a. The spring is compressed by 0.174 m.
b. The vertical distance the dart travels from its position when the spring is compressed to its highest position is 9.6 m.
c. The horizontal velocity of the dart at that time is 13.74 m/s.
d. The horizontal distance from the equilibrium position at which the dart hits the ground is 19.236 m.
What is potential energy?The energy by virtue of its position is called the potential energy.
a. Given is the potential energy stored in the compressed spring of a dart gun, with a spring constant of 62.00 N/m, is 0.940 J.
PE of spring = 1/2 kx²
Put the values, we get
P.E = 0.940 = 1/2 x 62 x²
x = 0.174 m
Thus, the spring is compressed by 0.174 m.
b. Given is a 0.010 kg dart is fired straight up.
The vertical height is find out by
0.940 J = (0.010 kg) (9.8 m/s²) h
h = 9.6 m
Thus, the vertical distance the dart travels from its position is 9.6 m
c. From the conservation of energy principle, total mechanical energy is conserved.
1/2 mv² =mgh
v = √2gh
Plug the values, we get
v = √2 x 9.8x 9.6
v = 13.74 m/s
Thus, the horizontal velocity is 13.74 m/s.
d. Time that dart spends in air, t = √2h/g
t = √(2x9.6)/9.81
t = 1.4 s
The horizontal distance from the equilibrium position at which the dart hits the ground.
Horizontal distance = (Velocity on x direction) x time
Horizontal distance = 13.74 m/s x 1.4s
Horizontal distance = 19.236 m
Thus, the horizontal distance is 19.236 m.
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the following equation shows the position of a particle in time t, x=at2i + btj where t is in second and x is in meter. A=2m/s2, b=1m/s. Find
A, the average velocity of the particle in the time interval t1=2sec and t2=3sec
B, the velocity and acceleration at any time t.
C, the average acceleration in the time interval given in part (a)
(a) The average velocity of the particle in the time interval t₁=2sec and t₂=3sec is 10 m/s.
(b) The velocity and acceleration at any time t is v = (2ati + bj) m/s and a = 2ai m/s²
(c) The average acceleration in the time interval given in part (a) is 4 m/s².
Position of the particlex = at²i + btj
x = 2t²i + tj
Average velocity, at t₁=2sec and t₂=3secΔv = Δx/Δt
x(2) = 2(2)²i + 2j
x(2) = 8i + 2j
|x(2)| = √(8² + 2²) = 8.246
x(3) = 2(3)²i + 3j
x(3) = 18i + 3j
|x(3)| = √(18² + 3²) = 18.248
Δv = (18.248 - 8.246)/(3 - 2)
Δv = 10 m/s
Velocity and acceleration at any time, tx = at²i + btj
v = dx/dt
v = (2ati + bj) m/s
a = dv/dt
a = 2ai m/s²
Average accelerationa = 2ai m/s²
a = 2(2)(1)
a = 4 m/s²
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There are several ways to model a compound one type of model is shown ?what is the chemical formula for the molecule modeled?
The is organic compound with the correct chemical formula C4H9O2.
What is a model?A model is a representation of reality. A model serves the purpose of prediction as well as explanation.
Looking at the model of the molecule we can see that it is the organic compound with the correct chemical formula C4H9O2. The molecule is shown in the image attached to this answer.
Missing parts:
There are several ways to model a compound. One type of model is shown.
What is the chemical formula for the molecule represented by the model?
CHO
C4H9O2
C4H8O
C3H8O2
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Question 1 of 25
In the covalent compound CO₂, the Greek prefix used to represent the anion is
Answer:
di
Explanation:
The prefix is di. CO2 is carbon dioxide. di means 2.
Compare/Contrast the Jovian planets in terms of their size (vs. Earth), composition (elemental), location (relative to the Sun), major moons (name a few), orbital period (Earth years), and rotational period (Earth time).
a) Jupiter
b) Saturn
c) Uranus
d) Neptune
Jupiter is the largest. the closest Jovian planet to the sun is Jupiter and most farthest is Neptune. moons of Jupiter are Europa, lo, Ganymede, etc. Saturn has an orbital period equal to 29 earth years. Uranus's rotational period is equal to 17h 14m.
In terms of size-
Earth- 6,371 kmJupiter- it is 11 times larger than the earth in terms of diameterSaturn- it is the next largest planet. Saturn is 9 times bigger than the earth. Uranus- it is roughly 4 times larger than the earth. Neptune-it is roughly 4 times larger than the earth same as Uranus.In terms of location-
Jovian planets are generally farther from the sun while terrestrial plants are closer to the sun. therefore Jupiter, Saturn, Uranus, and Neptune are away from the sun whole earth is closer to the sun.
In terms of moons-
Jovian planets have more moons as compared to earth. Jupiter has 53 moon, Uranus has 27 Miranda, ariel ,Oberon) while the earth has one moon.
In terms of the orbital period-
Jovian planets have a longer orbital period than earth as they are further from the sun.
In terms of the rotational period-
The rotational period of the Jovian planet is approximately 10 to 17 hours.
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A skier is standing on a horizontal patch of snow. She is holding onto a horizontal tow rope, which is about to pull her forward. The skier’s mass is 59 kg, and the coefficient of static friction between the skies and the snow is 0.14. What is the magnitude of the maximum force that the tow rope can apply to the skier without causing her to move?
The magnitude of the maximum force that the tow rope can apply to the skier without causing her to move will be 81.03 N,
What is the friction force?It is a type of opposition force acting on the surface of the body that tries to oppose the motion of the body. its unit is Newton (N).
It is defined as the product of the coefficient of friction and normal reaction.
On resolving the given force and acceleration. Mathematically aion in the different components and balancing the equation gets. Components in the x-direction.
The normal force is balanced by weight;
N = mg
The magnitude of the maximum force that the tow rope can apply to the skier without causing her to move is;
F = μN
F= μmg
F=0.14 × 59 kg × 9.81 m/s²
F = 81.03 N
Hence, the magnitude of the maximum force will be 81.03 N,
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Particles q1, 92, and q3 are in a straight line.
Particles q1 = -5.00 x 10-6 C,q2 = +2.50 x 10-6 C,
and q3= -2.50 x 10-6 C. Particles q1 and q2 are
separated by 0.500 m. Particles q and q3 are
separated by 0.250 m. What is the net force on q2?
Remember: Negative forces (-F) will point Left
Positive forces (+F) will point Right
-5.00 x 10-6 C
91
0.500 m
+2.50 x 10-6 C
+92
-2.50 x 10-6 C
93
0.250 m
Answer:
-1.35 N
Explanation:
Force due to q1
F = 9 × 10⁹ × 5 × 10⁻⁶ × 2.5 × 10⁻⁶ / 0.5²F = 450 × 10⁻³F = 0.45 N (+)Force due to q2
F = 9 × 10⁹ × 5 × 10⁻⁶ × 2.5 × 10⁻⁶ / 0.25²F = 1800 × 10⁻³F = 1.8 N (-)Net Force
0.45 - 1.8-1.35 NThree small but dense objects are located in the x-y plane as shown in the figure. The objects have the following masses: mA = 3.19 kg, mB = 2.55 kg and mC = 1.41 kg.
Determine the x and the y coordinates of the center of the mass of this system. The objects are small in size, they can be treated as point masses.
x coordinate: ?
y coordinate: ?
The x and the y coordinates of the center of the mass of this system will be 43.1 m and 3.12 m respectively.
What is the center of mass?A location is established in relation to an object or set of objects in the center of mass. It is the system's average position across all of its components.
Given data;
There are three little objects that are densely spaced out in the x-y plane.;
The value of the masses
m₁=1.41 kg
m₂=2.55 kg
m₃=3.19 kg
[tex]\rm X_{cm} =\frac{ (W_1x_1 + W_2x_2 + W_3x_3)}{(W_1 + W_2 + W_3)} \\\\\ X_{cm} ==\frac{1.41 \times 2 + 2.55 \times 6 +3.19 \times 4}{1.41+2.55+3.19} \\\\ X_{cm} =4.31 \ m[/tex]
[tex]\rm Y_{cm} =\frac{ (W_1y_1 + W_2y_2 + W_3y_3)}{(W_1 + W_2 + W_3)} \\\\\ X_{cm} ==\frac{1.41 \times 2 + 2.55 \times 4 +3.19 \times 7}{1.41+2.55+3.19} \\\\ X_{cm} =3.12 \ m[/tex]
Hence, the x and the y coordinates of the center of the mass of this system will be 4.31 m and 3.12 m respectively.
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The internal energy of a gas is 500 J. The gas is compressed adiabatically, and its volume decreases by 100c * m ^ 3 If the pressure applied on the gas during compression is 3.00 atm, what is the internal energy of the gas after the adiabatic compressio
The internal energy of the gas after the adiabatic compression will be 30.398 × 10⁶ J
What is work done by gas?When energy is moved from one store to another, work is completed. Work done on the gas is taken as -ve.
Given data;
pressure(P)=3.0 atm = 303975 N/m²
The initial volume, V₁
work is done on the gas., W=?(-ve)
Change in heat, ΔQ=0
Change in the internal energy of the gas., ΔE
The work done on the gas;
W = -PΔV
W= - 303975 N/m² × 100 cm³
W = - 30.3 × 10⁶ J
The internal energy is found as;
ΔE=q+w
ΔE= 0-30.3 × 10⁶ J
ΔE= -30.3 × 10⁶ J
E₂-E₁= -30.3 × 10⁶ J
E₂ = -30.3 × 10⁶ J +500
E₂ = 30.398 × 10⁶ J
Hence, the internal energy of the gas after the adiabatic compression will be 30.398 × 10⁶ J
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Help with this :
What device does not store electric current or charge?
a) Capacitor
b) Transforme
c) vacuum tube
I know a capacitor is a device for storing charge, but it also says from a physical point of view, a capacitor does not store charge or electric current, but simply latent mechanical energy.
So what will be the answer?
Answer:
You are correct, the answer is capacitor
A room has a 60 Watt, a 100 Watt and a 150 Watt light bulb. How much does it
cost to use all the lamps for 2.5 hours at $0.08/ kWh?
The cost to use all lamps is $62.
room has 60 watts, 100 watts, and 150 watt light bulbs.Duration of using bulbs=2.5 hours power =$0.08kWh
power=energy/time
(60+ 100+150)=energy/2.5
energy=775 joule
cost for 1 hour=$0.08
= 775 * 0.08
= $62
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Answer:
6.2 cents
Explanation:
(60+100+150/1000)*2.5*8=6.2 cents
A surfer on top of a wave takes 10 seconds to travel a distance of 40 meters. What is the speed of the wave the surfer is riding on?
Select one:
a. 0.25 m/s
b. 4 m/s
c. 40 m/s
d. 400 m/s
Answer:
B. 4 m/sExplanation:
The formula for Speed is distance per time.
Therefore Speed = Distance / TimeData
D = 40 m
T = 10 sec
S = ?
Speed = 40m /10sec
To find the speed , divide the distance by the time.
Note : the unit for Speed is meter /second
Speed = 4 m/sTherefore the speed of the wave, the surfer is riding on is 4 m/s.
How much work does a football player do in the weight room when he squats 150 kg up a distance of 1 meter?
How much work does he do if he does 3 sets of 10 squats in a row?
Answer:
See below
Explanation:
The work done equals the increase in Potential Energy
PE = mgh
= 150 * 9.81 * 1 = 1471.5 j
3 sets of 10 is 30 times this = 44145 j
The amount of work done by a football player in the weight room when he squats 150 kg will be equal to 1471.5 J.
What is potential energy?Potential energy is a form of stored energy that is dependent on the relationship among different components. When a spring is compressed or stretched, its potential energy increases. If a steel ball is raised above the floor as opposed to falling to the ground, it has more potential energy. It is capable of carrying out additional work when raised.
Potential energy is a feature of systems rather than of particular bodies or particles; for instance, the system created up of Earth and the elevated ball has more energy stored as they become further apart.
Potential energy develops in systems components whose configurations, or spatial arrangement, determine the amount of the forces they apply to one another.
As per the instructions given in the question,
Work performed is equivalent to Potential Energy Increase,
PE = mgh
= 150 × 9.81 × 1
PE = 1471.5 J
Also,
3 sets of 10 are 30 times this = 44145 J
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which one of the following is true about Tesite stress
It is defined as the stress that results in the elongation of the material
A magnetic field is __________ at one end of a bar magnet. What one word completes the sentence?
Answer: stronger
Explanation: the poles magnetism is concentrated at the poles
A magnetic field is the strongest at one end of a bar magnet.
What is meant by magnetic field ?The region in which the force of magnetism acts around a magnetic material or a moving electric charge is known as the magnetic field.
Here,
A bar magnet can be considered as a dipole with a north pole at one end and south pole at the other.
A magnetic field can be measured leaving the dipole at the north pole and returning the magnet at the south pole. If a magnet is cut in two, two magnets or dipoles are created out of one.
The magnetic poles, the region at each end of a magnet where the external magnetic field is strongest. A bar magnet suspended in Earth's magnetic field orients itself in a north–south direction. The north-seeking pole of such a magnet, or any similar pole, is called a north magnetic pole.
Here,
A magnetic field is the strongest at one end of a bar magnet.
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Help me ASAP!!!!
If two balls have the same volume, but ball A has twice as much mass as ball B, which one will have the greater density?
A. Ball A
B. Ball B
C. Their Densities are equal.
Answer: A) Ball A
Explanation:
Density = m/v where m is mass and v is volume
This means the greater the mass, the greater the density.
Because of Ball A's greater mass it would have the greater density.
what is the frequency of the photon emitted by a hydrogen atom when its electron drops from the n = 6 to n = 4 energy level?
The frequency of the photon emitted by a hydrogen atom is [tex]26.2*10^-^4 hz[/tex]
What are Photons?A particle representing a quantum of light or other electromagnetic radiation. A photon carries energy proportional to the radiation frequency but has zero rest mass.
In the case of light, the frequency, symbolized by the Greek letter nu (ν), of any wave equals the speed of light, c, divided by the wavelength λ:
v = c/λ
Since the wavelength λ is in the bottom of the fraction, the frequency is inversely proportional to the wavelength.
v = c/λ
v= [tex]\frac{3*10^8}{434*10^-^9} = 6.91*10^1^4 Hz[/tex]
By using Rydberg's formula,
1/λ [tex]= Rz^2(\frac{1}{n_1^2} - \frac{1}{n_2^2})[/tex]
1/λ = [tex]109677 *(\frac{1}{4^2} - \frac{1}{6^2}) = 3808.22 cm^-^1[/tex]
λ = [tex]26.2*10^-^4 hz[/tex]
[tex]26.2*10^-^4 hz[/tex] is frequency of the photon emitted by a hydrogen atom.
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If a crane worker lifts a crate with a mass of 250 kg from the ground to a
shipping container that is 20 meters off the ground, by how much has the
worker increased the gravitational potential energy of the crate? (Recall that g
= 9.8 m/s²)
A. 75,000 J
B. 61,000 J
C. 83,000 J
D. 49,000 J
D.
The gravitational of a body is possessed by the body due to the virtue of its position.
The formula for gravitational potential energy is,
P.E = mgh joules
Substituting the values
196*9.8*250= 49k
Which of the following is not a use of nuclear chemistry in industry?
thickness gauges
tracers
leak detectors
stimulate plant growth
Stimulating plant growth is not a use of nuclear chemistry in industry. Thus, the correct option is D.
What is Nuclear Chemistry?Nuclear chemistry may be defined as the sub-branch of chemistry that involves the investigation of physical and chemical characteristics of elements that are affected by transformations in the configuration of the atomic nucleus.
Thickness gauges measure the thickness, density, and fill levels and are utilized in manufacturing to make sure that an entire product or a set of products are of identical thickness.
Tracers are utilized in tracing the actual composition of radioactive decay through the chemical compounds. While the leak detectors monitor the actual and constant flow of water through a given system precisely.
Therefore, the correct option for this question is D.
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Answer:
it is d
Explanation:
Point P is on the rim of a wheel of radius 2.0 m. At time t = 0, the wheel is at rest, and P is on the x-axis. The wheel undergoes a uniform
angular acceleration of 0.01 rad/s² about the centre
Answer:
r = 2.0m
when t = 0, the angular displacement is zero.
Explanation:
When the angular acceleration is 0.01 m/s2, you can calculate
angular acceleration = change in angular velocity/ time
For a physics experiment, a solid cube is suspended from a spring scale. The gravitational force exerted on the cube is 0.714 N as measured when the object is suspended from a spring scale. When the suspended cube is submerged in water (ρ = 1000 kg/m3), the scale reads 0.450 N. What is the side of this cube in cm
The side of this cube will be 2.9996 cm. The net force on the solid cube is acting upward.
What is buoyancy force?
A fluid exerts an upward force against the weight of a partly or completely submerged item. The weight of the overlying fluid causes pressure to rise with depth in a column of fluid.
Given data;
Actual weight.W=0.714 N
Apparent weight,W'=0.450 N
The density of water,ρ=1000 kg/m³
The net force on the solid cube is;
Apparent weight = actual weight - buoyancy force
Buoyancy force = Actual weight - apparent weight
F=W-W'
F = 0.714 - 0.450
F= 0.264 N
The buoyancy force(F) is found as;
F = ρgV
0.264 = 1000 × 9.81 × V
V=2.69 × 10⁺⁵
The volume of a cube is found as;
V=a³
2.69 × 10⁺⁵ m³=a³
a=0.02996 m
As we know that 1 m = 100 cm
a=2.996 cm
Hence, the side of this cube will be 2.9996 cm.
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the road from city A to city B is described by a car with Vm 40 km / h. When the car turns (from B to A) the average speed is 60 km / h. Find the average round trip speed.
Answer:
Let distance between two cities is x km . So total distance travelled bus x+x=2x km and time taken was=(x/40)+(x/60)=(3x+2x)/120=5x/120=x/24 hrs . So avg speed is 2x/(x/24)=48 km per hr.
or
dt1=60km1h
dt2=30km1h
2dt1+t2=r¯
d=60t1
d=30t2
60t1=30t2
2t1=t2
2dt1+(2t1)=r¯
2(60t1)t1+2t1=r¯
2(60t1)=r¯(t1+2t1)
120=r¯+2r¯
r¯=1203
r¯=40km/h
A small mass of m = 187 g hangs from a string of length l = 1.21 m.
Calculate the initial speed v the mass m should be given at the bottom, so that the string reaches a maximum angle of θ = 36.5°?
The initial speed v, the mass m should be given at the bottom, so that the string reaches a maximum angle is 2.16 m/s.
What is mechanical energy?The mechanical energy is the sum of kinetic energy and the potential energy of an object at any instant of time.
M.E = KE +PE
Given is a small mass of m = 187 g hangs from a string of length l = 1.21 m. The string reaches a maximum angle of θ = 36.5. The acceleration due to gravity, g = 9.8 m/s²
The vertical height of the point mass h = l- lcosθ
h = 1.21 - (1.21cos 36.5°)
h = 0.2373 m
The conservation of energy principle states that total mechanical energy remains conserved in all situations where there is no external force acting on the system.
Kinetic energy = Potential energy
1/2 mv²= mgh
Substituting the values, we have
1/2 x v² = 9.8 x 0.2373
v = sqrt [2 x9.8 x 0.2373]
v= 2.16 m/s
Thus, the initial speed v the mass m should be given at the bottom, so that the string reaches a maximum angle is 2.16 m/s.
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The three waves shown in the picture below are equal in wavelength, but are travelling at different speeds. Given this information, which wave has the highest frequency?
Select one:
a. 1
b. 2
c. 3
d. Can't tell from the information given.
Wave 3 will have the highest frequency. Option c is correct.
What is the frequency?
Frequency is defined as the number of repititions of a wave occurring waves in 1 second.
Frequency is given by the formula as,
[tex]\rm v = \lambda \times f[/tex]
If the wavelength of the wave is content the velocity of the wave is directly propotional to the frequency.
The velocity of wave 3 is maximum. So that the wave 3 will have the highest frequency.
Hence option c is correct.
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A house has a roof (colored gray) with the dimensions shown in the drawing. Determine the magnitude of the net force that the
atmosphere applies to the roof when the outside pressure drops suddenly by 13.2 mm of mercury, before the pressure in the attic can
adjust.
The magnitude of the net force that the atmosphere applies to the roof when the outside pressure drops suddenly is 1.9 x 10⁵ N.
What is pressure?The pressure is the amount of force applied per unit area.
Pressure p = Force/Area
Given is a house has a roof (colored gray) with the dimensions shown in the drawing. The outside pressure drops suddenly by 13.2 mm of mercury, before the pressure in the attic can adjust.
The pressure difference ΔP = 13.2 mm of Hg
The length of the roof l = 14.5m
the breadth of the roof h = 4.21m
The force exerted by pressure is
Force, F = P x A
= (13.2 mm of Hg) [(133 N/m²) /1 mm of Hg ](14.5 x 4.21)
= 107,170.6 N
Then the net vertical force
Fnet = 2F cos30
Fnet = 2 ( 107,170.6) cos30
Fnet = 185625 N
Fnet =1.9 x 10⁵ N
The direction of the force is downwards, since the horizontal components of the forces cancel each other.
Hence, magnitude of the net force is 1.9 x 10⁵ N
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Given the following specific heat capacities, which material was have the largest change in temperature if 10 grams of each substance absorbs 100 calories of heat?
Substance Heat Capacity - Cal / (g oC)
aluminum 0.22
copper 0.093
lead 0.0305
silver 0.056
Answer:
Explanation:
Comment
You could calculate it out by assuming the same starting temperature for each substance. (You have to assume that the substances do start at the same temperature anyway).
That's like shooting 12 with 2 dice. It can be done, but aiming for a more common number is a better idea.
Same with this question.
You should just develop a rule. The rule will look like this
The greater the heat capacity the (higher or lower) the change in temperature.
The greater the heat capacity the lower the change in temperature
That's not your question. You want to know which substance will have the greatest temperature change given their heat capacities.
Answer
lead. It has the smallest heat capacity and therefore it's temperature change will be the greatest.
Find the relationship
[tex]\\ \rm\Rrightarrow Q=mc\Delta T[/tex]
[tex]\\ \rm\Rrightarrow 100=10c\Delta T[/tex]
[tex]\\ \rm\Rrightarrow 10=c\Delta T[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{10}{c}=\Delta T[/tex]
[tex]\\ \rm\Rrightarrow \Delta T\propto \dfrac{1}{c}[/tex]
So lower the c higher ∆T
Lead has the largest change in T as it has least capacity
143°C = _____
416 K
-130 K
0 K
143 K
An asteroid is moving along a straight line. A force acts along the displacement of the asteroid and slows it down. The asteroid has a
mass of 3.8x 104 kg, and the force causes its speed to change from 6700 to 4600m/s. (a) What is the work done by the force? (b) If the
asteroid slows down over a distance of 2.4x 10 m determine the magnitude of the force.
The work done by the force is 7. 89 * 10^8 Joules and the magnitude of the force is 3. 3* 10 ^7 Newton
How to determine the work done
a. Work done = force * change in velocity = Impulse
Note that:
Force = mg
mass = 3.8x 104 kg
g = 10m/s²
Substitute into the formula for force
Force = 3.8* 10^4 * 10= 3.8* 10^5 Newton
Change in velocity = 6700 - 4600 = 2100 m/s
Work done = force *change in velocity
Work done = 3.8* 10^5 * 2100
Work done = 7. 89 * 10^8 Joules
b. Magnitude of the force = work done ÷ distance
Force = [tex]\frac{7. 89 * 10^8 }{2.4* 10}[/tex]
Force = 3. 3* 10 ^7 Newton
Therefore, the work done by the force is 7. 89 * 10^8 Joules and the magnitude of the force is 3. 3* 10 ^7 Newton
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A diver shines a light up to the surface of a flat glass-bottomed boat at an angle of 37◦ relative to the normal. If the indices of refraction of air, water, and glass are 1.0, 1.33, and 1.4 respectively, at what angle does the light leave the glass (relative to its normal)? Answer in units of ◦ .
Answer:
Approximately [tex]53^{\circ}[/tex], assuming that the upper and lower surfaces of the glass on this boat are parallel.
Explanation:
Assume that the upper and lower surfaces of the glass at the bottom of this ship are parallel. Refer to the diagram attached. The two normals would also be parallel to each other.
The following angles would be alternate interior angles between the two normals:
The angle at which the light enters the glass, andThe angle at which the light leaves the glass.Since the two normals are parallel to each other, these two angles would have the same value. Let [tex]\theta_{\text{glass}}[/tex] denote the value of both of these angles.
Let [tex]\theta_{\text{src}}[/tex] denotes the angle at which a beam of light leaves the original medium (angle of incidence.) Let [tex]\theta_{\text{dst}}[/tex] denote the angle at which this beam of light enters the new medium.
Let [tex]n_\text{src}[/tex] and [tex]n_\text{dst}[/tex] denote the refractive indices of the original and the new medium, respectively. By Snell's Law:
[tex]\begin{aligned}\frac{\sin(\theta_{\text{dst}})}{\sin(\theta_{\text{src}})} = \frac{n_{\text{src}}}{n_{\text{dst}}}\end{aligned}[/tex].
Let [tex]\theta_{\text{water}}[/tex] denote the angle at which the beam of light in this question leaves the water. Let [tex]\theta_{\text{air}}[/tex] denote the angle at which this beam of light enters the air. It is given that [tex]\theta_{\text{water}} = 37^{\circ}[/tex], while [tex]\theta_{\text{air}}[/tex] is the value that needs to be found.
Let [tex]n_{\text{air}}[/tex], [tex]n_{\text{water}}[/tex], and [tex]n_{\text{glass}}[/tex] denote the refractive index of air, water, and glass, respectively. By Snell's Law:
[tex]\begin{aligned}\frac{\sin(\theta_{\text{glass}})}{\sin(\theta_{\text{water}})} = \frac{n_{\text{water}}}{n_{\text{glass}}}\end{aligned}[/tex].
[tex]\begin{aligned}\frac{\sin(\theta_{\text{air}})}{\sin(\theta_{\text{glass}})} = \frac{n_{\text{glass}}}{n_{\text{air}}}\end{aligned}[/tex].
Thus:
[tex]\begin{aligned} & \frac{\sin(\theta_{\text{air}})}{\sin(\theta_{\text{water}})} \\ =\; & \frac{\sin(\theta_{\text{glass}})}{\sin(\theta_{\text{water}})}\times \frac{\sin(\theta_{\text{air}})}{\sin(\theta_{\text{glass}})} \\ =\; & \frac{n_{\text{water}}}{n_{\text{glass}}}\times \frac{n_{\text{glass}}}{n_{\text{air}}} \\ =\; & \frac{n_{\text{water}}}{n_{\text{air}}}\end{aligned}[/tex].
Since [tex]\theta_{\text{water}} = 37^{\circ}[/tex]:
[tex]\begin{aligned} & \sin(\theta_{\text{air}})\\ =\; & \sin(\theta_{\text{water}}) \times \frac{\sin(\theta_{\text{air}})}{\sin(\theta_{\text{water}})} \\ =\; & \sin(\theta_{\text{water}})\times \frac{n_{\text{water}}}{n_{\text{air}}} \\ =\; & \sin(37^{\circ}) \times \frac{1.33}{1.0} \\ \approx \; & 0.800 \end{aligned}[/tex].
Therefore:
[tex]\begin{aligned}\theta_{\text{air}} &= \arcsin(\sin(\theta_{\text{air}})) \\ & \approx \arcsin(0.800) \\ &\approx 53^{\circ} \end{aligned}[/tex].
In other words, this beam of light would leave the glass at approximately [tex]53^{\cic}[/tex] from the normal.
A 63.3 kg wood board is resting on very smooth ice in the middle of a frozen lake. A 35.7 kg boy stands at one end of the board. He walks from one end of the board to the other end with a velocity of 1.47 m/s relative to the ice in the positive direction. What is the velocity of the board relative to the ice?
The velocity of the board relative to the ice is zero, since both are at rest.
What is relative velocity?Relative velocity is the velocity of an object in relation to another reference object or point.
When two objects are travelling or moving with the same velocity in the same direction, the relative velocity one relative to the other is zero.
Also, when two objects are at rest, the relative velocity one relative to the other is zero.
Therefore, the velocity of the board relative to the ice is zero, since both are at rest.
Learn more about relative velocity at: https://brainly.com/question/24337516
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Where are electrons located in an atom?
A. in the nucleus
B. outside the nucleus
C. Either inside or outside the nucleus?
Answer for brainlist
Answer:
B. Outside the nucleus.
Explanation:
Electrons orbit the nucleus of the atom.
