
where n_blue is the refractive index for blue light (400 nm) and n_red is the refractive index for red light (700 nm).
[tex]n_{avg}[/tex] = (1.47 + 1.458) / 2 = 1.464
Now we can plug in the values and solve for θ2:
θ2 = [tex]Sin^{-1}(1.464/1 * sin(39.1°))[/tex] = 52.4°
Therefore, the angular width of the light ray inside the fused quartz is 52.4°.
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In the sketch below, the cylinder A has a mass of 13 kg and cross-sectional area of 2 m2 . The piston B has a cross-sectional area of 15000 mm2 and negligible weight. If the apparatus is filled with oil, ρ = 780 kg/m3 , with the aid of a complete free body diagram calculate the force F required for equilibrium.
the force F required for equilibrium is 128.397 N.
How do we calculate?
There are two main forces: the weight of the cylinder A and the hydraulic pressure acting on the piston B. The weight of A is given by:
W = m*g = 13 kg * 9.81 m/s^2 = 127.53 N
P = rho x gx h
where
h = (15000 mm^2) / (2 m^2) = 0.0075 m
pressure is:
P = 780 kg/m^3 * 9.81 m/s^2 * 0.0075 m = 57.79 N/m^2
Force = P*A
A = 15000 mm^2 = 0.015 m^2
Force = 57.79 N/m^2 * 0.015 m^2 = 0.867 N
Solving for the force required for equilibrium:
Force = W + P*A
Force = 127.53 N + 57.79 N/m^2 * 0.015 m^2
= 127.53 N + 0.867 N
= 128.397 N
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The electrical signals sent to the brain indicate the
loudness, pitch, and quality
pitch
of a sound wave.
loudness
quality
The electrical signals sent to the brain indicate the loudness, pitch, and quality of a sound wave.
Option A is correct
What are electrical signals?An electrical signal is described as a voltage or current which conveys information, usually it means a voltage. It is the term can be used for any voltage or current in a circuit.
The apparent strength of a sound wave is referred to as loudness, and it is commonly expressed in decibels. (dB). The perceived sound is louder the larger the amplitude of the sound wave.
The apparent highness or lowness of a sound is known as pitch, and it is based on the sound wave's frequency. When compared to lower frequency sound waves, higher frequency sound waves are perceived as having a higher pitch.
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How many volts are required to move a current of 3 A through a resistor of 1000 Ohms?
3000 volts are required to move a current of 3 A through a resistor of 1000 Ohms.
Ohm's law states that the voltage across a conductor is directly proportional to the current flowing through it, given a constant temperature and other conditions. The relationship between voltage, current, and resistance is expressed mathematically as V = IR, where V is the voltage across the conductor, I is the current flowing through it, and R is the resistance of the conductor.
Using Ohm's law, we can find the voltage required to move a current of 3 A through a resistor of 1000 Ohms:
V = I * R
where V is the voltage, I is the current, and R is the resistance.
Substituting the given values, we get:
V = 3 A * 1000 Ohms = 3000 volts
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(a) What is the characteristic time constant (in s) of a 25.5 mH inductor that has a resistance of 3.80 ?
(b) If it is connected to a 12.0 V battery, what is the current (in A) after 12.5 ms?
L/R = L / R is the formula for an RL circuit's time constant. 7.50 mH 3.00 = 2.50 ms with LR = 7.50 mH 3.00.
What does the RF circuit time constant mean?Circuit capacitance and circuit resistance combine to form the RC time constant ().(C). In contrast, a capacitor linked in series with a resistor takes time to charge up to around 36.8% of its full value. It is a significant metric since it represents the growth or decay rate of the circuit.
Tau is relatively simple since = RC. The time constant of an RC circuit is important because it ties the values of R and C to the capacitor voltage directly. A capacitor may be charged to a 63% charge by applying a single continuous charge, according to experiments.
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v=√gr tan 31.0 grados
This is an equation that can be used to calculate the velocity (V) required to launch an object from a ramp at an angle of 31.0 degrees with the horizontal, neglecting air resistance.
In the equation, g is the acceleration due to gravity (approximately 9.8 m/s^2) and r is the radius of curvature of the ramp. Since the radius is not given, we can assume it to be constant or ignore it altogether if it is not necessary.
The expression tan 31.0 degrees represents the slope of the ramp. By taking the tangent of the angle, we can determine the vertical component of the slope. This is important because it affects the force of gravity acting on the object. By taking the square root of the product of g and tan 31.0 degrees, we can determine the velocity needed to launch the object at the given angle.
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--The complete question is, What does this equation describes, V=√gr tan 31.0 grados?--
Suppose you are hiking down the Grand Canyon. At the top, the temperature early in the morning is a cool 3 °C. By late afternoon, the temperature at the bottom of the canyon has warmed to a sweltering 34 °C. What is the difference, between the higher and lower temperatures in Fahrenheit degrees.
The difference, between the higher and lower temperatures in Fahrenheit degrees is 87.8 °F.
What is the difference, between the temperatures?The difference, between the higher and lower temperatures in Fahrenheit degrees is calculated as follows;
The difference in the temperatures = 34 °C - 3°C = 31 °C
Convert the temperature to Fahrenheit degrees as follows;
31 °C = 1.8C + 32
31 °C = 1.8 x 31 + 32
31 °C = 87.8 °F
Thus, the difference, between the higher and lower temperatures in Fahrenheit degrees is calculated using the conversion factor.
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the total mass of an object is 25.8kg. what is the gravitational potential energy of the mass at an attitude of 27.66 m?
Answer:
7.00 KJ
Explanation:
GPE = mgh
m equals mass (kg)
g is a constant which equals 9.81 m/s
h equals height (m)
GPE = (25.8 kg)(9.81 m/s)(27.66 m)
GPE = 7,000.69 J or 7.00 KJ
How is thermal energy transferred during conduction? Check all that apply.
Thermal energy is transferred between particles that are not touching each other.
Thermal energy is transferred between particles that are in direct contact with each other.
Thermal energy is transferred between objects of different temperatures.
Thermal energy is transferred between objects of the same temperature.
Thermal energy is transferred from slow-moving particles to fast-moving particles.
Thermal energy is transferred from fast-moving particles to slow-moving particles.
The correct options for how thermal energy is transferred during conduction are " Thermal energy is transferred between particles that are in direct contact with each other.", "Thermal energy is transferred between objects of different temperatures.", and "Thermal energy is transferred from fast-moving particles to slow-moving particles." The correct options are B, C, and F.
During conduction, thermal energy is transferred through a material or between objects in direct contact with each other. The transfer of thermal energy occurs because of temperature differences between the two objects or regions. When two objects at different temperatures are in direct contact with each other, the hot object transfers thermal energy to the cold object through collisions between the particles of the two objects. The fast-moving particles in the hot object collide with the slow-moving particles in the cold object, transferring thermal energy from the hot object to the cold object. This process continues until the two objects reach thermal equilibrium, meaning they have the same temperature and there is no more net transfer of thermal energy between them.
Option A is not true because thermal energy is actually transferred between particles that are in direct contact with each other, not particles that are not touching each other.
Option D is not true because thermal energy does not transfer between objects that are already at the same temperature. Heat transfer only occurs when there is a temperature difference.
Option E is not true because thermal energy actually flows from hot objects to cold objects. Therefore, thermal energy is transferred from fast-moving particles to slow-moving particles, not the other way around.
Therefore, The correct answers are B, C, and F.
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Calculate the self-weight of a reinforced concrete beam of breadth Xmm; depth Ymm and length 2000mm. Take the unit weight of concrete as 24kN/mm³.
The self-weight of the reinforced concrete beam is 0.024 X Y X 2000 kN.
What is a reinforced concrete beam?A reinforced concrete beam is a structural element designed to withstand the load of a building or other construction. It is made by pouring concrete into a mold or form, and then reinforcing the concrete with steel bars or other reinforcement materials. Reinforced concrete beams are commonly used in the construction of buildings, bridges, and other infrastructure, and can be designed to support a variety of loads and spans.
To calculate the self-weight of the reinforced concrete beam, we first need to determine the volume of the beam, which can be calculated as:
Volume of beam = breadth x depth x length
Substituting the given values, we get:
Volume of beam = Xmm x Ymm x 2000mm
Next, we need to calculate the weight of this volume of concrete, which can be calculated as:
Weight of concrete = Volume of beam x Unit weight of concrete
Substituting the given value of the unit weight of concrete as 24kN/mm³, we get:
Weight of concrete = Xmm x Ymm x 2000mm x 24kN/mm³
Simplifying this expression, we get:
Weight of concrete = 0.024 X Y X 2000 kN
Therefore, the self-weight of the reinforced concrete beam is 0.024 X Y X 2000 kN.
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What is torque? In general terms
Torque is a measure of the force that can cause an object to rotate about an axis. (answer taken from Khan Academy).
Urgent:
Let's say you wanted to make a flute from one-inch PVC pipe. If the lowest desired note is C5 on the Equal Temperament Scale (523.25 Hz), what length should it be cut?
In order to produce the C5 note, the length of the one-inch PVC pipe should be cut to approximately 12.91 inches.
Length and frequency of wave productionThe formula to calculate the length of a pipe to produce a desired frequency is:
L = (v/2f) * n
Where:
L is the length of the pipev is the speed of sound in air (approximately 343 m/s at room temperature)f is the desired frequencyn is the harmonic numberTo find the length of the pipe needed to produce the C5 note with a frequency of 523.25 Hz, we can use the formula above and assume the fundamental frequency (n = 1):
L = (v/2f) * n = (343 m/s / 2 * 523.25 Hz) * 1
L = 0.3279 meters or 12.91 inches
Therefore, the length of the one-inch PVC pipe should be cut to approximately 12.91 inches to produce the C5 note.
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How long does it take a current of 5 mA to deliver 15c of charge
Answer:
50 minutes
Explanation:
Since we need to find time, Time or T = Q / I. Thus, the time taken for current of 5mA to deliver 15c of charge is 3000 seconds which is equivalent to 50 minutes.
11.
Which of the following animals do not communicate with infrasound?
bats
elephants
cats
giraffes
One particular lightbulb has a 0.22-meter length of the tungsten wire used as its filament. This tungsten wire filament has a resistance of 19 ohms at a temperature of 20°C. The tungsten wire filament has a resistance of 240 ohms when this bulb is operated at a potential difference of 120 volts.
Calculate the cross-sectional area of this tungsten wire filament. [Show all work, including the equation and substitution with units.]
Calculate the power of this lightbulb when it is being operated at a potential difference of 120 volts. [Show all work, including the equation and substitution with units.]
The cross-sectional area of this tungsten wire filament is 6.544 x 10⁻⁹m² and the power of this lightbulb when it is being operated at a potential difference of 120 volts is 60 watts.
What is resistance?The amount that a substance or a device obstructs the passage of an electric current is known as its resistance. It is described as the proportion of the voltage across a conductor to the current flowing through it.
How do you determine it?The resistance formula may be used to get the tungsten wire filament's cross-sectional area:
R = (ρ * L) / A
where R is the resistance, is the tungsten's resistivity, L is the wire's length, and A is its cross-sectional area.
The resistance of the wire is 19 ohms at 20 °C. To find A, we can rearrange the equations as follows:
A = (ρ * L) / R
Inputting the values results in:
A = (5.6 x 10^-8 Ωm * 0.22 m) / 19 Ω
A = 6.544 x 10^-9 m^2
The tungsten wire filament's cross-sectional area is 6.544 x 10^-9 m^2, as a result.
The power formula may be used to determine the lightbulb's power:
P = V^2 / R
where P denotes power, V denotes potential difference, and R denotes resistance of the tungsten wire filament at 120 volts.
The wire's resistance at 120 volts is 240 ohms. Inputting the values results in:
P = (120 V)^2 / 240 Ω
P = 60 W
Therefore, while the lightbulb is operating at a 120 volt potential difference, its output is 60 watts.
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alpha centauri is 4.2 light years away from the solar system (and jupiter) what acceleration would be needed to accelerate to the half way point and decelerate until arriving if the trip is to take 400 years.
Acceleration of approximately 0.023 m/s² would be required to reach the halfway point and then decelerate to arrive at Alpha Centauri in 400 years.
What is Acceleration?Acceleration is the amount at which the velocity of an object changes over time. An object can accelerate by changing its speed, direction of motion, or both.
Equation:The required acceleration can be calculated using the formula:
a = (2d) / (t²)
where:
d = distance to be covered (half the distance to Alpha Centauri in this case, which is 2.1 light years or 1.989 x 10¹³ km)
t = time taken to complete the trip (400 years or 1.26 x 10¹⁰ seconds)
Plugging in the values, we get:
a = (2 x 1.989 x 10¹³) / (1.26 x 10¹⁰)²
a ≈ 0.023 m/s²
Therefore, an acceleration of approximately 0.023 m/s² would be required to reach the halfway point and then decelerate to arrive at Alpha Centauri in 400 years.
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Find the moment of inertia about the y-axis for three masses in an equilateral triangle if m = 2.00 kg and the sides are 0.500 m. (The connecting rods are massless).
Two parallel plates of area 5.68∙10-³ m²
have equal and opposite charges of
4.38 10-11 C placed on them. What is
the electric field between the plates?
[?] N/C
the electric field between the plates is 436.7 N/C.
How do we calculate?The electric field between the plates of a parallel plate capacitor is given by:
E = σ/ε₀
where σ is the surface charge density and ε₀ is the permittivity of free space.
surface charge density =
σ = Q/A
σ = Q/A = (2 × 4.38 × 10^-11 C) / (2 × 5.68 × 10^-3 m²) = 3.861 × 10^-6 C/m²
We substitute this value of σ and the value of
ε₀ = 8.85 × 10^-12 F/m, we get:
E = σ/ε₀
E = (3.861 × 10^-6 C/m²) / (8.85 × 10^-12 F/m)
E = 436.7 N/C
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What approximate temperature is required to begin fusion in a star?
A. 93 billion kelvins
B. Fusion occurs randomly and is not based on temperature.
C. 14 million kelvins
D. 9 billion kelvins
Answer:
The approximate temperature required to begin fusion in a star is C. 14 million kelvins. This temperature is high enough to overcome the electrostatic repulsion between positively charged atomic nuclei, allowing them to fuse and form heavier elements.
You and your family are attending an annual 4th of July fireworks display. During the show, you observe that the sound from the exploding fireworks arrives 2.5 seconds after the light from the explosions. Knowing that the air temperature that night was 26°C, determine the distance (in meters) between you and the fireworks.
Round to the nearest whole number.
Technical Note: The setup for this problem assumes that the sound from the exploding firework takes time to reach you (on the order of a second) but that you see the explosion without a time delay. This is an oversimplification! However, light travels really, really fast (about 300,000,000 m/s). The light travel time at a fireworks show is on the order of millionths of a second, so for the purposes of this problem it is OK to approximate that you are seeing the fireworks without a time delay.
Please show all work!
Answer: The speed of sound in air depends on temperature, pressure, and humidity. For dry air at 26°C, the speed of sound is approximately 346 meters per second.
Let's call the distance between you and the fireworks "d". We can use the fact that the time it takes for the sound to reach you is 2.5 seconds longer than the time it takes for the light to reach you:
d = speed of sound x time delay
d = 346 m/s x 2.5 s
d = 865 meters
Therefore, the distance between you and the fireworks is approximately 865 meters.
A stone of mass 2 kg rolls off the flat roof of a building reaches the ground with a speed of 10 m/s.
a.Calculate the kinetic energy of the stone when it reaches the ground
b the gravitational potential energy of the stone when it was on the roof
cthe height of the roof. Neglect air resistance.
Answer:
KE = 100J and PE = 100J
Explanation:
[tex]KE = 0.5*m*v^2\\PE = m*g*h\\KE = 0.5*2*100 = 100 J[/tex]
Potential energy at the start has to equal the kinetic energy at the end due to conservation of energy
1. An object, constrained to move along the x-axis is acted upon by a force F(x) where = a = 5 N/m, b = -2N/m F(x) = ax + bx² The object is observed to proceed directly from x = 1m to x = 3.0m. How much work was done by the object by the force? Does the process of integration take into account the fact that the force F(x) changes sign in the interval.
Say an impulse is applied opposite the go-kart's direction of travel. What happens to
the go-kart if its momentum + impulse = 0?
The go kart stops comes to a stop.
The go kart slows down but keeps moving.
The go kart speeds up.
There is no change in the speed of the go kart.
If the impulse is strong enough and lasts for a sufficient amount of time, the go-kart will eventually come to a stop.
Option A is correct.
What is meant by impulse?impulse is described as the integral of a force, F, over the time interval, t, for which it acts. Since force is a vector quantity, impulse is also a vector quantity.
If the force is insufficient to stop the go-kart entirely, it will slow down but continue to move. The force and duration of the impulse, along with the mass and speed of the go-kart, will all affect how much deceleration occurs.
Given that momentum plus impulse equals zero, the go-kart's change in momentum as a result of the impulse will be equal in amount but will move in the opposite direction of its original momentum.
As a result, the go-kart's final momentum will be zero, suggesting that it has either stopped or is travelling very slowly.
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Assuming that H0 = 70 km/s/Mpc , calculate the mass of the parent galaxy.
A small satellite galaxy is moving in a circular orbit around a much more massive parent and just happens to be moving exactly parallel to the line of sight as seen from Earth. The recession velocities of the satellite and the parent galaxy are measured to be 6450 km/s and 6500 km/s , respectively, and the two galaxies are separated by an angle of 0.1∘ in the sky.
The mass of the parent galaxy is 3.42 x 10^12 solar masses assuming H0 = 70 km/s/Mpc.
How do we calculate?the equation for the mass of a galaxy is :
M = (v^2 * r) / G
H0 = 70 km/s/Mpc
v_satellite = 6450 km/s
v_parent = 6500 km/s
We apply the equation for the Hubble law, in order to find the distances to the galaxies:
d_satellite = v_satellite / H0 = 92.1 Mpc
d_parent = v_parent / H0 = 92.9 Mpc
θ = 0.1∘
d = d_satellite * (θ/60) = 0.026 Mpc
We have the equation for the mass of the parent galaxy as :
M = (v^2 * r) / G
M = (6500 km/s)^2 * (0.026 Mpc) / G = 3.42 x 10^12 solar masses
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What speed must you toss a baseball straight upwards so that it takes 5 seconds to return to you?
The velocity of tossing the baseball is 24.5 m/s.
Time taken by the ball, t = 5 s
Displacement of the ball, s = 0
An object can be kept moving without the application of force. The only time a force is needed is to keep an acceleration going. Additionally, there is a downward force as well as a downward acceleration in the case of an upwardly moving projectile.
Applying the second equation of motion,
s = ut + 1/at²
s = ut + 1/2 (-g)t²
0 = ut - 1/2 gt²
ut = 1/2 gt²
Therefore, the velocity of toss,
u = 1/2 gt
u = 1/2 x 9.8 x 5
u = 24.5 m/s
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