The 50 kg mass of the student, and the duration of 2 seconds for the motion of the elevator, gives;
1) 2,400J
2) 1,600 J
3) 1,600 J
4) 2,000 J
5) 2,000 J
6) 2,000 J
What is the formula for the work done by a force?Work done, W = Force × Distance
Mass of the student = 50 kg
Time of motion of the elevator = 2 seconds
Acceleration due to gravity, g = 10 m/s²
1) Direction of motion = Upwards
Initial velocity = 0
Upward acceleration = 2 m/s²
Height climbed, h = 0.5×2×2² = 4
Force of the student, F = m•g
F = 50 × 10 = 500
Apparent weight of student = 500 + 50×2 = 600
Therefore;
W = F × h
Work done = 600 × 4 = 2499
The work done by the elevator = 2400 J2) When the elevator is accelerating downwards, we have;
Apparent weight = F - m•a
Which gives;
Apparent weight = 500 - 100 = 400
W = 400 × 4 = 1600
Work done by the elevator = 1600 J3) Initial speed of elevator = 4 m/s
Deceleration = 2 m/s²
Distance, h = 4×2- 0.5×2×2² = 4
Apparent weight = 500 - 100 = 400
Work done = 400 × 4 = 1600
Work done by the elevator = 1600 J4) Direction of motion = Downwards
Distance, h = 4
Apparent weight = 500 + 100 = 600
Work done by the elevator = 2400 J5) The distance covered, h, is therefore;
h = 2 × 2 = 4
W = m•g•h
Which gives;
W = 50 × 10 × 4 = 2000
Work done by the elevator = 2000 J6) Height traveled, h = 4
Work done = 50 × 10 × 4 = 2000
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Calculate the mass, in grams, of 172 atoms of potassium, k (1 mol of k has a mass of 39.10 g).
By Avogadro's number, the mass is 1.12 x 10¯²⁰ gram.
We need to know about Avogadro's number to solve this problem. Avogadro's number is the number that explains how many atoms are in one mol. The Avogadro's number is
Na = 6,02 × 10²³ atoms / mol
From the question above, we know that
N = 172 atoms
Ar = 39.1
By using Avogadro's number, we can calculate the amount of potassium
N = Na . n
172 = 6,02 × 10²³ . n
n = 2.86 x 10¯²² mol
Find the mass
n = gr / Ar
2.86 x 10¯²² = gr / 39.1
gr = 1.12 x 10¯²⁰ gram
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Starting from rest, a 2-kg body acquires a speed of 8 m/s in 2 seconds. the net force acting on the body is:________
Starting from rest, a 2-kg body acquires a speed of 8 m/s in 2 seconds. the net force acting on the body is: 8 N
To solve this exercise the formula for net force and the formula for uniformly varied rectilinear motion (UVRM) to be applied are:
F = m * aa = (vf - vi) /tWhere:
F = Forcem = massa = accelerationvf = final velocityvi = initial velocityt = timeInformation about the problem:
m = 2 kgvf = 8 m/svi = 0 m/st = 2 sa = ?F = ?N = kg * m/s²Applying the formula for UVRM we can calculate the acceleration of the runner:
a = (vf - vi) /t
a = (8 m/s - 0 m/s) / 2s
a = 8 m/s / 2s
a = 4 m/s²
With the acceleration we can apply the net force formula and get:
F = m * a
F = 2 kg * 4 m/s²
F = 8 N
What is force?It is the physical magnitude that expresses the effort necessary to move the mass of one kilogram with an acceleration of one meter per second squared, this is expressed in units of the international system in Newton.
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An experiment is set up in a lab. Three different
materials - copper, iron, and glass are all placed
with one end of each rod in a pan of hot water.
Each rod has an equivalent amount of wax on the
opposite end. After a few minutes, each of the
wax beads have melted at different times.
What is the dependent variable in the
experiment?
A.time
B.rate of convection
C.rate of radiation
D.rate of conduction
Answer:
B.rate of convection
Explanation:
To what speed must an electron be accelerated from rest for it to have a de broglie wavelength of 100pm? what accelerating potential difference is needed?
To express of an electron we have to figure out the relationship between momentum and wavelength:
λ= [tex]\frac{h}{p}[/tex] =[tex]\frac{h}{mv}[/tex]
So, velocity of an electron will be:
v= me/λ[tex]e[/tex]h
h= Planck's constant
[tex]m_{e}[/tex] = mass of the electron
Now we will see what is its value:
V= h/mcλ
[tex]\frac{6.626 .10^{-34}J.s}{(9.109.10^{-31}kg).(100.10^{-12m)} }\\ 7.27.10^{6} m.s^{-1}[/tex]
Now, to express accelerating potential energy difference we will use kinetic energy and charge of electron
Kinetic energy: [tex]E_{K} =e_{E}[/tex]
But kinetic energy in terms of velocity is
:[tex]\frac{(9.109.10^{-31}kg).(7.27.10^{6}ms^{-1})^{2} }{2.(1.602.10^{-19} C)} \\=150.210^{-31} .10^{-31} .10^{12}.10^{19}V \\ = 1.502.10^{2}V[/tex]
What is kinetic energy?Kinetic energy is a type of power that a moving object or particle possesses. An item accumulates kinetic energy when work, which involves the transfer of energy, is done on it by exerting a net force. A moving object or particle has kinetic energy, which relies on both its mass and its rate of motion.we can calculate kinetic energy by first determining the work done W by a force, F, in a straightforward example. Consider a force parallel to a surface pushing a box of mass mm across a distance D along that surface.To know more about kinetic energy visit:
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Can someone help me with these five questions? With an explanation, please! Refer to these photos:
1) The body moved from 0 cm to 4 cm at a constant speed of 1 cm/s.
2) The object moved at a constant speed of 3 cm/s from 0 cm to 3cm
3) Two objects are speeding up and one object is slowing down.
4) The object moved from 4s to 8s at a constant speed of 4 cm/s
5) The horizontal line appears at 5 m/s is the second graph.
What is acceleration?We know that acceleration has to do with the change of of velocity of an object with time.
1) We can see that the position changes by equal amounts in equal time intervals thus the body moved from 0 cm to 4 cm at a constant speed of 1 cm/s.
2) Looking at the shape of the second graph we can see that the object moved at a constant speed of 3 cm/s from 0 cm to 3cm
3) From the images of the ticker tapes, we can see that two objects are speeding up and one object is slowing down.
4) From the fourth graph, we can see that the object moved from 4s to 8s at a constant speed of 4 cm/s
5) The graph in which the horizontal line appears at 5 m/s is the second graph.
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A cheetah can run at a maximum speed
108 km/h and a gazelle can run at a maximum speed of 79.9 km/h.
If both animals are running at full speed,
with the gazelle 75.8 m ahead, how long before
the cheetah catches its prey?
Answer in units of s.
The time taken by cheetah to catch its prey is 9.71 s.
What is speed?Speed is the defined as the distance covered per unit time by a moving body or object.
Speed = distance/timeThe speed of the gazelle = 79.9 km/h = 22.2 m/s
speed of the cheetah = 108 km/h = 30 m/s
Let distance covered by gazelle = d
distance covered bet cheetah = d + 75.8
The time taken is same for both = t
time = distance/speed
time taken by cheetah = d + 75.8/30
time taken by gazelle = d/22.2
equating both times: d + 75.8/30 = d/22.2
30 d - 22.2 d = 1682.76
d = 215.7 m
Therefore, time taken by cheetah = (215.7 + 75.8)/30
t = 9.71 s
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It takes an average car 130-140 feet to stop if they are going 55 mph. how many feet does it take for a tractor-trailer or a truck to stop going the same speed?
It will take 130-140 feet for a tractor-trailer or a truck to stop when going at the same speed.
The stopping distance of a body moving with constant acceleration can be calculated by using the following equation,
v^2 - u^2 = 2as
As the body has stopped, v will be zero.
v^2 - u^2 = 2as
The stopping distance comes out to be
s = u^2/2a
As the stopping distance is proportional to the square of the initial velocity of the body, the mass of the body does not have any effect on the stopping distance.
So, both a car and a tractor-trailer will have the same stopping distance when moving at the same speed.
Therefore, it will take 130-140 feet for a tractor-trailer or a truck to stop when going at the same speed.
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It will take 130-140 feet for a tractor-trailer or a truck to stop when going at the same speed.
The stopping distance of a body moving with constant acceleration can be calculated by using the following equation,
v^2 - u^2 = 2as
As the body has stopped, v will be zero.
v^2 - u^2 = 2as
The stopping distance comes out to be
s = u^2/2a
As the stopping distance is proportional to the square of the initial velocity of the body, the mass of the body does not have any effect on the stopping distance.
So, both a car and a tractor-trailer will have the same stopping distance when moving at the same speed.
Therefore, it will take 130-140 feet for a tractor-trailer or a truck to stop when going at the same speed.
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A ball starts from rest at the initial position xi = 0. The ball has a constant acceleration of 2.4m/s2.
With the use of second equation of motion formula, its position at time 3.7 s is 16.43 meters
What is Position ?A position is a point where an object can be located. The length between two positions is known as distance.
Given that a ball starts from rest at the initial position xi = 0. The ball has a constant acceleration of 2.4m/s², to know its position time 3.7 s, we will use the formula
X2 - X1 = ut + 1/2 × a × t²
Where
a = 2.4 m/s²t = 3.7 su = 0 (ball starts from rest)Substitute all the parameters into the formula
X2 - 0 = 0 + 1/2 × 2.4 × 3.7²
X2 = 1.2 × 13.69
X2 = 16.43 m
Therefore, its position at time 3.7 s is 16.43 meters
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Explain four things that atomic theory presently states 
Answer:
1. Atoms are the smallest units of matter.
2. Atoms are composed of protons, electrons, and neutrons.
3. The protons and neutrons are located in the nucleus, and the electrons orbit around the nucleus.
4. The properties of atoms are determined by the number of protons in the nucleus.
Explanation:
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Study the works of shannon and nyquist on channel capacity. each places an upper limit on the bit rate of a channel based on two different approaches. how are the two related?
in that scenario, the signaling rate is exclusively constrained by the channel bandwidth according to Nyquist's analysis of the theoretical capacity of a noiseless channel.
• What signaling rate can be accomplished over a channel with a certain bandwidth, a given signal power, and in the presence of noise was addressed by Shannon.
• Channel without errors The temperature of a material is defined as the average kinetic energy of its atoms or molecules, plus any other energy that can be transferred. In theory, the lower limit of temperature would be when all particles have zero energy
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Please help me with these few questions! I need them done soon. Only 3 questions.
Answer:
Block A - 19.3 Kg/L
Block B - 0.64 Kg/L
Block C - 0.70 Kg/L
Block D - 0.917 Kg/L
Block E - 3.53 Kg/L
1) Which block has the greatest density?
Block A
Block B
Block C
Block D
Block E
2) Which block has the lowest density?
Block A
Block B
Block C
Block D
Block E
3) Submit your data table and identify the substance each block is made of.
The block with the greatest density = Block A
The block with the lowest density = Block B
What is density?
The density of an object is the ratio of mass to volume of the object.
density = mass/volume
The given density of the object;
Density Block A = 19.3 Kg/LDensity Block B = 0.64 Kg/LDensity Block C = 0.70 Kg/LDensity Block D = 0.917 Kg/LDensity Block E = 3.53 Kg/LThus, we can conclude the following based on the density of the objects;
The block with the greatest density = Block A
The block with the lowest density = Block B
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How much work is done by the field to rotate this dipole from an orientation of 36.0?
The field to rotate this dipole from an orientation of 36.0 does a lot of work. In order to find out how much work is done, we need to consider the rotational energy of the dipole. The rotational energy is given by:
E = 1/2 * I * omega^2
where I is the moment of inertia of the dipole and omega is the angular velocity. From the given information, we can calculate the rotational energy to be:
E = 1/2 * I * (36.0 * 2 * pi / 360)^2
= 1/2 * I * 4 * pi^2
= 2 * I * pi^2
Thus, the work done by the field is:
W = 2 * I * pi^2 * 36.0
= 72 * I * pi^2
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On this position-time graph, what is the displacement between 5 s and 20 s
-50 m
-40 m
+40 m
+50 m
The displacement between 5 s and 20 s in the position-time grap is +40 m
What is displacement?Displacement is defined as the distance travelled in a specific direction. It can be obtained mathematically as:
Displacement = Displacement 2 - Displcemrnt 1
With the above information, we can obtain the displacement. Details below.
From the question given above, we can obtain the displacement as follow:
Displacement 1 at 5 s = 10 mDisplacement 2 at 20 s= 50 mDisplacement =?Displacement = Displacement 2 - Displcemrnt 1
Displacement = 50 - 10
Displacement = +40 m
Thus, the displacement is +40m
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Missing part:
See attached photo
9 one type of sunburn occurs on exposure to uv light of wavelength in the vicinity of 325 nm. (a) what is the energy of a photon of this wavelength? (b) what is the energy of a mole of these photons?
6.21 ×10⁻¹⁹ J energy of a photon of this wavelength
374028.3 J the energy of a mole of these photons
Evaluation :1) E =hc/λ
= (6.626×10⁻³⁴×3×10⁸)/(320*10⁹)
= 6.21×10⁻¹⁹ J
2) Of 1 mole E = Avogadro no.*Energy of one photon
= 6.21×10⁻¹⁹×6.023×10²³
= 374028.3 J
3) n×(6.21×10⁻¹⁹) = (10⁻³)
Thus n = 1.61×10¹⁵
How does one find the energy of a photon?
The energy of a photon are often calculated in two ways: If the photon's frequency f is known, we will use the formula E = h f . Planck proposed this equation, which is why it's known as Planck's equation. If the photon's wavelength is understood , the photon's energy are often calculated using the formula E = h c λ
What is the charge of photon?
A photon may be a tiny particle that comprises waves of electromagnetic radiation. As shown by Maxwell, photons are just electric fields traveling through space. Photons haven't any charge, no resting mass, and travel at the speed of sunshine
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A race car traveling northward on a straight, level track at a constant speed travels 0.762 km in 20.0 s. The return trip over the same track is made in 25.0 s.
(a)
What is the average velocity of the car in m/s for the first leg of the run?
m/s
(b)
What is the average velocity (in m/s) for the total trip?
m/s
Explanation:
i hope this is the right way to solve it
4. In 1994, a human powered submarine was designed at Boca Raton, Florida. It
achieved a maximum speed of 3.06 m/s. Suppose this submarine starts from
rest and accelerates at 0.800 m/s² until it reaches maximum speed. i) How long
did it take and ii) what distance did it travel?
The correct answer is S = 28.802 m.
Unless driven to change its condition by an external force, a body stays in its state of rest or uniform motion along a straight line. According to the law, a force is a factor that has the power to alter an object's status. Newton uses the inertia of rest, the inertia of motion, and the inertia of direction to explain his first law of motion.
From Newtons 1st equation of motion
V = u+at
3.06 = 0+0.8[tex]t_1[/tex]
[tex]t_1[/tex] = 3.825 s
Submarine travels [tex]t_2[/tex]= 5s with const velocity
and then again [tex]t_2[/tex]=5s for slowing to strip during slow,
0 = 3.06 - a × 5
a = 0.612 m/[tex]s^2[/tex]
Total time =[tex]t_1 + t_2 + t_3[/tex]
T = 13.825 s
Now [tex]v^2= u^2[/tex]+2as
[tex]S_1[/tex]= (3.06[tex])^2[/tex]/2×0.8
[tex]S_1[/tex] = 5.852 m
[tex]S_2[/tex] = Ut
[tex]S_2[/tex] = 3.06 × 5
[tex]S_2[/tex] = 15.3 m
[tex]S_3[/tex] = 0 - (3.06[tex]) ^2[/tex]/-2 × 0.612
[tex]S_3[/tex] = 7.65 m
Total displacement
[tex]S = S_1+S_2+S_3[/tex]
S = 28.802 m
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How much would the displacement (in meters) of a 80 N/m spring be if the force hanging was 200 N?
The displacement of the spring with a force constant of 80 N/m is 2.5 m.
What is displacement?Displacement can be defined as the difference between the final and initial position of a object in motion.
To calculate the displacement of the spring, we use the formula below.
Formula:
e = F/k............ Equation 1Where:
e = displacement of the springF = Force hanging on the springk = Spring constantFrom the question,
Given:
F = 200 Nk = 80 N/mSubstitute these values into equation 1
e = 200/80e = 2.5 mHence, the displacement of the spring is 2.5 m.
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Using the midpoint method, if the price falls from $100 to $50, the price elasticity of demand is
The absolute value of the price elasticity of demand is 0.46.
What is price elasticity of demand?
The price elasticity of demand is used to determine the quantity sought after for a good. When prices rise, demand declines for almost all products, but some products are more negatively impacted than others. When a price increases by 1% while all other factors remain constant, the price elasticity provides the percentage change in quantity required. A 1% increase in price results in a 2% decrease in demand when the elasticity is negative two. The effects of changes in other parameters on the needed quantity are evaluated by other elasticities (e.g. the income elasticity of demand for consumer income changes).
What does the microeconomic midpoint technique entail?
With the midpoint formula, percentage changes are calculated by dividing the change by the average, or halfway point, between the starting and final values. As a result, the outcome is the same regardless of the direction of the change.
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Question:
Price Quantity
250 0
200 30
150 70
100 110
50 150
0 190
Using the midpoint method, if the price falls from $100 to $50, the absolute value of the price elasticity of demand is
a. 0.31.
b. 0.46.
c. 1.25.
d. 2.17
Please somebody help me with this project! It's due tomorrow and I'm a bit stuck with it! I'd really appreciate it if anyone is willing to help.
Mass (kg) Volume (L) Density (Kg/L) Substance
Block A
Block B
Block C
Block D
Block E
Densities of Various Materials
Material Density (kg/L)
Wood - 0.40
Apple - 0.64
Plastic - 0.70
Ice - 0.92
Water - 1.00
Aluminum - 2.70
Diamond - 3.53
Lead - 11.3
Gold - 19.3
Questions:
1) Which block has the greatest density?
2) Which block has the lowest density?
3) Submit your data table and identify the substance each block is made of.
I tried to match them, not sure if they're correct:
Answer:
Block A - 19.3 Kg/L
Block B - 0.64 Kg/L
Block C - 0.70 Kg/L
Block D - 0.917 Kg/L
Block E - 3.53 Kg/L
In an 8.00 km race, one runner runs at a steady 11.3 km/h and another runs at 14.3 km/h . How far from the finish line is the slower runner when the faster runner finishes the race?
Answer:
1.69 km away from the finish line.
Explanation:
velocity =distance/time
time= distance/velocity so 8km/14.3km per hour equal to 80/143 hr or 0.559 hrs for second runner to finish race
therefore 0.559 multiply by velocity to give distance of first runner when second runner finish race
0.559 times by 11.3= 6.32 km (3 significant figures)
8 km - 6.32km
= 1.69 km away from the finish line.
An object is dropped from rest at a height of 127 m. find the distance it falls during its final second in the air.
The object will fall a distance during its final second in the air of: 81.967 m
The free fall formulas and the procedures we will use are:
t = √[ (2*h) / g]h = (g * t²)/2Where:
t = time takenh = height traveledg = acceleration due to gravityInformation of the problem:
h = 127 mg = 9.8 m/s²t = ?h(final second)= ?Applying the time formula we get:
t = √[ (2*h) / g]
t = √[ (2* 127 m) / 9.8 m/s²]
t = √[ 254 m / 9.8 m/s²]
t = √[ 25.918 s²]
t = 5.090 s
Calculating time traveled before the final second and we have:
t(final second) = t - 1 s
t(final second) = 5.090 s - 1 s
t(final second) = 4.090 s
Applying the height formula we get:
h = (g * t²)/2
h(final second) = (9.8 m/s² * (4.090 s)²)/2
h(final second) = (9.8 m/s² * 16.7281 s²)/2
h(final second) = 163.935 m/2
h(final second) = 81.967 m
What is free fall?It is when the object or mobile falls from a height (h) with a positive acceleration equal to the gravity, describing a vertical rectilinear travel.
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Converting Units!! Help please show work thank you !!!!
Answer: 5. 9000 meters
6. 0.12626 miles
7. 26.78 meters
8. 1 mile per minute
9. 468 km per hour
Explanation:
5. 1000 m=1 km
9 km * 1000 m/1 km=
9 * 1000/1 = 9000 meters
6. 63360 inches = 1 mile
8000 inches * 1 mile/63360 inches=
8000/63360=0.12626 miles
7. 100 cm=1 m
2678 cm * 1 m/100 cm=
2678 * 1/100=
2678/100=26.78 meters
8. 60 minutes=1 hour
60 mph * 1 hour/60 minutes=
60 * 1/60=1 mile per minute
9. 1000 m=1 km
1 hour=60 minutes
1 minute=60 seconds
60 seconds * 60 minutes/1 hour=
60 * 60/1=3600 seconds
130 meters * 3600 seconds/1 second=
130 * 3600/1=468000 meters per hour
468000 m* 1 km/1000 m=
468000 * 1/1000=468 km per hour
Which gas had the largest proportional increase in mass when moving from the upper troposphere to the surface? why?
The gas that has the largest proportional increase in mass when moving from the upper troposphere to the surface is water vapor.
What is the troposphere ?As we move away from the earth surface, we encounter a region of gases. This thin layer of gases that overlay the surface of the earth is what we call the atmosphere. There are many gases that are part of the atmosphere.
As we move away form the atmosphere, we encounter another region that lies shortly above the atmosphere called the troposphere. There is a lot of water in the troposphere because it is quite close to the earth surface.
Hence, the gas that has the largest proportional increase in mass when moving from the upper troposphere to the surface is water vapor.
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For a penny that weighs 2.493 gg, what is the molarity of the zn(no3)2zn(no3)2 if the resultant solution is diluted to 250.0 mlml with water?
The molarity of the zn(no3)2zn(no3)2 is 0.148 M
This is the Equation used Zn(s)+2HNO3(aq)⟶Zn(NO3)2(aq)+H2(g)
The mass in grammes of one mole of a chemical is its molar mass. The number of entities that are present in a material
A substance's molar mass is the volume of the material that contains one mole of the substance. Its basic definition is the weight of a single mole of a material. The atomic mass of each substance is multiplied by the subscript of that element in the chemical formula to determine the molar mass.
e.g. atoms, molecules, ions, is defined as a mole.
Any material has 6.022 x 1023 molecules in a mole.
Hence the molarity is 0.148M
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005 10.0 points
Two airplanes leave an airport at the same
time. The velocity of the first airplane is
700 m/h at a heading of 69.8°. The velocity
of the second is 620 m/h at a heading of 107.
How far apart are they after 1.9 h?
Answer in units of m.
Answer:
V1 = 700 cos 69.8 i + 700 sin 69.8 j vector components of V1
V1 = 241.7 i + 656.9 j in miles/hour
V2 = 620 cos 107 i + 620 sin 107 j
V2 = -181.3 i + 592.9 j
V = V1 - V2 = 423 i + 64 j rate of planes separation
1.9 V = 803.7 i + 121.6 j miles separation of planes after 1.9 hr
D = (803.7^2 + 121.6^2)^1/2 = 812.8 miles
Two spots on a tlc plate have very similar rf values. could they be the same compound? describe a tlc method to determine whether they are the same or different?
Create a plate with three points of reference. On the two side points put the two compounds separately and in the middle one combine both compounds.
The Rf value of a substance is used to identify the properties of that compound. The Rf value of polar compounds is lower, while the Rf value of non-polar compounds is higher. Three lanes are the most prevalent method for assessing too close spots. Compound A is in lane 1. Compound B is in lane 3. Both spots are in lane 2. This is known as a co-spot. If the co-spot exhibits a 'snowman' effect whenever the TLC is run, it indicates that perhaps the spots are, in a real sense, different compounds which are extremely close together. You could also try changing the solvent system, yet co-spot always comes first.
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If we connect the two flasks through a stopcock and we open the stopcock, what is the partial pressure of helium?
Partial pressure of helium =275.7 torr
Given data,
275 mL is the flask one volume.
Helium's pressure is 752 torr.
The second flask's volume is 475 mL.
722 torr is the argon pressure.
Partial pressure is equal to what?
As,
V2 is equal to 275 + 475 = 750 mL.
Using helium:
P₁V₁ = P₂V₂
P₂ = P₁V₁ /V₂
P₂ = 752 torr. 275 mL / 750 mL
P₂ = 206800 torr. mL /750 mL
P₂ = 275.7 torr
Therefore, Partial pressure of helium =275.7 torr
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john bought a bottled pickle with a metallic lid. However, he was not able to open it suggest a way with scientific reason to help her open the lid.
If a system does 37.0 kj of work on its surroundings and releases 105 kj of heat, what is the change in the internal energy of the system, in kj?
The change in the internal energy of the system in kilojoules is 142 kJ.
The internal energy of a system is defined as the sum of work done by a system or work done on a system and heat released by the system or heat gained by a system. Internal energy is represented by the symbol U. It is presented in units of kilojoules.
Work done by the system is W.
W = (-37) kJ
The heat released by the system is U.
U = (-105) kJ
The change in the internal energy of the system in kJ is,
Change in internal energy = Heat + Work done
∆ U = Q + W
∆ U = (-105) + (-37)
∆ U = 142 kJ
Therefore, the change in the internal energy of the system in kilojoules is 142 kJ.
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A bush pilot wants to fly her plane to a lake that is 250.0 km [N30.0°E] from her starting point. The plane has an air speed of 210.0 km/h, and a wind is blowing from the west at 40.0 km/h. (a) In what direction should she head the plane to fly directly to the lake? (b) If she uses the heading determined in (a), what will be her velocity relative to the ground? (c) How long will it take her to reach her destination?
(a) The plane must fly at an angle of N 35.5° E to immediately approach the lake.
(b) The velocity of the plane is 245.6 km/h.
(c) The time taken is 1.02 hours.
Lake displacement from the starting position, D = 250 km N 30° E
As the x-axis, let's choose the line connecting the plane's beginning point with the lake, which is located in the direction N 30° E.
D = 250 ^i km
The plane's airspeed,
v(p) = 210 km/h
From the east comes the wind. Therefore, using the coordinate system described above, the wind speed,
v(w) = 40 [ cos ( − 30° ) ^i + sin ( − 30°) ] km/h
v(w) ≈ ( 36.64 ^i − 20 ^j ) km/h
(a) To eliminate the perpendicular component of the wind velocity, move the plane in the direction θ with respect to the x-axis.
v(p) = 210 ( cos(θ) ^i + sin(θ) ^j ) km/h
In order for the y-component of the plane velocity to cancel out the y-component of the wind velocity, the correct angle must be calculated.
Therefore,
210 sin(θ) km/h = 20 km/h
sin(θ) = 20 / 210
θ ≈ 5.5°
Therefore, the aircraft should fly 5.5 degrees off of the x-axis. This means that the plane must fly at an angle of N 35.5° E to immediately approach the lake.
(b) The velocity relative to the ground is:
v = v(w) + v(p)
v = 210 ( cos 5.5° ^i + sin 5.5° ^j ) km/h + ( 36.64 ^i − 20 ^j ) km/h
v ≈ ( 209 ^i + 20 ^j ) km/h + ( 36.64 ^i − 20 ^j ) km/h
v = 245.6 ^i km/h
The plane is moving at a speed of 245.6 km/h relative to the ground.
(c) From the starting point, the time taken to reach the lake is:
time = distance/ speed
T = 250 km / 245.6 km/h
T ≈ 1.02 h
Therefore, from the starting position, it will take around an hour to get to the lake.
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