Answer
a) -2842 J
b) 2842 J
Explanation:
The escalator is moving the man of mass 58 kg till the height of 5 meters
So here;
m=58 kg
distance = height = h= 5 m
gravitational acceleration = g= 9.8 m/sec2
a) We know work is scalar product of force and displacement
i-e Work = F.S= FS cosθ, where θ is the angle between force vector and displacement vector
When escalator is moving up - the gravitational force is acting downward i- opposite to displcacement i-e angle between force and displacement is 180 degrees.
we have data
m= 58 kg
F=mg = 58×9.8=568.4 N
S=5 m
Work = F.S=FS cos 180°=568.4×5×(-1)= -2842 J
So the work done by gravitational force is -2842 J and -ve sign here indicates that distance is traveled in opposite direction of force.
b) When escalator is moving up the, force is exerted by the escalator equal to gravitational force and the displacement is in the same direction so the angle between force and displacement is 0 degrees
Work = F.S=FS cos (0)=568.4×5×1=2842 J
So work done by the gravitational force then will be 2842 J
So in both cases work is same but in opposite directions.
The average speed of a nitrogen molecule in air is proportional to the square root of the temperature in kelvins (K). If the average speed is 475 m/s on a warm summer day (temperature=300.0 K), what is the average speed on a frigid winter day (250.0 K)?
Answer:
v₂ = 395.83 m/s
Explanation:
given,
Average speed of nitrogen molecule, v₁ = 475 m/s
Temperature in summer, T₁ = 300 K
Average speed of nitrogen molecule in winter, v₂ = ?
Temperature in winter, T₂ = 250 K
The relation of average speed with temperature
[tex]v\ \alpha\ \sqrt{T}[/tex]
now,
[tex]\dfrac{v_2}{v_1} = \dfrac{\sqrt{T_2}}{\sqrt{T_1}}[/tex]
[tex]\dfrac{v_2}{475} = \dfrac{\sqrt{250}}{\sqrt{300}}[/tex]
v₂ = 0.833 x 475
v₂ = 395.83 m/s
The average speed on a frigid winter day is equal to v₂ = 395.83 m/s
A car went 60 km in 5/6 of an hour while a second car went 54 km in 2/3h. Which car was faster? How many times faster?
Answer:
The car that went 54 km in 2/3h was faster, 5/4 times faster than the other car
Explanation:
Average speed of a car is the ratio between the displacement [tex]\Delta x [/tex] and the time (t) it takes to do that displacement:
[tex]V_{avg}=\frac{\Delta x}{t} [/tex]
So, for the first car:
[tex]V_{avg1}=\frac{60km}{\frac{5h}{6}} =72\frac{km}{h} [/tex] (1)
for the second car we have:
[tex]V_{avg2}=\frac{60km}{\frac{2h}{3}} =90\frac{km}{h} [/tex] (2)
So, the second cart is faster than the first one. To find how many times divide speed 2 by speed 1:
[tex]\frac{90}{72}=\frac{5}{4} [/tex]
Spiders may "tune" strands of their webs to give an enhanced response at frequencies corresponding to the frequencies at which desirable prey might struggle. Orb web silk has a typical diameter of 0.0020 mm, and spider silk has a density of 1300 kg/m3. To give a resonance at 200Hz to what tension must a spider adjust a 16cm long strand of silk?
To find the tension in the silk strand, we can use the formula: T = (4 x L x f^2 x m x pi^2 x r^2) / (g x rho x sin(theta)). Plugging in the given values, we can solve for T.
Explanation:To find the tension in the silk strand, we can use the formula:
T = (4 x L x f^2 x m x pi^2 x r^2) / (g x rho x sin(theta))
Where:
T is the tension in the strand of silkL is the length of the strand (converted to meters)f is the desired frequency (converted to radians per second)m is the mass per unit length of the silk (density x cross-sectional area)pi is a mathematical constant (approximately 3.14159)r is the radius of the silk strand (half of the diameter)g is the acceleration due to gravity (approximately 9.8 m/s^2)rho is the density of the silktheta is the angle between the strand and the vertical direction (typically 90 degrees)Plugging in the given values:
L = 0.16 mf = 200 Hz (converted to radians per second by multiplying by 2 x pi)m = rho x (pi x r^2)pi = 3.14159r = 0.0010 m (half of the diameter)g = 9.8 m/s^2rho = 1300 kg/m^3theta = 90 degrees (converted to radians by multiplying by pi/180)By substituting these values into the equation and solving for T, we can find the tension in the silk strand.
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The spider must adjust the tension in a 16 cm strand of silk to approximately 0.185 N to achieve a resonance frequency of 200 Hz.
The formula for the fundamental frequency (f) of a stretched string is:
f = (1 / 2L) * √(T / μ)
Where:
f = frequency (200 Hz)L = length of string (0.16 m)T = tension in the string (N)μ = linear mass density (kg/m)First, we calculate the linear mass density (μ) of the spider silk, using:
μ = ρ * A
Where:
ρ = density (1300 kg/m³)A = cross-sectional area (m²)Given the diameter (d) of the strand is 0.0020 mm or 2.0 x 10⁻⁶ m, the cross-sectional area can be calculated as:
A = π * (d / 2)²
A = π * (1.0 x 10⁻⁶)² = π x 10⁻¹² m²
Therefore:
μ = 1300 kg/m³ * π x 10⁻¹² m² = 4.084 x 10⁻⁹ kg/m
Using the frequency formula, rearranged to solve for tension (T):
T = (2Lf)² * μ
T = (2 * 0.16 m * 200 Hz)² * 4.084 x 10⁻⁹ kg/m
T = 184.8272 x 10⁻⁹ N
T ≈ 0.185 N
The tension the spider must adjust to achieve a resonance at 200 Hz for a 16 cm long strand of silk is approximately 0.185 N.
After skiding down a snow-covered hill on an inner tube, Ashley is coasting across a level snowfield at a constant velocity of 2.7 m/s. Miranda runs after her at a velocity of 4.1 m/s and hops on the inner tube. How fast do the two of them slide across the snow together on the inner tube?
Answer:
3.3 m/s
Explanation:
The question is incomplete, here is the complete question:
After skiding down a snow-covered hill on an inner tube, Ashley is coasting across a level snowfield at a constant velocity of 2.7 m/s. Miranda runs after her at a velocity of 4.1 m/s and hops on the inner tube. How fast do the two of them slide across the snow together on the inner tube? Ashley's mass is 71 kg and Miranda's is 58 kg. Ignore the mass of the inner tube and any friction between the inner tube and the snow.
SOLUTION:
mass of Ashley (Ma) = 71 kg
mass of Miranda (Mm) = 58 kg
initial velocity of Ashley (Va) = 2.7 m/s
initial velocity of Miranda (Vm) = 4.1 m/s
Find the final velocity (Vf) at which they both slide together
from the conservation of momentum, initial momentum = final momentum
Ma.Va + Mm.Vm = (Ma + Mm) . Vf
[tex]Vf = \frac{Ma.Va + Mm.Vm}{Ma + Mm} \\ Vf=\frac{(71 x 2.7) + (58 x 4.1)}{71+58}[/tex]
Vf = (191.7 +237.8) / (129)
Vf = 3.3 m/s
In 1996, NASA performed an experiment called the Tethered Satellite experiment. In this experiment a 2.30 104-m length of wire was let out by the space shuttle Atlantis to generate a motional emf. The shuttle had an orbital speed of 7.50 103 m/s, and the magnitude of the earth's magnetic field at the location of the wire was 5.40 10-5 T. If the wire had moved perpendicular to the earth's magnetic field, what would have been the motional emf generated between the ends of the wire?
emf = 9.3 x 10³
Explanation:
When a conductor moves in the magnetic field , the emf is generated across its ends . Which can be calculated by the relation
emf ξ = B x l x v
here B is the magnetic field strength , l is the length of conductor and v is its velocity .
In our question B = 5.4 x 10⁻⁵ T
l = 2.30 x 10⁴ m and v = 7.5 x 10³
Thus ξ = 5.4 x 10⁻⁵ x 2.30 x 10⁴ x 7.5 x 10³ = 9.3 x 10³ Volt
6. A car, 1110 kg, is traveling down a horizontal road at 20.0 m/s when it locks up its brakes. The coefficient of friction between the tires and road is 0.901. How much distance will it take to bring the car to a stop?
To calculate the distance that it will take to bring the car to a stop, we can use the equations of motion. The force of kinetic friction can be calculated by multiplying the coefficient of friction by the normal force. Using the equations v = u + at and s = ut + 0.5at^2, we can find the distance.
Explanation:To calculate the distance that it will take to bring the car to a stop, we can use the equations of motion. The force of kinetic friction can be calculated by multiplying the coefficient of friction by the normal force. The normal force is equal to the weight of the car, which is given by the mass of the car multiplied by the acceleration due to gravity. The force of kinetic friction is equal to the mass of the car multiplied by the acceleration. Rearranging the equation F = ma to solve for acceleration gives us a = F/m. Substituting the force of kinetic friction for F and the mass of the car for m, we can find the acceleration. Using the equation v = u + at, where v is the final velocity (0 m/s), u is the initial velocity (20.0 m/s), a is the acceleration, and t is the time, we can solve for t. Finally, we can use the equation s = ut + 0.5at^2 to calculate the distance s that it will take to bring the car to a stop. Plugging in the values for u, t, and a will give us the answer.
A physics student with a stopwatch drops a rock into a very deep well, and measures the time between when he drops the rocks and when he hears the sound of the rock hitting the water below. If the speed of sound is 343 m/s, and the student measures a time of 6.20 s, how deep is the well?
Answer:
h= 161.06 m
Explanation:
Given that
Speed of the sound ,C= 343 m/s
Total time ,t= 6.2 s
lets take the depth of the well = h
The time taken by stone before striking the water = t₁
we know that
[tex]h=\dfrac{1}{2}gt_1^2[/tex]
[tex]t_1=\sqrt{\dfrac{2h}{g}}[/tex]
The time taken by sound =t₂
[tex]t_2=\dfrac{h}{343}[/tex]
The total time
t = t₁+ t₂
[tex]6.2 = \sqrt{\dfrac{2h}{g}}+\dfrac{h}{343}[/tex]
[tex]6.2 = \sqrt{\dfrac{2h}{9.81}}+\dfrac{h}{343}[/tex]
Now by solving the above equation we get
h= 161.06 m
Therefore the depth of the well will be 161.06 m.
In most energy sources, such as fossil fuels, where is the energy originally derived from?
A. the Sun
B. the Earth's core
C. the magnetic poles
D. the ocean currents
The energy is derived from A.sun.
Explanation:
The energy from sources like Fossil fuels is received from the Producers (Plants, algae) that receives the energy directly from sunlight for photosynthesis earlier long ago. This energy when the plant dies and decomposes over a long period of time and becoming a fossil fuel.Fossils fuels are the remaining of the organisms that lived long back ago they are the energy source for fossil fuel which are burnt in large numbers.Fossil fuels once burnt can never be reused again because their medium gets converted or transferred.Technician A says current is the same in each branch of a parallel circuit. Technician B says current is the same everywhere in a series circuit. Who is right?
Answer:
Technician B
Explanation:
The current amp value at the battery position is the current value. The current is the same everywhere for a series circuit without any connecting points. The current at the position of the battery is the same as in each resistor position.
Final answer:
Technician B is correct: current is the same in all parts of a series circuit. Technician A is incorrect: current divides in the branches of a parallel circuit and is not the same. The sum of branch currents equals the total current in parallel circuits.
Explanation:
Understanding Current in Series and Parallel Circuits
Technician B is correct when they say current is the same everywhere in a series circuit. In a series circuit, there is only one path for the current to flow, thus the current (I) is identical through any component in the series, as stated: I = I1 = I2 = I3. This principle is known as the first principle of series circuits. On the other hand, Technician A is incorrect in suggesting current is the same in each branch of a parallel circuit. In parallel circuits, the current divides at each junction and the total supplied current is the sum of the currents in the various branches.
So, in summary, in a series circuit, the current is constant through all components, and the total voltage drop across all components adds up to the voltage supplied by the source. In a parallel circuit, meanwhile, each resistance experiences the same voltage difference, while the current through each branch may vary depending on the resistance of that branch.
A carnival merry-go-round rotates about a vertical axis at a constant rate. A man standing on the edge has a constant speed of 3.66 m/s and a centripetal acceleration :a of magnitude 1.83 m/s2. Position vector :r locates him relative to the rotation axis. (a) What is the magnitude of :r? What is the direction of :r when :a is di- rected (b) due east and (c) due south?
The magnitude of the position vector :r is approximately 7.32 m. When the centripetal acceleration is directed due east, :r will also be due east. When the centripetal acceleration is directed due south, :r will also be due south.
Explanation:The magnitude of the position vector :r can be determined using the equation :a = :v^2 / r where :v is the speed of the man and :a is the centripetal acceleration. Rearranging the equation, we get :r = :v^2 / :a. Substituting the given values, we find :r = (3.66^2) / 1.83 which is approximately 7.32 m.
When the centripetal acceleration is directed due east, the position vector :r will be due east. When the centripetal acceleration is directed due south, the position vector :r will be due south.
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Fiora starts riding her bike at 18 mi/h. After a while, she slows down to 12 mi/h, and maintains that speed for the rest of the trip. The whole trip of 69 miles takes her 4.5 hours. For how long did she travel at 18 mi/h?
Answer:
t = 2.5 hours
Explanation:
given,
speed of the bike for t time= 18 mi/h
final speed of the bike after t time = 12 mi/h
total distance, D = 69 miles
total time, T= 4.5 hour
time for which speed of the bike is 18 mi/h = ?
we know distance = speed x time
now,
18 x t + 12 (4.5 - t) = 69
6 t + 54 = 69
6 t = 15
t = 2.5 hours
The bike was at the speed of 18 mi/h for 2.5 hours.
A protester carries his sign of protest, starting from the origin of an xyz coordinate system, with the xy plane horizontal. He moves 40 m in the negative direction of the x axis, then 20 m along a perpendicular path to his left, and then 25 m up a water tower.
(a) In unit-vector notation, what is the displacement of the sign from start to end?
(b) The sign then falls to the foot of the tower. What is the magnitude of the displacement of the sign from start to this new end?
Answer:
Part A:
[tex]Displacement\ vector= -40\hat i+20\hat j+25\hat k[/tex]
Part B:
Magnitude of displacement=44.721359 m
Explanation:
Given Data:
40 m in negative direction of the x axis
20 m perpendicular path to his left (considering +ve y direction)
25 m up a tower (Considering +ve z direction)
Required:
In unit-vector notation, what is the displacement of the sign from start to end.The magnitude of the displacement of the sign from start to this new end=?Solution:
Part A:
[tex]Displacement= (0-40)\hat i+(0+20)\hat j+(0+25)\hat k\\Displacement= -40\hat i+20\hat j+25\hat k[/tex]
where:
i,j,k are unit vectors
Part B:
Sign falls to foot of tower so z=0
[tex]Displacement= -40\hat i+20\hat j+0\hat k[/tex]
Magnitude of displacement:
[tex]Magnitude\ of\ displacement=\sqrt{(-40)^2+(20)^2+0^2} \\Magnitude\ of\ displacement=44.721359\ m[/tex]
Which materials should Hannah choose for her pot and spoon?
A. Hannah should choose copper for her pot because it has the lowest specific heat, and
she should choose wood for her spoon because it has the highest specific heat.
B. Hannah should choose wood for her pot because it has the highest specific heat, and
she should choose copper for her spoon because it has the lowest specific heat.
C. Hannah should choose wood for her pot because it has the highest specific heat, and
she should choose rubber for her spoon because it has the second highest specific
heat.
D. Hannah should choose copper for her pot because it has the lowest specific heat, and
she should choose steel because it has the second lowest specific heat.
A. Hannah should choose copper for her pot because it has the lowest specific heat, and she should choose wood for her spoon because it has the highest specific heat
Explanation:
The specific heat capacity of a substance is the amount of heat required to increase the temperature of 1 kg of the substance by 1 degree.
Mathematically:
[tex]C=\frac{Q}{m\Delta T}[/tex]
where
Q is the amount of heat supplied to the substance
m is the mass of the subtsance
[tex]\Delta T[/tex] is the increase in temperature
This means that:
A substance with higher specific heat needs a lot of energy to raise its temperatureA substance with higher specific heat needs a small amount of energy to increase its temperatureIn this situation, we want:
A material with low specific heat for the pot, because the pot must be able to transmit heat efficiently, so it must be able to become hot (=increase its temperature) with a small amount of heatA material with high specific heat for the spoon, so that the spoon does not become too hot too fast (because it takes a lot of energy to increase its temperature)Therefore, the most reasonable choice in this situation is:
A. Hannah should choose copper for her pot because it has the lowest specific heat, and she should choose wood for her spoon because it has the highest specific heat
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A vertical steel beam in a building supports a load of 6.0×10⁴. If the length of the beam is 4.0m and it's cross-sectional area is 8.0×10^-3m². Find the diameter of the beam which is compressed along its length
Answer:
DL = 1.5*10^-4[m]
Explanation:
First we will determine the initial values of the problem, in this way we have:
F = 60000[N]
L = 4 [m]
A = 0.008 [m^2]
DL = distance of the beam compressed along its length [m]
With the following equation we can find DL
[tex]\frac{F}{A} = Y*\frac{DL}{L} \\where:\\Y = young's modulus = 2*10^{11} [Pa]\\DL=\frac{F*L}{Y*A} \\DL=\frac{60000*4}{2*10^{11} *0.008} \\DL= 1.5*10^{-4} [m][/tex]
Note: The question should be related with the distance, not with the diameter, since the diameter can be found very easily using the equation for a circular area.
[tex]A=\frac{\pi}{4} *D^{2} \\D = \sqrt{\frac{A*4}{\pi} } \\D = \sqrt{\frac{0.008*4}{\\pi } \\\\D = 0.1[m][/tex]
the phrase positive to positive negative to ground is correct when jump starting a car true or false
Answer: TRUE
Explanation:Jump starting a car is a process of starting a car whose battery is Dead,which means it doesn't have enough battery life to start a Car.
The process involves bringing both cars close to each other and Connecting the positive side of a good battery to the positive side of the Dead battery using a JUMPER CABLES,
Connect the positive cable to the positive side of the working battery,
Connect the Negative cable to the Negative side of the working battery,
Finally,connect the Negative cable to a grounded meta part of the car we want to JUMP START.
The phrase "positive to positive, negative to ground" is true when jump starting a car.
Explanation:The phrase "positive to positive, negative to ground" is true when jump starting a car.
When jump starting a car, it is important to connect the positive terminals of both the donor and recipient vehicles using jumper cables. Then, the negative terminal of the recipient vehicle should be connected to a grounded metal surface, such as the engine block or a bolt on the frame.
By following this phrase, you ensure that the electrical current flows in the correct direction, providing a safe and effective way to start a car with a dead battery.
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Which statement correctly compares sound and light waves?
A) Both light and sound waves need matter to carry energy from one place to another.
B) Neither light nor sound waves need matter to carry energy from one place to another.
C) Light waves carry energy paral
Answer:
D) Sound waves carry energy parallel to the motion of the wave, while light waves carry energy perpendicular to it.
Explanation:
A) This is incorrect because Light waves do not need a medium to pass through it while Sound waves need a medium to pass through it.
B) This is incorrect as explained above.
C) This is incorrect because Light waves do not carry energy parallel to the motion of the wave.
Light waves are transverse waves, as so they carry energy perpendicular to the motion of the wave while Sound waves are longitudinal waves and so, they carry energy parallel to the motion of the wave.
D) This is correct because Sound waves carry energy parallel to the motion of the wave.
Sound waves are transverse waves, as so they carry energy parallel to the motion of the wave while Light waves are longitudinal, as so they carry energy perpendicular to the motion of the wave.
Answer:
D-Sound waves carry energy parallel to the motion of the wave, while light waves carry energy perpendicular to it.
Explanation:
Halley's comet moves about the Sun in an elliptical orbit, with its closest approach to the Sun being 0.59 A.U. and its greatest distance being 35 A.U. (A.U. is the Earth-Sun distance). If the comet's speed at closest approach is 47 km/s, what is its speed when it is farthest from the Sun?
Answer:
Explanation:
Given
Halley's closest distance from sun is [tex]r_1=0.59\ A.U.[/tex]
Greatest distance is [tex]r_2=35\ A.U.[/tex]
Comet's speed at closest approach is [tex]v_1=47\ km/s[/tex]
As there is no external torque so angular momentum of comet about the sun is conserved
[tex]L_1=L_2[/tex]
[tex]mr_1^2\times \omega _1=mr_2^2\times \omega _2[/tex]
where [tex]\omega =angular\ velocity [/tex]
This can be written as [tex]\omega =\frac{v}{r}[/tex]
Therefore
[tex]mr_1^2\times \frac{v_1}{r_1}=mr_2^2\times \frac{v_2}{r_2}[/tex]
[tex]r_1\times v_1=r_2\times v_2[/tex]
[tex]0.59\times 47=35\times v_2[/tex]
[tex]v_2=0.79\ km/s[/tex]
If you don't answer this in the next 5 seconds, tomorrow morning you will step on a LEGO trying to grab the milk from the fridge.
Answer:
d = 78 [km]
Explanation:
The displacement shift was from Tipton to Iowa city, so we have:
d1 = 27[km]
Then he travels back for 15[km]
d2 = 15[km]
Finally he returns back to Iowa city the displacement 36 [km]
d3 = 36[km]
d = d1 + d2 + d3
d = 27 + 15 + 36
d = 78 [km]
When connected to a battery, a lightbulb glows brightly. If the battery is reversed and reconnected to the bulb, the bulb will glow (a) brighter (b) dimmer (c) with the same brightness (d) not at all
Answer: c) with the same brightness
Explanation: The load in this case the bulb, is not polarized ( it has no positive and negative points) thus any connection relative to the battery (source) will have no effect on it brightness.
Also, brightness is a function of current and in this case the voltage ( from battery) and resistance of load (bulb) is constant, and according to ohms law (V=IR) if the current is constant at the first connection, it will be the same at the reversed connection.
Final answer:
When a battery is reversed and reconnected to a lightbulb, the bulb will glow with the c) same brightness because the alteration does not change the magnitude of the voltage or the resistance in the circuit.
Explanation:
When a battery is reversed and reconnected to a lightbulb, the bulb will glow with the same brightness. This is because the brightness of a bulb in a simple circuit primarily depends on the voltage across the bulb and the resistance in the circuit. Reversing the battery does not change the magnitude of the voltage or the resistance; it merely changes the direction of current flow.
In addition to this, lightbulbs, being resistive elements, respond to the magnitude of the current. As long as the total voltage remains the same, reversing the battery's specific direction does not affect the brightness, thus the correct answer is (c) with the same brightness.
A boy is sledding down a hill and has an initial speed of +12 m/s. He continues to speed up and reaches a final velocity of +18m/s after traveling for 12 seconds what distance does the boy travel?
Answer:
180m
Explanation:
V = Final velocity = 18
U = Initial Velocity = 12
a = Acceleration = (18-12)/12 = 6/12 = 0.5
d = ?
V² = U² + 2ad
18² = 12² + 2*0.5*d
324 = 144 +d
d = 324 - 144
d = 180m
Final answer:
The boy travels a distance of 180 meters. This calculation is based on the kinematic equations for uniformly accelerated motion using the given initial and final velocities and the time taken.
Explanation:
The subject of the question is Physics, and it appears to be at a High School level. The problem deals with kinematics, specifically the equations of motion for an object with constant acceleration. To find the distance traveled by the boy sledding down the hill, we can use the kinematic equation: s = ut + ½ at², where s is the distance, u is the initial velocity, t is the time, and a is the acceleration. The initial speed u is given as +12 m/s, the final velocity v is +18 m/s, and the time t is 12 seconds. We first find the acceleration using the formula a = (v - u) / t. Substituting the known values, we get a = (18 m/s - 12 m/s) / 12 s = 0.5 m/s². Now we can calculate the distance s using the kinematic equation: s = (12 m/s)(12 s) + ½(0.5 m/s²)(12 s)² = 144 m + 36 m = 180 m. Therefore, the boy travels a distance of 180 meters.
What is the angular diameter (in arcseconds) of an object that has a linear diameter of 75 cm and a distance of 2 km?
Answer:
The angular diameter is 77.35 arc-seconds.
Explanation:
The angular diameter, as shown in the figure, is the angle [tex]x[/tex] subtended by the the diameter of the object.
Before we do the calculation, we first convert everything to meters.
The diameter of the of the object in meters is
75cm =0.75m,
and the distance to the object in meters is
2 km = 2000 m.
Now, from trigonometry we get:
[tex]tan (\frac{x}{2} )= \dfrac{radius}{length} = \dfrac{0.75/2}{2000} \\\\\dfrac{x}{2} = tan^{-1}(\dfrac{0.75/2}{2000})\\\\\dfrac{x}{2}= 0.0107\\\\\boxed{x= 0.0215^o}[/tex]
and since 1 degree = 3600 arc-seconds, [tex]x[/tex] in arc-seconds is
[tex]x= 0.0215*3600 \\\\\boxed{x= 77.35''}[/tex]
A 56.0kg ice skater spins about a vertical axis through her body with her arms horizontally outstretched, making 2.50 turns each second. The distance from one hand to the other is 1.5m. Biometric measurements indicate that each hand typically makes up about 1.25 % of body weight.
Part A) horizontal force must her wrist exert on her hand F=150N
Express the force in part (a) as a multiple of the weight of her hand?
Answer:
Net force = 129.4, Force as multiple of weight of her hand = 18.84
Explanation:
Given Data:
Total body weight = 56.0 kg ;
no. of turns = 2.5/second ;
hand to hand distance = 1.5m ;
weight of hand = 1.25% of body weight ;
Solution:
mass of hand = [tex]\frac{1.25}{100}[/tex]*56 = 0.7kg ;
radius = d/2 = 1.5/2 = 0.75m ;
Now we need to find velocity, as we know that velocity can be calculated by dividing distance by time
v = d/t = [tex]\frac{2.5*2*3.14*0.75}{1}[/tex] = 11.775 m/s or 12 m/s;
a.
The formula to calculate force is given as
F = mv²/r = (0.7*11.775²)/0.75 = 129.4 N
b.
To calculate force as multiple of weight on her hand, we need to calculate the gravitational force W on her hand first.
W = gm = 9.81 * 0.7 = 6.867 N
Now the wieght on her hand can be represented by
[tex]\frac{Force_{net} }{weight of hand}[/tex] = 129.4 / 6.867 = 18.84
The force that the ice skater exerts on her hand (150N) is roughly 22 times the weight of her hand (6.86N). She achieves this by spinning with her arms outstretched.
Explanation:The skater's hand, as given by biometric measurements, makes up about 1.25% of her body weight. Since her body weight is 56.0kg, her hand weight would be 0.0125 * 56.0kg = 0.7kg. In terms of newtons (N), when we consider the acceleration due to gravity as approximately 9.8 m/s², the weight of her hand becomes 0.7kg * 9.8 m/s² = 6.86N. Thus, if we're asked to express the force that her wrist exerts on her hand (150N) as a multiple of the weight of her hand, we'll divide the two forces. Namely, F_hand/F_weight = 150N/6.86N which is approximately 21.86. Therefore, the force her wrist exerts on her hand is roughly 22 times the weight of her hand.
Learn more about Force and Weight here:https://brainly.com/question/35877739
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to prevent a manual-type torch from damage, it is made of a special plastic that resists what?
Answer:
heat
Explanation:
An overweight boy and a skinny girl are balanced on a massless seesaw. If they both move forward such that they are one-half their original distance from the pivot point, what will happen to the seesaw?
The seesaw will average out a little bit, and not be as tilted to one side as before.
Racing greyhounds are capable of rounding corners at very high speeds. A typical greyhound track has turns that are 45 m diameter semicircles. A greyhound can run around these turns at a constant speed of 16 m/s .What is its acceleration in m/s^2?What is its acceleration in units of g?
Answer:
In m/s^2:
a=11.3778 m/s^2
In units of g:
a=1.161 g
Explanation:
Since the racing greyhounds are capable of rounding corners at very high speed so we are going use the following formula of acceleration for circular paths.
[tex]a=\frac{v^2}{r}[/tex]
where:
v is the speed
r is the radius
Now,
[tex]a=\frac{16^2}{45/2}\\ a=11.3778 m/s^2[/tex]
In g units:
[tex]a=\frac{11.3778\ g}{9.8}\\ a=1.161\ g[/tex]
Newton's Law of Cooling says that the rate of cooling of an object is proportional to the difference between its own temperature and the temperature of its surrounding. Write a differential equation that expresses Newton's Law of Cooling for this particular situation.
Answer:
[tex]\frac{dQ}{dt} =-hA\Delta T(t)[/tex]
Explanation:Newton.s law of cooling states that the rate of cooling of an object is proportional to the difference between its own temperatures and temperature of its surroundings. Mathematically,
[tex]\frac{dQ}{dt} =-hA [T(t)-T(s)]\\[/tex]
[tex]\frac{dQ}{dt} =-hA\Delta T(t)[/tex]
where [tex]Q[/tex] is the heat transfer
[tex]h[/tex] is heat transfer coefficient
[tex]A[/tex] is the heat transfer surface area
[tex]T[/tex] is the temperature of the object's surface
[tex]T(s)[/tex] is the temperature of the surroundings
Final answer:
Newton's Law of Cooling can be expressed using a differential equation: dQ/dt = -k(T - Ts).
Explanation:
Newtons's Law of Cooling states that the rate of cooling of an object is proportional to the difference between its temperature and the temperature of its surroundings. In this particular situation, we can express this law using a differential equation:
dQ/dt = -k(T - Ts)
Where:
dQ/dt represents the rate of heat transfer or coolingk is the proportionality constantT is the temperature of the objectTs is the temperature of the surroundingsThe sound produced by the speakers at a rock concert has a power of 0.181 W. What sound intensity do you hear when you are standing 20.5 m away?
Answer:
The sound intensity heard standing 20.5 m away = 0.0000343 W/m² = 3.43 × 10⁻⁵ W/m²
Explanation:
Intensity of sound at some distance r away is calculated as (power of the sound/surface area of wall of imaginary sphere at distance r)
Power of the sound = 0.181 W
Surface area of wall of imaginary sphere = 4πr² = 4π(20.5²) = 5281.02 m²
Intensity = 0.181/5281.02 = 0.0000343 W/m² = 3.43 × 10⁻⁵ W/m²
What is the magnitude of energy of a photon of light (in J) that is emitted when an excited electron in a hydrogen atom falls from n = 4 down 1 energy levels?
Answer:
[tex]2.044 * 10^{-18}[/tex] J
Explanation:
Parameters given:
[tex]n_{1} = 4\\\\n_{2} = 1[/tex]
We know that the electron fell from level 4 to level 1. We can use the Rydberg's equation to find the [tex]2.044 * 10^{-18}[/tex] that is emitted by the electron in the process. Rydberg's equation is given as:
1/λ = [tex]R * (\frac{1}{(n_{2})^2} - \frac{1}{(n_{1})^2})[/tex]
where R = Rydberg's constant = [tex]1.0973731568508 * 10^{7}[/tex]
1/λ = [tex]1.0973731568508 * 10^{7} (\frac{1}{1^{2}} - \frac{1}{4^{2}} } )[/tex]
1/λ = [tex]1.0973731568508 * 10^{7} (\frac{1}{1} - \frac{1}{16} } )[/tex]
1/λ = [tex]1.0973731568508 * 10^{7} * \frac{15}{16}[/tex]
1/λ = [tex]1.029 * 10^{7}[/tex] [tex]m^{-1}[/tex]
∴ λ = [tex]9.72 * 10^{-8}[/tex] m
Energy of the photon is given by:
E = (hc)/λ
where
h = Planck's constant = [tex]6.62607004 * 10^{-34} m^2 kg / s[/tex]
c = speed of light = 299792458 m / s
∴ E = [tex]\frac{6.62607004 * 10^{-34} * 299792458}{9.72 * 10^{-8}}[/tex]
E = [tex]2.044 * 10^{-18}[/tex] J
The energy of the photon is [tex]2.044 * 10^{-18}[/tex] J
Final answer:
The energy of a photon emitted when an electron in a hydrogen atom falls from n=4 to n=3 can be found using the Rydberg formula. The constant R (Rydberg constant) along with the energy levels n1 and n2 are used in the formula to calculate this energy in joules.
Explanation:
The magnitude of energy of a photon of light that is emitted when an excited electron in a hydrogen atom falls from n = 4 to n = 3 can be calculated using the Rydberg formula for the energy difference between two hydrogen energy levels. In this case, since the question only specifies a drop of one energy level, we'll correct the typo where it currently indicates a fall from n=4 to n=1, and we'll proceed with the fall from n=4 to n=3. The formula to use is:
E = R × (1/n1² - 1/n2²)
where:
R is the Rydberg constant (2.179 × 10⁻¹⁸ J),
n1 and n2 are the principal quantum numbers (integers) for the initial and final energy levels, respectively.
The calculation is then:
E = 2.179 × 10⁻¹⁸ J × (1/3² - 1/4²) = 2.179 × 10⁻¹⁸ J × (1/9 - 1/16) = 2.179 × 10⁻¹⁸ J × (7/144)
After calculating the above expression, you will get the energy in joules of the photon emitted due to the electron's transition.
What is the excess charge on a conducting sphere of radius r = 0.31 m if the potential of the sphere is 1375 V and V = 0 at infinity?
Given Information:
Radius = r = 0.31 m
Potential difference = V = 1375 Volts
Required Information:
charge = q = ?
Answer:
q = 4.741x10⁻⁸ C
Solution:
[tex]V = kq/r[/tex]
Where k = 8.99x10⁹ N.m²/C² is the Coulomb's constant
Re-arranging the equation to find the q
[tex]q = Vr/k[/tex]
q = (1375*0.31)/8.99x10⁹
q = 4.741x10⁻⁸ C = 47.41 nC
If the voltage of the secondary side of the transformer is less than ? and the voltage of the primary side of the transformer exceeds ? to ground, the secondary side shall be grounded.?
Answer:
50 V / 150 V
Explanation:
Final answer:
The question discusses the grounding of a transformer based on voltage levels and defines the characteristics of step-down and step-up transformers in terms of voltage and current. Transforming the power efficiently is crucial, and the number of windings plays a significant role in determining the output voltage and current.
Explanation:
The question pertains to transformers and their operating principles regarding voltage, current, and the number of windings. If the voltage at the secondary side of a transformer is less than 50 volts and the primary side exceeds 150 volts to ground, the secondary side shall be grounded.
When a transformer has fewer windings in the secondary coil compared to the primary coil, it is a step-down transformer, meaning the secondary voltage is less than the primary voltage. Conversely, a step-up transformer has more windings in the secondary coil, resulting in a higher secondary voltage compared to the primary voltage.
In the context of primary and secondary properties of transformers, option (a) the Primary voltage is higher than secondary voltage defines a step-down transformer. Additionally, (c) the Primary current is higher than secondary current is not typically true for a step-down transformer.
Instead, the primary current would be lower than the secondary current since power (P = IV) is conserved across the transformer. Therefore, if the voltage decreases, the current must increase to maintain the equivalent power (assuming ideal conditions with no power losses).