The value of a, if the system of forces is in equilibrium is 2.
What is the value of a for the equilibrium force?
If the system of forces is in equilibrium the sum of all the forces will be equal to zero.
∑F = 0
2i -j + k + 3i + 4j + 4k + 5i + 3j + 3k - (3i+2k + 4i-5j + ak -4i-2j+4k) = 0
The value of a is calculated by summing all the corresponding vectors and equating them.
10i + 6j + 8k - (3i -7j + 6k + ak ) = 0
10i + 6j + 8k - 3i + 7j - 6k - ak = 0
7i + 13 j + 2k - ak = 0
2k - ak = 0
ak = 2k
a = 2
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What's one major difference between the earth's greenhouse effect and an actual greenhouse?
Select one:
a.
Heat escapes from a greenhouse more easily than it does from Earth's atmosphere
b.
The glass in a greenhouse traps heat, while greenhouse gases in the atmosphere absorb and recycle heat
c.
There is no significant difference; both work pretty much the same way
d.
Actual greenhouses are cold in winter, while the greenhouse effect has led to warm winters across the earth
The difference between the earth's greenhouse effect and an actual greenhouse is that the glass in a greenhouse traps heat, while greenhouse gases in the atmosphere absorb and recycle heat. That is option B.
What is a green house gas?The greenhouse gas is the type of gas that is found in the earth's atmosphere that has the ability to absorb heat from the earth's environment.
Examples of greenhouse gases include the following:
carbon dioxide, methane, nitrous oxide, and water vapor.An ordinary greenhouse is used to grow crops such as tomatoes and tropical flowers. Heat is bring trapped inside these houses as the sun shines during the day time.
Therefore, it can be concluded that the major difference between the earth's greenhouse effect and an actual greenhouse is that the glass in a greenhouse traps heat, while greenhouse gases in the atmosphere absorb and recycle heat.
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A magazine rack has a center of gravity 16 cm above the floor, as shown in the figure below (Figure 1). Through what maximum angle, in degrees, can the rack be tilted without falling over?
The magazine rack can turn through 73 degrees without falling over
What is the angle?We know that we can be able to obtain the angle that has been turned when we obtain the tangent of the angle that is made by the direction of the ball.
Now we know that we can be able to get the ange that has been turned when we apply the idrea of a righta ngled triangle. In which case, we would have the following;
Angle turned = tan-1 (16/5)
= 73 degrees
Thus, the angle that is turned is 73 degrees.
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A proton follows the path shown in (Figure 1) . Its initial speed is v0 = 2.8×106 m/s.
What is the proton's speed as it passes through point P?
Express your answer to two significant figures and include the appropriate units.
The proton's speed as it passes through point P is Vp = 1.72 × 10^6 m/s
What is a proton?A proton is described as a stable subatomic particle, symbol p , H⁺, or ¹H⁺ with a positive electric charge of +1 e elementary charge.
From the question have the following parameters
A fixed charge, Q = -10 nC
Initial position of charge particle, proton (q), ro = 3mm
Final position of charge particle, proton (q),
rp = 4mm
Initial velocity of charged particle,
vo =2.8 x 10^6 m/s
Let
vp be the final speed of proton
We then Apply conservation of Energy:
Initial (Potential + kinetic) Energy = Final (Potential + kinetic) Energy
kQq ro + 1/2mVo² = kQq rp + 1/2mVp²
m = 1.67 x 10^-27
Substituting the values and converting from mm to meters, we have that)
Vp = 1.72 × 10^6 m/s
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There exist two parallel 1 m x 1 m x ~0 m (infinitesimally thin) conducting plates sitting
parallel to each other and the xz-plane. The positively charged plate is at y = 0, and the negatively
charged plate is at y = 0.01 m. An electron is released from rest in between the charged plates. Explain
why the electron moves in the proper direction in terms of the forces acting on the electron.
An electric field is a region in which electric charges sustain electrical conduction. An electric field describes the electrical environment around an electron.
What is meant by electric force?The electric force is the force between two charged bodies due to electric charges. The electric field at a point indicates the force experienced by a positive unit test charge at that point.
In this case, electrons move to higher potentials. Since the electric field is directed from the positive plate to the negative plate, electron acceleration occurs towards the negative plate and the negative plate is deflected towards the positive plate.
In this case, the electrostatic force is F = E q,
Here the electric field E = V/d is constant and the charge on the electron is constant, so the force on the electron is constant. Hence, the electron moves in the proper direction in terms of the forces acting on the electron.
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Anne exerts a force of 34.1 N to pitch a softball. She moves the ball 1.8 meters before releasing it. What amount of work did Anne do on the ball?
Formula for work:
[tex]w=Fd[/tex]
work(measured in joules) = force(measured in newtons) * distance(measured in meters)
__________________________________________________________
Given:
[tex]F=34.1N[/tex]
[tex]d=1.8m[/tex]
[tex]w=?[/tex]
__________________________________________________________
Finding work:
[tex]w=Fd[/tex]
[tex]w=34.1\times1.8[/tex]
__________________________________________________________
Answer:
[tex]\fbox{w = 61.38 Joules}[/tex]
Which statement correctly compares sound and light waves?Both light and sound waves need matter to carry energy from one place to another.Neither light nor sound waves need matter to carry energy from one place to another.Light waves carry energy parallel to the motion of the wave, while sound waves carry energy perpendicular to it.Sound waves carry energy parallel to the motion of the wave, while light waves carry energy perpendicular to it.
Sound waves carry energy parallel to the motion of the wave, while light waves carry energy perpendicular to it.
What is energy parallel?Energy parallel is a type of energy efficiency strategy that seeks to reduce the amount of energy used in a building or facility by utilizing multiple energy sources instead of relying solely on one. This type of energy efficiency strategy works by drawing energy from multiple sources, such as solar, geothermal, wind, and water energy, and combining them to power a single building or facility. By utilizing multiple energy sources, energy parallel helps to reduce the overall amount of energy used in a building or facility, thus improving its overall energy efficiency. Additionally, this type of energy efficiency strategy helps to reduce the amount of energy that is wasted or lost by utilizing energy sources that are renewable and more sustainable.
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A ladder, length L, with mass M, leans against a frictionless wall at an angle of θ=70° as shown.
1) If the ladder is in static equilibrium,
The net force is zero but the net torque is not.
The net torque is zero but the net force is not.
The net force and net torque are both zero.
Neither net force nor net torque is zero.
2) Which of these free body diagrams best represents the forces on the ladder?
3) At which of the following locations can we put the rotation axis we use when calculating torques?
Only at the center of the ladder.
Only at the bottom left end of the ladder.
Only at the top right end of the ladder.
We can choose any of these locations for the rotation axis.
4) For the rest of these problems, we're using the top right end of the ladder as our pivot point. What is the magnitude of the torque from the force of gravity, around this point?
L* M g* sin (θ)
L* M g* cos (θ)
(L/ 2)* Mg g* sin (θ)
(L/ 2)* M g* cos (θ)
Metal panels that are designed to act as stressed-skin panels are attached directly to the structural frame of the building with
a. bags
b. straps
c. clips
d, mats
Metal panels that are designed to act as stressed-skin panels are typically attached directly to the structural frame of the building using straps, clips, or mats.
Straps are typically used to connect the panel to a supporting member, while clips are used to secure the panel to a non-supporting member. Mats are used to provide additional support for the panel and to distribute the load evenly across the panel.
This is beneficial for the structural integrity of the building since it ensures that the panel will not be subjected to too much stress in one specific area. Additionally, it allows for better load distribution, which can help to reduce the overall weight of the building, as well as reduce stress on the individual panels.
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our solar system______Spur, of the_______arm of the milky way galaxy
Answer: At least 100 billion stars, including our Sun, make up the Milky Way, a spiral galaxy with a diameter of around 100,000 light-years. In the Milky Way, where are we located? The Orion Arm, also known as the Orion Spur, is a short, incomplete arm between the Sagittarius and Perseus arms that is close to where our Sun is positioned.
Explanation:
in a certain town ,50% of the households own a celullar phone,40% own a pager, and 20% own both a cellular phone and a pager. what is the probability that a randomly chosen household own either a cellular phone or a pager?
Answer:
0.18
Explanation:
20/110=0.18
If you have no weight in outer space (ie. far from any planet or star or any other massive object) what is the acceleration due to gravity that you would experience?
If you have no weight, then the acceleration due to gravity is zero.
What is the acceleration due to gravity?We know that the acceleration due to gravity of the object would have to be the acceleration that would be granted to a body because it is within the sphere of the gravitational pull of the earth.
We must know that the weight of the object is the product of the mass and the acceleration due to gravity. If the object is weightless, the implication of that is that the acceleration due to gravity is zero at that point.
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A wire X of Resistance 200, is replaced by wire Y of Resistance 35 A. Both wires are made of the same material, Wire Y is double the area of wire X Wire Y has a length of 2.5m.
Find the length of wire X
Length
- If wire X is connected to a battery of emf-12V. Calculate the current in the wire.
Current
-Calculate the charge passing through the wire in 5 minutes
Charge.
iv-Calculate the Energy consumed by the wire in half an hour.
(a) The length of wire X is 7.14 m.
(b) The current in the wire is 0.06 A.
(c) The charge passing through the wire in 5 minutes is 18 C.
(d) The Energy consumed by the wire in half an hour is 1,296 J.
What is the length of wire X?
The length of wire X is calculated by applying the following formula as shown below;
ρ = RA / L
where;
R is the resistance of the wireA is the area of the wireL is the length of the wireSince the wires are made of the same material, resistivity of wire X = resistivity of wire Y
let wire X = 1
let wire Y = 2
R₁A₁ / L₁ = R₂A₂ / L₂
L₁ = ( R₁A₁L₂ ) / ( R₂A₂ )
L₁ = ( 200Ω x A₁ x 2.5 m ) / ( 35Ω x 2A₁ )
L₁ = 7.14 m
The current flowing in wire X is calculated as follows;
V = IR
I = V / R
where;
V is the voltageR is the resistanceI = ( 12 V ) / ( 200Ω )
I = 0.06 A
The charge passing through the wire in 5 minutes is calculated as follows;
Q = It
Q = 0.06 A x ( 5 x 60 s )
Q = 18 C
The Energy consumed by the wire in half an hour is calculated as;
E = Pt
where;
P is powert is timeE = (IV) x ( t )
E = ( 0.06 A x 12 V ) x ( 30 mins x 60 s )
E = 1,296 J
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If α=40°, β=60°, and M=4.0 kg, determine the tension in string 1 shown.
The magnitude of the tension in string 1 is 20 N.
option D is the correct answer.
What is the tension in string 1?The magnitude of the tension in string 1 is calculated by applying the following kinematic equation.
T₁ cosα + T₂ cosβ = W cos90 ---- ( 1 )
T₁ sinα + T₂ sinβ = W sin90 ----- ( 2 )
Substitute the given values for β and α, to determine the value of Tension T₁ and Tension T₂.
-T₁ cos(40) + T₂ cos(60) = W cos90
-0.766T₁ + 0.5T₂ = 0
0.5T₂ = 0.766T₁
T₂ = ( 0.766T₁ ) / 0.5
T₂ = 1.53 T₁ ----- (3)
T₁ sinα + T₂ sinβ = W sin90
T₁ sin(40) + T₂ sin(60) = (4 x 9.8) sin90
0.64T₁ + 0.886T₂ = 39.2
Substitute the value of T₂ into the above equation as shown below.
The tension in string 1 is calculated as follows;
0.64T₁ + 0.886(1.53 T₁) = 39.2
0.64T₁ + 1.33T₁ = 39.2
1.97T₁ = 39.2
T₁ = 39.2 / 1.97
T₁ = 19.99 N ≈ 20 N
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the orientation of an mrna codon relative to a trna anticodon is best described as: a. antiparallel. b. parallel. c. perpendicular. d. non-complementary.
The orientation of an mRNA codon corresponding to a tRNA anticodon is best described as A: antiparallel.
An anticodon is a three-base sequence, paired with a particular amino acid, that a tRNA molecule brings to the associated codon of the mRNA during translation. The anticodon sequence is said to be complementary to the mRNA, using base pairs in the anti-parallel direction. The tRNA anticodon 3-UAC-5 will make pair with the mRNA codon.
Thus, the orientation of an mRNA codon relative to a tRNA anticodon is said to be antiparallel.
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An atom of an element can change into an atom of another element if it is:
A. extremely stable
B. radioactive and it's nucleus can trap or emit particles
C. an ion and it's atomic number is larger than it's mass number
D. an isotope and it has more electrons than neutrons
Answer:
B. radioactive and it's nucleus can trap or emit particles
Explanation:
Each element is unique because of the number of protons it possesses. All the atoms of one particular element will have same amount of protons. Thus, if I want to change an atom of an element into atom of another element, i must have a way to mess with the proton count and such. These are seen in radioactive process like fusion, fission, nuclear decay etc.
Which of the following energy sources are in some way derived from the Sun?
Answer:
Wave Energy and Biomass Energy sources.
Explanation:
The main sources of energy available on earth are Coal, Geothermal, Nuclear, Petroleum, Hydro, Biomass, and Wave, from which nuclear and geothermal are resultant of radioactive materials whereas Coal and Petroleum are resultant of Fossil Fuels.
Biomass energy is produced by living organisms, for example, corn is used as biomass material, which stores energy through photosynthesis, and the photosynthesis process is only possible with Sun.
Wave energy is resultant of the sun's uneven heating of the ocean which makes tides and then the motion of the waves utilize to harness the energy.
(Figure 1) shows Sue along the straight-line path between her home and the cinema, where d=3.2 mi. Assume the positive direction is to the right.
Part A
If Sue walks home, what is her displacement if her home is the origin?
Express your answer in miles.
Part B
If Sue walks home, what is her displacement it the cinema is the origin? Assume the positive direction is to the right. Express your answer in miles.
(a) If Sue walks home, her displacement if her home is the origin is -2 mi.
(b) If Sue walks home, her displacement if the cinema is the origin is -5.2 mi.
What is the displacement of an object?The displacement of an object is the change in the position of an object.
Mathematically, the formula for the displacement of an object is given as;
Δx = xf - xi
where;
xf is the final position of the objectxi is the initial position of the objectIf Sue walks home, her displacement if her home is the origin is calculated as;
Δx = xf - xi
Δx = 0 mi - 2 mi
Δx = - 2mi
If Sue walks home, her displacement if the cinema is the origin is calculated as;
Δx = xf - xi
Δx = 0 mi - (2 mi + 3.2 mi )
Δx = 0 mi - 5.2 mi
Δx = -5.2 mi
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a 0.40 kg object is moving on a frictionless surface with a speed of 30 m/s. A force of 2.0N is applied continually until the velocity of the object has been reversed. How long was the force applied?
The time the force was applied to the obeject of mass 0.4 kg is 12 seconds
What is impulse?
Impulse is the product of force and time.
To calculate how long the force was applied, we use the formula of impulse.
Formula:
Ft = m(v-u).................. Equation 1Where:
F = Forcet = Timem = Massv = Final velocityu = Initial velocityFrom the question,
Given:
m = 0.4 kgv = -30 m/s (reversed)u = 30 m/sF = -2.0 N (Acting against the direction of motion)Substitute these values into equation 1 and solve for t
-2.0t = 0.4(-30-30)-2.0t = -24t = -24/-2t = 12 secondsHence, the time is 12 seconds
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What is the gravitational force on a 987 kg satellite orbiting
5.1 × 10⁴ m above the surface of Earth? Assume the mass of Earth is
5.97 × 10²⁴ kg.
Answer:
The gravitational force on the satellite can be calculated using the formula:
F = G * ((m1 * m2) / r^2)
Where:
F is the gravitational force
G is the gravitational constant (6.67 × 10^-11 N*m^2/kg^2)
m1 is the mass of the first object (in this case, the satellite)
m2 is the mass of the second object (in this case, Earth)
r is the distance between the two objects
Plugging in the given values, we have:
F = (6.67 × 10^-11 N*m^2/kg^2) * ((987 kg * 5.97 × 10²⁴ kg) / (5.1 × 10⁴ m)^2)
= 9.06 × 10^-6 N
Therefore, the gravitational force on the satellite is approximately 0.00000906 N.
Explanation:
The amount of energy released in the cellular respiration is similar to the amount released when methane reacts with oxygen. Why does our body not burn?
Each step of the energy released during cellular respiration is accompanied by the synthesis of ATP. Only a tiny fraction of energy is converted to heat that's why our body doesn't burn.
In a nutshell, what is cellular respiration?The process through which organisms use oxygen to break down food molecules in order to get chemical energy for cellular processes is known as cellular respiration. The cells of animals, plants, and fungi, as well as those of algae and other protists, all engage in cellular respiration.
What is the location of cellular respiration?Cells produce energy through a process called cellular respiration. Prokaryotic and eukaryotic cells both have mitochondria and cytoplasm where cellular respiration takes place.
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7. A pendulum consists of a ball of mass m suspended at the end of a massless cord of length L as shown. The pendulum is drawn aside through an angle of 60° with the vertical and released. At the low point of its swing, the speed of the pendulum ball is
(A) gL
(B) 2gL
(C) 1/2gL
(D) gL
The speed of the pendulum ball is determined as √ (gL).
option A is the correct answer.
What is the speed of the pendulum ball?
The speed of the pendulum ball is calculated by applying the law of conservation of energy as shown below.
Potential energy of the ball at top = Kinetic energy of the ball at bottom
U = K.E
mgh = ¹/₂mv²
v = √ ( 2gh)
where;
g is acceleration due to gravityh is the change in height of the pendulum ballThe change in height of the pendulum ball is given as;
h = L - Lcosθ
where;
θ is the angle of inclination of the pendulumh = L - Lcos(60)
h = L - ¹/₂L
h = ¹/₂L
The speed of the pendulum ball is calculated as;
v = √ (2g x ¹/₂L)
v = √ (gL)
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(b)
The aorta transports blood from the heart to the body.
In a person at rest:
blood travels at a mean speed of 10 cm/s in the aorta
blood travels at a mean speed of 0.5 mm/s in the capillaries
the speed of blood decreases at a rate of 0.4 cm/s² as blood travels from the
aorta to the capillaries.
Calculate the time it takes for blood to travel from the aorta to the capillaries.
Assume that the speed of blood decreases at a constant rate.
Use the equation:
rate of decrease in speed=
Give your answer to 2 significant figures.
change in speed
time
The time it takes for blood to travel from the aorta to the capillaries is 20 seconds. This can be calculated using the equation: t = v₁ - v₂ / a , where v₁ is the initial velocity (10 cm/s), v₂ is the final velocity (0.5 mm/s), and a is the acceleration (0.4 cm/s²). Therefore, t = 10 cm/s - 0.5 mm/s / 0.4 cm/s² = 20 s.
What is the frequency if you have a period of 5.1 seconds
Answer:
0.20 Hz
Explanation:
Period formula:
T = 1 / f
rearrange to solve for T (which is period)
F = 1/T
= 1/5.1
= 0.20 Hz
If you want 3 sig figures it would go up to 0.196, but I just rounded to two to get 0.20.
The immediate source of the intercellular fluid surrounding
all human body cells is
A) blood plasma
B) enzymatic secretions
C) glomerular filtrations
D) lymphatic tissue
Answer: lymphatic tissue
Explanation:
If you double the diameter of a cylindrical wire, you double its conductivity but reduce its resistivity by one half.
Please Explain.
Answer:
Resistivity and conductivity are reciprocal quantities.
Doubling one will cause the other to be reduced to one half.
what happens to a vector when it is multiplied by a negative number that is not equal to negative one?
A. only the magnitude changes
B. The vector does not change
C. Both magnitude and direction change
D. Only the direction changes
The thing that happens to a vector when it is multiplied by a negative number that is not equal to negative one is A. only the magnitude changes
What happens if you multiply a vector by a negative number?except that the vector's arrow will point in the other direction when multiplied by a negative integer. A vector, for instance, will become half as long in the same direction when multiplied by 1/2, whereas it will become twice as long but directed when multiplied by 2.
A vector's direction is reversed but the magnitude is left unchanged when multiplied by a negative one. The direction and magnitude of the vector are reversed when multiplied by any other negative quantity.
Therefore, option A is correct.
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Find the magnitude of the sum of these two vectors.
Answer:
sol:
tanβ=[tex]\frac{101*sin(60)}{85+101*cos(60)}[/tex]
β=[tex]tan^{-1}[/tex](0.64552)
β=32.84
therefore, the direction is 32.84
A 1.2 kg object hanging from a spring of force constant 300 N/m oscillates with a maximum speed of 30 cm/s. (a) What is its maximum displacement? When the object is at its maximum displacement, find (b) the total energy of the system, and (c) the gravitational potential energy. (Choose potential energy as zero when the object is in equilibrium).
The maximum displacement = 0.0189 m
The Total energy of the system = 1.188 J
The Gravitational potential energy = 0.22 J
Let m be = Mass of the object = 1.2 kg
As given K = Spring Constant of the spring = 300 N/m
Let v denote = Maximum speed with which the body oscillates = 30 cm/s
Let 'x' be the maximum displacement of the body
x²= mv²/k=1.2* 0.3 /300= 0.0189
Total energy= kinteric energy+potential energy =kx²/2 + mv²/2
=1.188J
The Gravitational potential energy of the system is
E=Mgx=1.2*9.8*0.0189
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The 1.2 kg object's maximum displacement when it is suspended from a spring with a 300 N/m force constant oscillates at a maximum speed of 30 cm/s. This displacement is equal to 0.0189 m.
How to calculate displacement and energy?When the object is displaced to its maximum, the system's total energy is 1.188 J.
The energy of gravity is equal to 0.22 J.
Allow m to be equal to 1.2 kg, the object's mass.
K = Spring as stated. Springs have a constant of 300 N/m.
the body can oscillate at a maximum speed of 30 cm/s (let v signify this).
Suppose that "x" represents the body's largest displacement.
x²= mv²/k=1.2* 0.3 /300= 0.0189
Total energy = interstellar energy + potential energy = kx2/2 + mv2/2
=1.188J
According to the system's gravitational potential energy,
E=Mgx=1.2*9.8*0.0189
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The velocity v of a particle at a time tis given by;
v=at+ b/(t +c)
Determine the dimensions of a, b and c.
Answer:
Here in the question the dimensions of a ,b and c can be calculated by using the principal of homogeneity
A runner begins a race from rest and reaches a final speed of 22mph. It takes 3.45s. If the runner's mass is 76.4 kg and 1 mile = 1,609.34m. A) What is the runner's acceleration?
B) What is the magnitude of the downward force acting on the runner?
Acceleration:
a = (22 mph - 0 mph) / (3.45s) = 6.37 mph/s
Magnitude of the Downward Force:
F = m*a = 76.4 kg * 6.37 mph/s = 484.53 N
