Explanation:
There are three ways in which the thermal transfer (heat) occurs:
1. By Conduction, when the transmission is by the direct contact.
2. By Convection, heat transfer in fluids (like water or the air, for example).
3. By Radiation, by the electromagnetic waves (they can travel through any medium and in vacumm or empty space)
Since outter space is vacuum (sometimes called "empty"), energy cannot be transmitted by convection, nor conduction. It must be transmitted by electromagnetic waves that are able to travel with or without a medium.
A conducting bar rests on two parallel horizontal rails 50 cm apart forming a square area. The resistance of the bar and the rails is assumed to be constant and equal to 0.05 Ω. A uniform magnetic field 0.5 T is perpendicular to the plane of the rails. The value of the field is uniformly reduced to zero in a time of 0.1 s. What is the maximum value of the force acting on the bar during that time?
Answer:
Force = 6.25 N
Explanation:
Given:
Distance between the rails, l = 50cm = 0.5m
since it is forming a square area. thus, area = 0.5² m²
Resistance of the bar = 0.05Ω
Magnetic field, B = 0.5T
Time = 0.1s
Now,
The value for EMF is given as
EMF = (ΔArea x Field) /time
substituting the values in the above equation we get
EMF = (0.5² x 0.5) /0.1 = 1.25 Volts
now,
Current, i = EMF/ Resistance
substituting the values in the above equation we get
i = 1.25/0.05 = 25 A
Now the force is given as:
Force = i x l x B
Force = 25 x 0.5 x 0.5
Force = 6.25 N
A source emits a sound and is represented by the red dot in this map. Four people are located around the source, and the circles represent the sound wave.
As the source moves west, which person hears the highest pitch?
-person A
-person B (not correct)
-person C
-person D
Answer:
person A
Explanation:
because the sound is moving twords them
In the context of the Doppler Effect, person A will hear the highest pitch if they are located to the west of the moving sound source. The correct answer is a.
Explanation:As the source of the sound moves west, the observer who would hear the highest pitch is the one located to the west of the source, i.e., in the direction of the source's movement.
Since the source is moving towards the west, according to the Doppler Effect, the sound waves are compressed, and the wavelength is reduced in the direction of motion (west). This results in a higher frequency, which corresponds to a higher pitch, being heard by the observer in that direction.
If person A is to the west of the source, then person A will hear the highest pitch. It's important to note that person B has been indicated as not correct, hence, if person A is in the correct position relative to the westward movement of the source, person A will experience the higher pitch sound as compared to the others positioned differently.
A wire of resistivity ρ must be replaced in a circuit by a wire of the same material but four times as long. If, however, the total resistance is to remain as before, the diameter of the new wire mustA- be four times the original diameter.B- be one-fourth the original diameter.C- be the same as the original diameter.D- be one-half the original diameter.E- be two times the original diameter.
Answer:
E. two times the original diameter
Explanation:
Resistance of a wire is:
R = ρ L/A
where ρ is the resistivity of the material, L is the length, and A is the cross-sectional area.
For a round wire with diameter d:
R = ρ L / (¼ π d²)
The two wires must have the same resistance, so:
ρ₁ L₁ / (¼ π d₁²) = ρ₂ L₂ / (¼ π d₂²)
The wires are made of the same material, so ρ₁ = ρ₂:
L₁ / (¼ π d₁²) = L₂ / (¼ π d₂²)
The new length is four times the old, so 4 L₁ = L₂:
L₁ / (¼ π d₁²) = 4 L₁ / (¼ π d₂²)
1 / (¼ π d₁²) = 4 / (¼ π d₂²)
Solving:
1 / (d₁²) = 4 / (d₂²)
(d₂²) / (d₁²) = 4
(d₂ / d₁)² = 4
d₂ / d₁ = 2
So the new wire must have a diameter twice as large as the old wire.
What area of the country is the main benefactor of the electricity generated by the hoover dam?
Answer:
Explanation:
Arizona Nevada and California. That includes some pretty big cities. Los Angeles, Las Vegas, San Diego to name 3.
A substance can absorb heat energy by the process of
Answer:
conduction,convection,radiation
Based on the processes of heat transfer, substance can absorb heat energy by the process of conduction, convection and radiation.
What is heat energy?Heat energy is the energy due to temperature difference between two bodies.
Heat energy always flow from hotter to colder bodies.
The processes of heat transfer are as follows:
conduction convection radiationTherefore, a substance can absorb heat energy by the process of conduction, convection and radiation.
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Objects in free-fall ___. A:do not experience air resistance B: do not experience gravity C: are accelerating faster than 9.8 m/s/s D: are completely weightless
Answer:
A any air resistance
Explanation:
a body in freefall donot experience
Objects in free-fall motion, do not experience air resistance as it only moves under the effect of gravity. Therefore, option (A) is correct.
What are free fall and air resistance?Free fall can be described as a motion of an object in which the force of gravity is the sole force acting upon it. An object moving upwards will not consider being falling. But if the body falls under the influence of gravity is said to be in free fall.
Free fall can be described as a type of motion in which no air resistance is considered and only gravity is considered. All bodies under free fall with the same rate of acceleration, regardless of their masses.
A body that falls through the air, has suffered some degree of air resistance. Air resistance can be described as the collisions of the surface of an object with gas molecules in the air. The factors that affect air resistance are the cross-sectional area and the speed of the body.
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A grinding wheel is in the form of a uniform solid disk of radius 7.00 cm and mass 2.00 kg. It starts from rest and accelerates uniformly under the action of the constant torque of 0.600 N,m that the motor exerts on the wheel. (a) How long does the wheel take to reach its final operating speed of 1 200 rev/min? (b) Through how many revolutions does it turn while accelerating?
Answer:
Part a)
[tex]t = 1.03 s[/tex]
Part b)
[tex]N = 10.3 rev[/tex]
Explanation:
Mass of the disc is given as
m = 2.00 kg
radius of the disc is given as
r = 7 cm
so moment of inertia of the disc is given as
[tex]I = \frac{1}{2}mr^2[/tex]
[tex]I = \frac{1}{2}(2)(0.07)^2[/tex]
[tex]I = 4.9 \times 10^{-3} kg m^2[/tex]
Now given that torque on the disc is
[tex]\tau = 0.600 Nm[/tex]
so here the angular acceleration is given as
[tex]\alpha = \frac{\tau}{I}[/tex]
[tex]\alpha = \frac{0.600}{4.9 \times 10^{-3}}[/tex]
[tex]\alpha = 122.45 rad/s^2[/tex]
Part a)
if disc start from rest and then achieve final speed as 1200 rpm then
[tex]f = 1200/60 = 20 rev/s[/tex]
so final speed is
[tex]\omega = 2\pi(20) = 40\pi rad/s[/tex]
now the time taken to reach this speed is given as
[tex]\alpha t = \omega[/tex]
[tex](122.45) t = 40\pi[/tex]
[tex]t = 1.03 s[/tex]
Part b)
Number of revolution in the same time is given as
[tex]N = \frac{\omega_o + \omega}{4\pi} t[/tex]
[tex]N = \frac{40\pi + 0}{4\pi}(1.03) = 10.3 rev[/tex]
You are at an amusement park and decide to ride the biggest roller coaster there. The coaster gets to the top of its highest hill and stops there for a dramatic pause. At this point the coaster has what type of energy? A. Electrical B. Nuclear C. Potential D. Kinetic
Answer:
C. Potential energy
Explanation:
At this point the roller coaster is just waiting to be dropped into moving energy, kinetic energy. But at the moment that its at the top, its just potential energy.
At the highest point of the hill, the coaster has potential energy, therefore the correct option is C.
What is mechanical energy?Mechanical energy is the combination of all the energy in motion represented by total kinetic energy and the total stored energy in the system which is represented by total potential energy.
As total mechanical energy is the sum of all the kinetic as well as potential energy stored in the system.
As the coaster is stopped at the highest point it has zero kinetic energy the only form of energy it contains is potential energy.
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Suppose you were bungee jumping from a bridge while blowing a hand-held air horn. How would someone remaining on the bridge hear the pitch of the air horn as time increased?
a. The pitch would get progressively lower (i.e., smaller frequency)
b. The pitch would get progressively higher (i.e., larger frequency)
c. The pitch would remain the same (i.e., constant frequency)
Answer:
Answer to the question:
Explanation:
a. The pitch would get progressively lower (i.e., smaller frequency)
A person on the bridge would hear the pitch of an air horn during a bungee jump become lower as the jumper descends and higher as the jumper ascends, due to the Doppler effect.
Explanation:During a bungee jump, if someone is blowing an air horn, a person on the bridge would experience a change in the perceived pitch of the sound due to the Doppler effect. As you move away from the observer on the bridge, the pitch of the air horn would sound lower. This is because the frequency of the sound waves reaching the observer decreases as the distance between the air horn increases during the descent. Conversely, as the bungee jumper ascends and gets closer to the bridge, the frequency increases and the pitch sounds higher to the observer.
The correct answer to the question is:
a. The pitch would get progressively lower (i.e., smaller frequency) as the bungee jumper moves away from the bridge, and would get progressively higher (i.e., larger frequency) as the jumper ascends back towards the bridge.
A battery-operated car utilizes a 12.0 V system. Find the charge (in C) the batteries must be able to move in order to accelerate the 850 kg car from rest to 25.0 m/s, make it climb a 2.30 ✕ 102 m high hill, and then cause it to travel at a constant 25.0 m/s by exerting a 4.00 ✕ 102 N force for an hour.
Answer:
The required charge is 3.175 × 10⁶ C
Explanation:
Given:
Potential difference, ΔV = 12.0 V
mass of the car (m) = 850 kg
velocity of the car, v = 25.0 m/s
Height of the hill upto which car traveled, h = 2.3 × 10² m = 230 m
Now, the energy required to accelerate the car from rest to 25 m/s will be
E₁ = kinetic energy of the car = [tex]\frac{1}{2}mv^2[/tex]
on substituting the values we get
E₁ = [tex]\frac{1}{2}850\times 25^2[/tex]
or
E₁ = 2.65 × 10⁵ J
Now, the potential energy gained by the car at the height 'h' will be
E₂ = mgh = 850 × 9.8 × 230 = 1.91 × 10⁶ J
Also, the energy required to make the car travel at the constant speed of 25.0 m/s with the force of 4 × 10² N for an hour will be
W = Force × displacement
now, the displacement will be = velocity × time = 25 m/s × 1hr = 25 × 3600 = 90000 m [as 1 hr = 3600 seconds]
substituting in the above equation, we get
W = 4.0 × 10² N × 90000 m = 36 × 10⁶ J
Now, the electric potential energy (ΔU) is given as:
ΔU = qΔV
where, q is the charge
Now this electric potential energy is required to do all the work in the above cases
thus,
ΔU = E₁ + E₂ + W
or
qΔV = E₁ + E₂ + W
on substituting the values in the above equation, we get
q × 12 = 2.65 × 10⁵ J + 1.91 × 10⁶ J + 36 × 10⁶ J
or
q = (3.81 × 10⁷)/12
or
q = 3.175 × 10⁶ C
Hence, the required charge is 3.175 × 10⁶ C
A horizontal block-spring system with the block on a frictionless surface has total mechanical energy E = 50.9 J and a maximum displacement from equilibrium of 0.204 m. (a) What is the spring constant? N/m (b) What is the kinetic energy of the system at the equilibrium point? J (c) If the maximum speed of the block is 3.45 m/s, what is its mass? kg (d) What is the speed of the block when its displacement is 0.160 m? m/s (e) Find the kinetic energy of the block at x = 0.160 m. J (f) Find the potential energy stored in the spring when x = 0.160 m. J (g) Suppose the same system is released from rest at x = 0.204 m on a rough surface so that it loses 12.2 J by the time it reaches its first turning point (after passing equilibrium at x = 0). What is its position at that instant? m
(a) 2446 N/m
When the spring is at its maximum displacement, the elastic potential energy of the system is equal to the total mechanical energy:
[tex]E=U=\frac{1}{2}kA^2[/tex]
where
U is the elastic potential energy
k is the spring constant
A is the maximum displacement (the amplitude)
Here we have
U = E = 50.9 J
A = 0.204 m
Substituting and solving the formula for k,
[tex]k=\frac{2E}{A^2}=\frac{2(50.9)}{(0.204)^2}=2446 N/m[/tex]
(b) 50.9 J
The total mechanical energy of the system at any time during the motion is given by:
E = K + U
where
K is the kinetic energy
U is the elastic potential energy
We know that the total mechanical energy is constant: E = 50.9 J
We also know that at the equilibrium point, the elastic potential energy is zero:
[tex]U=\frac{1}{2}kx^2=0[/tex] because x (the displacement) is zero
Therefore the kinetic energy at the equilibrium point is simply equal to the total mechanical energy:
[tex]K=E=50.9 J[/tex]
(c) 8.55 kg
The maximum speed of the block is v = 3.45 m/s, and it occurs when the kinetic energy is maximum, so when
K = 50.9 J (at the equilibrium position)
Kinetic energy can be written as
[tex]K=\frac{1}{2}mv^2[/tex]
where m is the mass
Solving the equation for m, we find the mass:
[tex]m=\frac{2K}{v^2}=\frac{2(50.9)}{(3.45)^2}=8.55 kg[/tex]
(d) 2.14 m/s
When the displacement is
x = 0.160 m
The elastic potential energy is
[tex]U=\frac{1}{2}kx^2=\frac{1}{2}(2446)(0.160)^2=31.3 J[/tex]
So the kinetic energy is
[tex]K=E-U=50.9 J-31.3 J=19.6 J[/tex]
And so we can find the speed through the formula of the kinetic energy:
[tex]K=\frac{1}{2}mv^2 \rightarrow v=\sqrt{\frac{2K}{m}}=\sqrt{\frac{2(19.6)}{8.55}}=2.14 m/s[/tex]
(e) 19.6 J
The elastic potential energy when the displacement is x = 0.160 m is given by
[tex]U=\frac{1}{2}kx^2=\frac{1}{2}(2446)(0.160)^2=31.3 J[/tex]
And since the total mechanical energy E is constant:
E = 50.9 J
the kinetic energy of the block at this point is
[tex]K=E-U=50.9 J-31.3 J=19.6 J[/tex]
(f) 31.3 J
The elastic potential energy stored in the spring at any time is
[tex]U=\frac{1}{2}kx^2[/tex]
where
k = 2446 N/m is the spring constant
x is the displacement
Substituting
x = 0.160 m
we find the elastic potential energy:
[tex]U=\frac{1}{2}kx^2=\frac{1}{2}(2446)(0.160)^2=31.3 J[/tex]
(g) x = 0
The postion at that instant is x = 0, since it is given that at that instant the system passes the equilibrium position, which is zero.
The response provides calculations for determining the spring constant, the kinetic energy at the equilibrium point, and the mass of the block. It explains the relevant formulas and step-by-step solutions for each part of the question.
Spring Constant Calculation: Using the formula for total mechanical energy, E = [tex]1/2kA^2[/tex], where A is the maximum displacement, the spring constant is calculated as k = [tex]2E / A^2[/tex]. Substituting the given values, k = 2 * 50.9 / [tex](0.204)^2[/tex] = 500 N/m.
Kinetic Energy at Equilibrium: At the equilibrium point, all energy is in the form of potential energy; hence, the kinetic energy is zero.
Mass Calculation: Using the formula for maximum speed vmax = sqrt(E / m), where E is the total mechanical energy and m is the mass, the mass is calculated as m = E / [tex]vmax^2[/tex]. Substituting the values, m = 50.9 / [tex](3.45)^2[/tex]= 4.82 kg.
The approximate distance between Mars and Earth is about 1.34 × 108 miles. How many seconds would it take for TV pictures transmitted from the Viking space vehicle on Mars's surface to reach Earth? Enter your answer in scientific notation.
Answer:
Time taken from transmission = 719.61 seconds or 11.99 minutes
Explanation:
Given data:
The distance between the mars and the earth = 1.34 × 10⁸ miles
Now, converting the distance into meters
1 mile = 1.61 km = 1610 m
thus, we have
1.34 × 10⁸ miles = 1610 × 1.34 × 10⁸ m = 2.1574 × 10¹¹ m
Now, the picture will travel with the speed of light i.e 2.998 × 10⁸ m/s
also,
Time = Distance/speed
thus we have,
Time taken from transmission = (2.1574 × 10¹¹ m)/(2.998 × 10⁸ m/s)
or
Time taken from transmission = 719.61 seconds or (719.61/60 = 11.99 minutes)
The time it takes for TV pictures transmitted from the Viking space vehicle on Mars's surface to reach Earth is approximately 7.17 × 10^2 seconds.
Explanation:To calculate the time it takes for TV pictures transmitted from the Viking space vehicle on Mars's surface to reach Earth, we need to convert the distance between Mars and Earth from miles to meters. The approximate distance between Mars and Earth is 1.34 × 108 miles, which is approximately 2.15 × 1011 meters. The speed of light is approximately 3 × 108 meters per second. Dividing the distance by the speed of light, we can calculate the time it takes: 2.15 × 1011 meters / (3 × 108 meters per second) = 7.17 × 102 seconds.
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Suppose that the moment of inertia of a skater with arms out and one leg extended is 3.0 kg⋅m2 and for arms and legs in is 0.90 kg⋅m2 . If she starts out spinning at 5.2 rev/s , what is her angular speed (in rev/s) when her arms and one leg open outward?
Answer:
Her angular speed (in rev/s) when her arms and one leg open outward is [tex]1.56\frac{rev}{s}[/tex]
Explanation:
Initial moment of inertia when arms and legs in is [tex]I_i=0.90 kg.m^{2}[/tex]
Final moment of inertia when her arms and on leg open outward, [tex]I_f=3.0 kg.m^{2}[/tex]
Initial angular speed [tex]w_i=5.2\frac{rev}{s}[/tex]
Let the final angular speed be [tex]w_f[/tex]
Since external torque on her is zero so we can apply conservation of angular momentum
[tex]\therefore L_f=L_i[/tex]
=>[tex]I_fw_f=I_iw_i[/tex]
=>[tex]w_f=\frac{I_iw_i}{I_f}=\frac{0.9\times5.2 }{3.0}\frac{rev}{s}=1.56\frac{rev}{s}[/tex]
Thus her angular speed (in rev/s) when her arms and one leg open outward is [tex]1.56\frac{rev}{s}[/tex]
A block of mass m attached to a horizontally mounted spring with spring constant k undergoes simple harmonic motion on a frictionless surface. How would the maximum speed of the block be affected if the spring constant was increased by a factor of 4 while holding the amplitude of oscillation constant?
Answer:
The maximum speed would double
Explanation:
The maximum speed of a mass-spring system is given by:
[tex]v=\omega A[/tex]
where
[tex]\omega[/tex] is the angular frequency
A is the amplitude of the motion
The angular frequency in a spring-mass system is
[tex]\omega=\sqrt{\frac{k}{m}}[/tex]
where
k is the spring constant
m is the mass
Substituting inside the first equation,
[tex]v=\sqrt{\frac{k}{m}} A[/tex]
In this problem:
- the spring constant is increased by a factor 4: k' = 4 k
- the amplitude remains constant: A' = A
So the new maximum speed would be
[tex]v'=\sqrt{\frac{4k}{m}} A= \sqrt{4} (\sqrt{\frac{k}{m}}A)= 2v[/tex]
So, the maximum speed would double.
The maximum speed of the block in simple harmonic motion is not affected by changes in the spring constant when the amplitude of oscillation is held constant.
Explanation:The maximum speed of the block in simple harmonic motion is not affected by changes in the spring constant when the amplitude of oscillation is held constant.
The maximum speed of the block is determined by the amplitude of oscillation. As long as the amplitude remains the same, increasing the spring constant by a factor of 4 will not change the maximum speed.
Therefore, the maximum speed of the block would not be affected if the spring constant was increased by a factor of 4 while holding the amplitude of oscillation constant.
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An artificial heart valve was tested for its ability to function under extreme conditions, to a maximum flow rate of 4.00 x 10-4 m3/s. What speed would this correspond to for an average red blood cell within a blood vessel of cross-sectional area 5.00 x 10-6 m2?
Answer:
80 m/s
Explanation:
Rate of flow of blood, Volume per second = 4 x 10^-4 m^3/s
Area of blood vessel, A = 5 x 10^-6 m^2
So, Volume per second = area x velocity of blood
velocity of blood = (4 x 10^-4) / (5 x 10^-6) = 80 m/s
The speed of blood is 80 m/s.
What's the first thing you should do after retrieving a boat onto a trailer?
Answer:
Set the parking brake of the towing vehicle, and put it in park (or first gear if you have a manual transmission).
Move the vessel onto the trailer far enough to attach the winch line to the bow eye of the vessel. ...
Shut off the engine, and raise the engine or outdrive.
Pull the vessel out of the water.
Explanation:
The first thing you should do after retrieving a boat onto a trailer is to secure the boat to the trailer. This is important to ensure the boat remains stable and safe during transportation.
Here are the steps to secure the boat to the trailer:
1. Position the boat properly: Align the boat on the trailer so that it is centered and evenly distributed. Make sure the boat is positioned in such a way that the weight is balanced and evenly distributed across the trailer.
2. Attach the bow strap: The bow strap is a strong, adjustable strap that is used to secure the front (bow) of the boat to the trailer. Connect one end of the bow strap to the trailer and the other end to a secure point on the boat's bow. Make sure the strap is tight and secure, but not overly tightened to the point of damaging the boat.
3. Connect the stern tie-downs: Stern tie-downs are straps or ropes used to secure the rear (stern) of the boat to the trailer. Attach one end of each stern tie-down to the trailer and the other end to a secure point on the boat's stern. Make sure the stern tie-downs are tight and secure, but again, avoid over-tightening.
4. Check the connections: After attaching the bow strap and stern tie-downs, double-check all the connections to ensure they are properly secured. Give each strap a gentle tug to make sure it is tight and won't come loose during transport.
5. Secure loose items: Before hitting the road, secure any loose items in the boat, such as life jackets, paddles, or fishing gear. These items should be properly stowed and secured to prevent them from shifting or falling out during transportation.
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A team of sled dogs starts pulling a sled at the start of a dog-sledding race. The total mass of the sled is
205 kg, including the driver and load, and the net force acting on the sled is 744 N to the north. What is
the sled's acceleration?
Newton's 2nd law: F = m a
Divide each side by m :. a = F/m
Plug in the 2 given numbers:
a = 744N / 205kg
Acceleration = 3.63 m/s^2 north
Using the formula for acceleration (Newton's second law), the sled's acceleration is calculated to be approximately 3.63 m/s² to the north.
Explanation:The question is asking about acceleration, which in Physics is defined as the rate of change of velocity per unit of time. This is a concept in Newton's second law of motion which can be expressed with the formula F = ma. Here, F is the net force on the object, m is the mass of the object, and a is the acceleration of the object.
Therefore, we can solve the given problem by rearranging the formula to a = F/m.
In this scenario, the net force (F) is 744 N and the mass (m) is 205 kg. Substituting the values into the formula we have:
a = F/m = 744 N / 205 kg = approximately 3.63 m/s² (rounded to two decimal places).
Therefore, the sled's acceleration is approximately 3.63 m/s², directed to the north.
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A rectangular field is 300 meters long and 300 meters wide. What is the area of the field in square kilometers? Do not round your answer. Be sure to include the correct unit in your answer.
Answer:
Area of the rectangular field in kilometers is 0.09 [tex]km^2[/tex]
Explanation:
We know that 1 kilometers = 1000 meters
since we need to find the area in unit of kilometers
therefore converting length and width into kilometers
1000 meters = 1 kilometers
300 meters =[tex]\frac{300}{1000} = 0.3[/tex]
Likewise width = 0.3 km
Area = length x width
= 0.3km x 0.3 km
= 0.09 [tex]km^2[/tex]
A climber using bottled oxygen accidentally drops the oxygen bottle from an altitude of 4500 m. If the bottle fell straight down this entire distance, what is the velocity of the 3-kg bottle just prior to impact at sea level? (Note: ignore air resistance)
Answer:
300 m/s
Explanation:
As the cylinder drops off so its initial velocity is zero.
h = 4500 m, g = 10 m/s^2, u = 0
Use third equation of motion
v^2 = u^2 + 2 g h
v^2 = 0 + 2 x 10 x 4500
v^2 = 90000
v = 300 m /s
Final answer:
The velocity of the oxygen bottle just before impact at sea level, having fallen straight down from an altitude of 4500 m ignoring air resistance, is approximately 297.4 m/s.
Explanation:
To calculate the velocity of the oxygen bottle just before impact, we can use the principles of physics, specifically the conservation of energy or kinematics under the influence of gravity. Assuming air resistance is negligible, all potential energy (PE) of the bottle at the altitude of 4500 m will be converted into kinetic energy (KE) just before impact.
The potential energy (PE) at the height is given by PE = m*g*h, where m is mass, g is the acceleration due to gravity (approximately 9.81 m/s2), and h is the height from which it falls. The kinetic energy (KE) just before impact is given by KE = 0.5 * m * v2, where v is the velocity.
Setting PE equal to KE, we have m*g*h = 0.5 * m * v2. Solving for v (and noting that the mass cancels out), we find v = sqrt(2*g*h). Plugging in the values, we get v = sqrt(2*9.81*4500), which calculates to a velocity of approximately 297.4 m/s.
Two loudspeakers are located 2.59 m apart on an outdoor stage. A listener is 21.6 m from one and 22.7 m from the other. During the sound check, a signal generator drives the two speakers in phase with the same amplitude and frequency. The transmitted frequency is swept through the audible range (20 Hz to 20 kHz). (a) What is the lowest frequency fmin, one that gives minimum signal (destructive interference) at the listener's location
Answer:
Frequency [tex]f_{min,1}=155.90\ Hz[/tex]
Explanation:
Given data:
The distance between the speakers, d = 2.59 m
The distance between the listeners, ΔL = 22.7 - 21.6 = 1.1 m
Now, For a destructive interference, we know that
[tex]\frac{\Delta L}{\lambda}=0.5,1.5,2.5,.........[/tex]
where, λ = wavelength
thus,
frequency [tex]f_{min,n}=\frac{(n-0.5)v}{\Delta L}[/tex]
where,
v = speed of sound = 343 m/s
for n = 1
we get
frequency [tex]f_{min,1}=\frac{(1-0.5)\times 343}{1.1}[/tex]
or
Frequency [tex]f_{min,1}=155.90\ Hz[/tex]
The mass of a string is 5.5 × 10-3 kg, and it is stretched so that the tension in it is 230 N. A transverse wave traveling on this string has a frequency of 160 Hz and a wavelength of 0.66 m. What is the length of the string?
Answer:
The length of the string is 0.266 meters.
Explanation:
It is given that,
Mass of the string, [tex]m=5.5\times 10^{-3}\ kg[/tex]
Tension in the string, T = 230 N
Frequency of wave, f = 160 Hz
Wavelength of the wave, [tex]\lambda=0.66\ m[/tex]
We need to find the length of the string. Let l is the length of the string. The speed of a transverse wave is given by :
[tex]v=\sqrt{\dfrac{T}{M}}[/tex]
M is the mass per unit length, M = m/l
[tex]v=\sqrt{\dfrac{lT}{m}}[/tex]
[tex]l=\dfrac{v^2m}{T}[/tex]
The velocity of a wave is, [tex]v=\nu\times \lambda[/tex]
[tex]l=\dfrac{(\nu\times \lambda)^2m}{T}[/tex]
[tex]l=\dfrac{(160\ Hz\times 0.66\ m)^2\times 5.5\times 10^{-3}\ kg}{230\ N}[/tex]
l = 0.266 meters
So, the length of the string is 0.266 meters. Hence, this is the required solution.
Answer:
L = 0.275 m
Explanation:
velocity of transverse wave in a stretched string is given as
[tex]v =\sqrt \frac{T}{\mu}[/tex]
where T = tension = 230N
μ = linear density
[tex]μ = \frac[m}{L}[/tex]
where length L is in meters
Velocity = [tex]n\lambda[/tex]
so we have after equating both value of velocity
[tex]\sqrt \frac{T}{\mu} = n\lambda[/tex]
[tex]\frac{T}{\mu} =(n\lambda)^{2}[/tex]
μ = [tex]\frac{T}{(n\lambda)^{2}}[/tex]
μ = [tex] \frac{230}{(160*0.66)^{2}}[/tex]
μ = 0.020 kg/m
but μ = [tex]\frac[m}{L}[/tex]
so length of string is
L = [tex]\frac{5.5*10^{-3}}{0.020}[/tex]
L = 0.275 m
A railroad freight car, mass 15,000 kg, is allowed to coast along a level track at a speed of 2.0 m/s. It collides and couples with a 50,000-kg second car, initially at rest and with brakes released. What is the speed of the two cars after coupling?
Answer:
The speed of the two cars after coupling is 0.46 m/s.
Explanation:
It is given that,
Mass of car 1, m₁ = 15,000 kg
Mass of car 2, m₂ = 50,000 kg
Speed of car 1, u₁ = 2 m/s
Initial speed of car 2, u₂ = 0
Let V is the speed of the two cars after coupling. It is the case of inelastic collision. Applying the conservation of momentum as :
[tex]m_1u_1+m_2u_2=(m_1+m_2)V[/tex]
[tex]V=\dfrac{m_1u_1+m_2u_2}{(m_1+m_2)}[/tex]
[tex]V=\dfrac{15000\ kg\times 2\ m/s+0}{(15000\ kg+50000\ kg)}[/tex]
V = 0.46 m/s
So, the speed of the two cars after coupling is 0.46 m/s. Hence, this is the required solution.
The speed of the two cars after coupling is 0.857 m/s.
Explanation:To find the speed of the two cars after coupling, we can apply the law of conservation of momentum. The momentum of both cars before the collision is equal to the momentum of both cars after the collision. Since the second car is initially at rest, its initial momentum is zero. The momentum of the first car is given by its mass times its speed. By setting up an equation with the initial momentum of the first car and the final momentum of both cars combined, we can solve for the final speed of the two cars after coupling.
Using the equation:
mass1 * v1i = (mass1 + mass2) * vf
Substituting the given values:
(15,000 kg) * (2.0 m/s) = (15,000 kg + 50,000 kg) * vf
Simplifying the equation gives:
vf = 0.857 m/s
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The power (P) required to run a motor is equal to the voltage (E) applied to that motor times the current (I) supplied to the motor. If the motor data says the motor uses 180 watts of power and the voltage applied to the motor is 120 volts, how much current will the motor require?
Final answer:
The motor will require a current of 1.5 amperes to operate at 180 watts with an applied voltage of 120 volts, based on the formula for electric power P = IV.
Explanation:
To calculate the current required by the motor, we will use the formula for electric power, which is P = IV, where P is the power in watts, I is the current in amperes, and V is the voltage in volts.
Given:
The power consumed by the motor (P) = 180 watts
The voltage applied to the motor (V) = 120 volts
We need to solve for I (current):
I = P / V
I = 180 W / 120 V
I = 1.5 A
Therefore, the motor will require 1.5 amperes of current when operating at 180 watts of power with a voltage of 120 volts.
Since air is a mixture, it does not have a "molar mass." However, for calculation purposes, it is possible to speak of its "effective molar mass." (An effective molar mass is a weighted average of the molar masses of a mixture's components.) If air at STP has a density of 1.285 g/L, its effective molar mass is ________ g/mol.
Answer:
The effective molar mass of air at STP is 28.82 g/mol.
Explanation:
At STP, the value of pressure is 1 atm.
At STP, the temperature is equal to 273.15 K
P = 1atm, T = 273.15 K
Density of the gas at STP ,d= 1.285 g/L
[tex]PV=nRT[/tex] (Ideal gas equation)
[tex]PV=\frac{\text{Mass of air}}{\text{Molar mass of air(M)}}RT[/tex]
[tex]Density=\frac{Mass}{Volume}[/tex]
[tex]P\times M=d\times RT[/tex]
[tex]M=\frac{1.285 g/L}{1 atm}\times 0.0821 atm L/mol K\times 273.15 K[/tex]
M = 28.81 g/mol
The effective molar mass of air at STP is 28.82 g/mol.
Final answer:
The effective molar mass of air at standard temperature and pressure (STP), given its density of 1.285 g/L, is approximately 28.8 g/mol. This value is a weighted average based on the major components of air, mainly nitrogen and oxygen.
Explanation:
If air at STP has a density of 1.285 g/L, its effective molar mass is determined using the density and the ideal gas law. Given in the discussion, the effective molar mass of dry air is approximately 28.8 g/mol. This effective molar mass is a weighted average of the major components of air, primarily nitrogen (N₂) and oxygen (O₂), which account for about 80% and 20% of air's composition, respectively. At standard temperature and pressure (STP), 1 mole of any gas occupies 22.4 L. Therefore, the molar mass can be related to the density of the gas at these conditions to find its effective molar mass.
Using the information provided and considering the average composition of air, the calculation confirms that the effective molar mass of air at STP, considering its density of 1.285 g/L, is closely approximated to be 28.8 g/mol. This value is essential for various calculations in chemistry and environmental science, including converting between the mass of air and the number of moles of air, which is useful in stoichiometric calculations and understanding the behavior of gases under different conditions.
The magnetic field at the earth's surface can vary in response to solar activity. During one intense solar storm, the vertical component of the magnetic field changed by 2.8 μT per minute, causing voltage spikes in large loops of the power grid that knocked out power in parts of Canada.
What emf is induced in a square 190km on a side by this rate of change of field?
Answer:
[tex]EMF = 1684.67 Volts[/tex]
Explanation:
As we know that EMF is induced in a closed conducting loop if the flux linked with the loop is changing with time
So we can say
[tex]EMF = \frac{d\phi}{dt}[/tex]
now we have
[tex]\phi = BA[/tex]
here since magnetic field is constant so we have
[tex]EMF = A\frac{dB}{dt}[/tex]
now we have
[tex]A = (190 \times 10^3)(190 \times 10^3)[/tex]
[tex]A = 3.61 \times 10^{10} m^2[/tex]
now we have
[tex]EMF = 3.61\times 10^{10} (\frac{2.8 \times 10^{-6}T}{60 s})[/tex]
[tex]EMF = 1684.67 Volts[/tex]
Using Faraday's Law and given values, the induced emf in a 190 km square loop subjected to a changing magnetic field. The calculated emf is approximately -1692 volts.
To find the emf induced in a square loop due to a changing magnetic field, we can use Faraday's Law of Electromagnetic Induction.
This law states that the magnitude of the induced emf around a closed loop is proportional to the rate of change of the magnetic flux through the loop.
Rate of change of the magnetic field dB/dt : 2.8 μT/minSide length of the square (L): 190 km = 190,000 mConvert the rate of change of the magnetic field to Tesla per second (T/s):
2.8 μT/min = 2.8 × 10⁻⁶ T/min
Since there are 60 seconds in a minute:
r2.8 × 10⁻⁶ T/60 s ≈ 4.67 × 10⁻⁸ T/s
Calculate the area (A) of the square:
A = L × L = (190,000 m) × (190,000 m) = 3.61 × 10¹⁰ m²
Compute the induced emf (E) using Faraday's Law:
E = -A × dB/dt
E = - (3.61 × 10¹⁰ m²) × (4.67 × 10⁻⁸ T/s) ≈ -1692 V
Therefore, the emf induced in the square loop is approximately -1692 volts.
The electronegativity of nonmetals is relatively __________ as compared to the electronegativity of metals.
We have that Metals are elements that mostly produce ions of Positive charges eg [tex]Na^{2+}[/tex]
While Non metals tends to have negatively charged ions as like [tex]O^-[/tex]
We have that The electro negativity of nonmetals is relatively High as compared to the electro negativity of metals which is Low
From the question we are told
The electro negativity of nonmetals is relatively __________ as compared to the electro negativity of metals.
Generally
Metals are elements that mostly produce ions of Positive charges eg [tex]Na^{2+}[/tex]
While Non metals tends to have negatively charged ions as like [tex]O^-[/tex]
Therefore
From the definition above
Metals are elements that mostly produce ions of Positive charges eg [tex]Na^{2+}[/tex]
While Non metals tends to have negatively charged ions as like [tex]O^-[/tex]
We have that The electro negativity of nonmetals is relatively High as compared to the electro negativity of metals which is Low
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A car of mass m accelerates from speed v_1 to speed v_2 while going up a slope that makes an angle theta with the horizontal. The coefficient of static friction is mu_s, and the acceleration due to gravity is g. Find the total work W done on the car by the external forces.
Answer:
Work done by external force is given as
[tex]Work_{external} = mgLsin\theta + \mu mgLcos(\theta) + \frac{1}{2}mv_2^2 - \frac{1}{2}mv_1^2[/tex]
Explanation:
As per work energy Theorem we can say that work done by all force on the car is equal to change in kinetic energy of the car
so we will have
[tex]Work_{external} + Work_{gravity} + Work_{friction} = \frac{1}{2}mv_2^2 - \frac{1}{2}mv_1^2[/tex]
now we have
[tex]W_{gravity} = -mg(Lsin\theta)[/tex]
[tex]W_{friction} = -\mu mgcos(\theta) L[/tex]
so from above equation
[tex]Work_{external} - mgLsin\theta - \mu mgLcos(\theta) = \frac{1}{2}mv_2^2 - \frac{1}{2}mv_1^2[/tex]
so from above equation work done by external force is given as
[tex]Work_{external} = mgLsin\theta + \mu mgLcos(\theta) + \frac{1}{2}mv_2^2 - \frac{1}{2}mv_1^2[/tex]
Using the formula for work, Match the Force × Distance problems with their correct "Work Performed" answer. The first example has been completed for you.Force × Distance = Work Performed 10 newtons 6 meters =60 ng Click the item in the left column. Use the plus sign to move it up or the minus sign to move it down until it matches the correct entry in the right column. Lock your answer in place by clicking the square beside the item. (A check mark means it is locked.)5 ft.-lbs 40 pounds 100 feet 62 n-m 2.5 pounds 24 inches 200 ft.-lbs. 62 newtons 1 meter 40,000 ft.-lbs. 1 ton 20 foot 4000 ft.-lbs. 400 pounds 0.5 feet
Using the formula for work (Work = Force x Distance), force and distance pairs are matched to their corresponding 'Work Performed' measurements. This process involves converting all measurements to the metric system (newtons and meters) to calculate the work performed in newton-meters (n-m).
Explanation:The formula for work is Work = Force x Distance. Force is usually measured in newtons (N), and distance is measured in meters (m), so work is measured in newton-meters (n-m). One foot-pound (ft-lb) is equivalent to 1.35582 n-m and one pound is equivalent to 4.44822_newtons_ in the metric system. Therefore, the provided force and distance pairs can be matched to the correct 'Work Performed' answer as follows:
5 ft-lbs = 5 * 1.35582 = 6.7791 n-m (Approximately 7 n-m)40 pounds 100 feet = (40 * 4.44822_newtons_) * (100 * 0.3048_meters_) = 53096 n-m (Approximately 520 n-m)2.5 pounds 24 inches = (2.5 * 4.44822_newtons_) * (24 * 0.0254_meters_) = 6.8058 n-m (Approximately 7 n-m)62 newtons 1 meter = 62 * 1 = 62 n-m1 ton 20 foot = (2000 pounds * 4.44822_newtons_) * (20 * 0.3048_meters_) = 54680.4 n-m (Approximately 55000 n-m)400_pounds_ 0.5 feet = (400 * 4.44822_newtons_) * (0.5 * .3048_meters_) = 271.258 n-m (Approximately 270 n-m)Learn more about Workhttps://brainly.com/question/30763018
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In a follow-up experiment, two identical gurneys are placed side-by-side on a ramp with their wheels locked to eliminate spinning. Gurney 1 has a dummy placed on it to give it a total mass of 200 kg, while Gurney 2 is loaded with a dummy that makes it only 50 kg overall. If the ramp has a coefficient of friction of μs, which gurney is more likely to slide down the ramp?
Given the same ramp angle and coefficient of friction, the lighter gurney (50kg) is more likely to slide down the ramp since it requires less friction force to stay stationary as compared to the heavier gurney (200kg).
Explanation:The likelihood of the gurneys sliding down the slope depends upon the balance of forces on each. The force due to gravity on each gurney is mg sin θ, where m is mass, g is acceleration due to gravity, and θ is the angle of the ramp. The force of static friction on each gurney is μs N = μs mg cos θ, where μs is the coefficient of static friction, and N is the normal force, which equals mg cos θ.
In order for the gurneys not to slide, the friction force (μs mg cos θ) must be equal to or greater than the force due to gravity (mg sin θ). For a larger mass (like gurney 1 with the 200 kg dummy), the friction force is greater, so it is more likely to stay put. On the other hand, the smaller mass (gurney 2 with the 50 kg dummy) suffers less friction force due to its lesser weight. Therefore, as long as the angle of the ramp and the coefficient of friction are the same for both gurneys, gurney 2 (50 kg) is more likely to slide down the ramp.
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The atomic radius of main-group elements generally increases down a group because ________.
Answer:
The principal quantum number of the valence orbitals increases.
Explanation:
The atomic radius of main-group elements generally increases down a group because the principal quantum number of the valence orbitals increases.
The atomic radius of main-group elements increases down a group because the valence electron shell is getting larger and there is a larger principal quantum number, so the valence shell lies physically farther away from the nucleus.
Explanation:The atomic radius of main-group elements generally increases down a group because as you go down a column of the periodic table, the valence electron shell is getting larger and there is a larger principal quantum number, so the valence shell lies physically farther away from the nucleus. This trend can be summarized as follows:
As the atomic number increases down a group, there is an increase in the positive nuclear charge.However, there is also an increase in the number of occupied principal energy levels.Higher principal energy levels consist of orbitals which are larger in size than the orbitals from lower energy levels.The effect of the greater number of principal energy levels outweighs the increase in nuclear charge, and so atomic radius increases down a group.