Answers
First, use Newton's Second Law on each mass.
Mass 1.\(T-W_1=m_1a\)Mass 2.\(\Sigma F_y=m_2a\to W_2-T=m_2a_{}\)Solve the second equation for T.
\(T=W_2-m_2a\)Combine the equations.
\(W_2-m_2a-W_1=m_1a_{}\)But the weight force is mg.
\(m_2g-m_2a-m_1g=m_1a\)Solve for a.
\(\begin{gathered} m_2g-m_1g=m_1a+m_2a \\ a(m_1+m_2)=m_2g-m_1g \\ a=\frac{m_2g-m_1g}{m_1+m_2} \end{gathered}\)Let's say the masses are m_1 = 2 kg and m_2 = 5 kg.
\(\begin{gathered} a=\frac{5\cdot9.8-2\cdot9.8}{2+5} \\ a=\frac{49-19.6}{7} \\ a=\frac{29.4}{7} \\ a=4.2\cdot\frac{m}{s^2} \end{gathered}\)Therefore, the acceleration of the system is 4.2 m/s^2.
Related Questions
A certain transformer doubles input voltage. If the primary coil has 10 A of current, then the current in the
secondary coil is
O 25 A.
O 5 A.
O none of the above
O 2A.
O 10 A.
Answers
According to the given statement then the current in the secondary coil is 5A.
The correct option is B.
What does secondary coil in transformer do?Transformers have at least two windings or coils, as seen in the experiment above. The primary is referred to as such, and the secondary as such. AC electricity enters the primary coil here. Where the current is induced to carry out any sort of energy transfer is in the secondary coil.
Briefing:According to the question,
Current in primary coil, I\(_i_n\) = 10A
Power = V\(_i_n\)I\(_i_n\) = V\(_o_u_t\)I\(_o_u_t\)
Then
By substituting the values,
V\(_i_n\)* 10 =V\(_i_n\)I\(_o_u_t\)
By applying cross-multiplication,
10 = 2I\(_o_u_t\)
I\(_o_u_t\) = 10/2
= 5A
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The complete question is -
A certain transformer doubles input voltage. If the primary coil has 10 A of current, then the current in the secondary coil is
A- 25 A.
B- 5 A.
C- none of the above
D- 2A.
E- 10 A.
Part 3 Waves on a string-with a loose end The reflected
wave interferes with the original wave and creates standing wave composed of
nodes and antinodes if the frequency is just right: Instead of a node an antinode
will always exist at the loose end: (This happens because the phase of the wave
is not inverted upon reflection from loose end and therefore always constructively
interfere at that position:) Draw and measure the frequency of the 1st harmonic
(node near driver end followed by an antinode on loose end) Settings: amplitude:
0.05 cm tension: high damping: none turn on: Loose End What fraction of a
wavelength is this? Hz Click Restart' to observe the standing wave. 2. Predict the
frequencies of several higher harmonics: Use the wave simulator to test each of
your calculated harmonics Draw and label the standing waves for each of the
harmonics you discovered: Divide each higher harmonic by the first harmonic:
Are the higher harmonics even-number or odd-number multiples of the first
harmonic?
Answers
The first harmonic of the standing wave on a string with a loose end represents half a wavelength.
The fraction of a wavelength represented by the first harmonic is 1/2.
The higher harmonics of a standing wave on a string with a loose end are odd-number multiples of the first harmonic.
1. The first harmonic of a standing wave on a string with a loose end occurs when there is a node near the driver end and an antinode at the loose end. To measure the frequency of the first harmonic, we need to determine the fraction of a wavelength represented by this standing wave.
The first harmonic of the standing wave on a string with a loose end represents half a wavelength.
The first harmonic of a standing wave on a string with a loose end consists of a node near the driver end and an antinode at the loose end. This configuration creates the simplest standing wave pattern.
In a standing wave, a node is a point where the amplitude of the wave is always zero, representing a point of minimum displacement. An antinode, on the other hand, is a point of maximum displacement, where the amplitude is at its highest.
Since the loose end does not invert the phase of the wave upon reflection, the reflected wave and the original wave constructively interfere at the loose end, resulting in an antinode.
In the first harmonic, there is exactly half a wavelength between the node near the driver end and the antinode at the loose end.
Therefore, the fraction of a wavelength represented by the first harmonic is 1/2.
2. To predict the frequencies of higher harmonics, we can use the relationship that the frequency of each harmonic is a multiple of the frequency of the first harmonic. The higher harmonics can be calculated as follows:
Second Harmonic: The second harmonic consists of two nodes and one additional antinode compared to the first harmonic. The fraction of a wavelength for the second harmonic is 1/2 * 2 = 1. Thus, the second harmonic has a frequency that is twice that of the first harmonic.
Third Harmonic: The third harmonic consists of three nodes and two additional antinodes compared to the first harmonic. The fraction of a wavelength for the third harmonic is 1/2 * 3 = 1.5. Thus, the third harmonic has a frequency that is three times that of the first harmonic.
Fourth Harmonic: The fourth harmonic consists of four nodes and three additional antinodes compared to the first harmonic. The fraction of a wavelength for the fourth harmonic is 1/2 * 4 = 2. Thus, the fourth harmonic has a frequency that is four times that of the first harmonic.
In general, the higher harmonics of a standing wave on a string with a loose end are odd-number multiples of the first harmonic.
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3.1
power
Every day a certain household uses a 4.4 KW electric stove for 70 minutes, seven 150 W light bulbs for 7
hours each and miscellaneous appliances amounting to 1.8 KW/h. The 4 KW hot water cylinder switches
on for a total of 120 minutes during the day. If electricity cost 50c a KW/h. what is the monthly electricity
bill. (5 marks)
Answers
Answer:
The value is \(C = 30729\ c\)
Explanation:
From the question we are told that
The power rating of the stove is \(P = 4.4 KW = 4.4 *10^{3} \ W\)
The duration of its use everyday is \(t_1 = 70 \ minutes = 1.167 \ hours\)
The rating of the light bulbs is \(P_2' = 150 W\)
The number is \(n = 7\)
The power rating of the total bulb is \(P_2 = 7 * 150 = 1050 \ W\)
The duration of its use everyday is \(t_2 = 7 hours\)
The power rating of miscellaneous appliance \(P_3 = 1.8 \ KW = 1.8 *10^{3} \ W\)
The duration of its use everyday is \(t_3 = 1 hour\)
The power rating of hot water \(P = 4 KW = 4 *10^{3} \ W\)
The duration of its use everyday is \(t_4 = 120 \ minutes = 2 hours\)
Generally the total electrical energy used in 1 month is mathematically represented as
\(E = P_1 * t_1 * 30 + P_2 * t_2 * 30 + P_3 * t_3 * 30+ P_4 * t_4 * 30\)
=> \(E = 4.4*10^{3} * 1.167 * 30 + 1050 * 7 * 30 + 1.8 *1 * 30+ 4*10^{3} * 2 * 30\)
=> \(E = 614598 \ W \cdot h\)
=> \(E = 614.6 \ K W \cdot h\)
Generally the monthly electricity bill is mathematically represented as
\(C = 614.6 * 50\)
=> \(C = 30729\ c\)
A solenoid used to produce magnetic fields for research purposes is 2.1 m long, with an inner radius of 28 cm and 1000 turns of wire. When running, the solenoid produced a field of 1.3 T in the center. Given this, how large a current does it carry?
Answers
Answer:
I = 2172.46 A
Explanation:
Given that,
The length of a solenoid, l = 2.1 m
The inner radius of the solenoid, r = 28 cm = 0.28 m
The number of turns in the wire, N = 1000
The magnetic field in the solenoid, B = 1.3 T
We need to find the current carried by it. We know that, the magnetic field in a solenoid is given by :
\(B=\mu_o nI\\\\or\\\\B=\mu_o \dfrac{N}{L}I\\\\I=\dfrac{BL}{\mu_o N}\)
Put all the values,
\(I=\dfrac{1.3\times 2.1}{4\pi \times 10^{-7}\times 1000}\\\\I=2172.46\ A\)
So, it carry current of 2172.46 A.
Gauss's law combines the electric field over a surface with the area of the surface. From Coulomb's law we know that the electric field falls off as 1/r2 of the distance r from the charge. How does the surface area change with r ?
Answers
The change in surface area of Gaussian surface with radius (r) is 8πr.
Electric field from Coulomb's lawThe electric field experienced by a charge is calculated as follows;
\(E = \frac{Q}{4\pi \varepsilon_o r^2}\)
where;
E is the electric fieldQ is the charger is the radiusThe electric field reduces by a factor of \(\frac{1}{r^2}\)
Surface area of a Gaussian surface;The surface area of a sphere is given as;
\(A = 4\pi r^2\)
Change in area with r\(\frac{dA}{dr} = 8\pi r\)
Thus, the change in surface area of Gaussian surface with radius (r) is 8πr.
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Particles q₁ +8.0 μC, q2 +3.5 μC, and
93-2.5 μC are in a line. Particles q₁ and q2 are
separated by 0.10 m and particles q2 and q3 are
separated by 0.15 m. What is the net force on
particle q₂?
Remember: Negative forces (-F) will point Left
Positive forces (+F) will point Right
+8.0μ.C
+91
0.10 m
+3.5 C
+92
0.15 m
-2.5μ C
93
Answers
The net force on particle q₂, located between particles q₁ and q₃, is approximately 189000 N. The force exerted by particle q₁ on q₂ is positive and equals 252000 N, while the force exerted by particle q₃ on q₂ is negative and equals -63000 N.
To find the net force on particle q₂, we need to calculate the individual forces exerted on q₂ by particles q₁ and q₃ and then determine their sum.
The force between two charged particles can be calculated using Coulomb's law:
F = k * |q₁ * q₂| / r²
Where F is the force between the particles, k is the electrostatic constant (k ≈ 9.0 x \(10^9\) Nm²/C²), q₁ and q₂ are the charges of the particles, and r is the distance between them.
First, let's calculate the force exerted on q₂ by q₁:
F₁₂ = k * |q₁ * q₂| / r₁₂²
F₁₂ = (9.0 x \(10^9\) Nm²/C²) * |(8.0 μC) * (3.5 μC)| / (0.10 m)²
F₁₂ ≈ 252000 N
The force is positive because q₁ and q₂ have opposite charges.
Next, let's calculate the force exerted on q₂ by q₃:
F₂₃ = k * |q₂ * q₃| / r₂₃²
F₂₃ = (9.0 x \(10^9\)Nm²/C²) * |(3.5 μC) * (-2.5 μC)| / (0.15 m)²
F₂₃ ≈ -63000 N
The force is negative because q₂ and q₃ have the same charge.
Finally, we can find the net force on q₂ by summing the individual forces:
Net force = F₁₂ + F₂₃
Net force = 252000 N + (-63000 N)
Net force ≈ 189000 N
The net force on particle q₂ is approximately 189000 N.
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A particular heat engine does 10,000 J of work on a gas on the compression stroke, and the gas does 60,000 joules of work on the power stroke. Which of the following PV diagrams indicates the net work done by the heat engine in one cycle?
Answers
For a cyclic heat engine process, the PV diagram will be a closed loop. The area inside the loop will represent the amount of work done during the cycle.
The work done is given as,
\(W=\text{work done by the gas-work done on the gas}\)Substituting all known values,
\(\begin{gathered} W=60000\text{ J-10000 J} \\ =50000\text{ J} \end{gathered}\)Therefore, option (c) is the correct choice.
describe 5 steps you would take when trouble shooting a test kit
Answers
Answer:
1. Information Gathering
2. Analysis and Planning.
3. Implementation of a solution.
4. Assessment of the effectiveness of the solution.
5. Documentation of the incident.
A 3.59 kg block is released from rest 53.0 m above the ground. When it has fallen 21.3 m, what is its kinetic energy
Answers
\(\implies\)1115.2 Joules
Given :-\(\red{\leadsto}\:\)\(\textsf{Height\: at \:rest\:} \)\(\sf,h_2= 53.0m \)
\(\green{\leadsto}\:\)\(\textsf{Height\: to\:which\;block\:}\)\(\sf,h_1= 21.3 \)
Solution :-\(\maltese\)As the block falls , the change in potential energy will be converted into kinetic energy
\(\leadsto\)Potential Energy at rest at height,\(h_2\) = \(\sf mgh_2\)
\(\leadsto\)Potential Energy when fell at height,\(h_1\) = \(\sf mgh_1\)
\(\\\)
\(\leadsto\)Kinetic energy= Change in Potential energy = = \(\sf mgh_2-mgh_1\)
\(\begin{gathered}\implies\quad \sf mg(h_2-h_1) \\\end{gathered} \)
\(\begin{gathered}\implies\quad \sf mg(53.0-21.3) \\\end{gathered} \)
\(\begin{gathered}\implies\quad \sf 3.59 \times 9.8\times (53.0-21.3) \\\end{gathered} \)
\(\begin{gathered}\implies\quad \sf 3.59 \times 9.8\times 31.7\\\end{gathered} \)
\(\begin{gathered}\implies\quad \boxed{\sf{1115.2\: Joules}}\\\end{gathered} \)
On a distance-time graph, what is shown when the curve is flat going from left to the right?
A. a negative speed
B. no speed
C. a positive speed
D. It does not mean anything.
Please help me !!im on a test
Answers
Two balls are held at a point 75m above the ground . One of the balls is projected vertically down with a velocity 10meters per second and the other released at the same time to fall freely . calculate the difference in time for the arrival on the ground . acceleration is 10 .
Answers
The difference in time for the arrival on the ground 7.5 second.
What is acceleration?Acceleration is rate of change of velocity with time. Due to having both direction and magnitude, it is a vector quantity. Si unit of acceleration is meter/second² (m/s²).
Initial height of the two balls: h = 75 meter.
Acceleration due to gravity: g = 10 m/s².
The time difference between ball vertically projected down with a velocity 10meters per second and the ball released at the same time to fall freely is = 75/10 second = 7.5 second.
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What is sound waves
Answers
Sound waves are a type of mechanical wave that propagate through a medium, typically air but also other materials such as water or solids.
Characteristics of sound wavesFrequency: the frequency of a sound wave refers to the number of cycles or vibrations it completes per second and is measured in Hertz (Hz).
Amplitude: the amplitude of a sound wave refers to the maximum displacement or intensity of the wave from its equilibrium position. It represents the loudness or volume of the sound, with larger amplitudes corresponding to louder sounds and smaller amplitudes corresponding to softer sounds.
Wavelength: the wavelength of a sound wave is the distance between two consecutive points in the wave that are in phase, such as from one peak to the next or one trough to the next. It is inversely related to the frequency of the wave.
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the -----is a basic unit of work or energy
Answers
The joule is a basic unit of work or energy
Answer:
Joule
Explanation:
If you ever feel like you are not doing enough work or energy in your life, just remember that you are constantly producing joules. Every time you move a muscle, breathe, blink, or even think, you are using up some joules. And every time you plug in your phone, laptop, or toaster, you are transferring some joules. Joules are everywhere, and they are awesome.
But how awesome are they? Well, let's put them in perspective. One joule is enough to lift an apple one meter off the ground. That may not sound impressive, but what if you had a million joules? Then you could lift a car one meter off the ground. Or what if you had a billion joules? Then you could launch a rocket into space. Or what if you had a trillion joules? Then you could... well, I don't know what you could do with that much energy, but it would be something amazing.
So, the next time you feel low on energy, just think of all the joules you have at your disposal. You are a powerhouse of work and energy, and you can do anything you set your mind to. Just don't forget to measure it in joules.
A motorcycle stoop is at a traffic light, when the light turns green, the motorcycle accelerates to a speed of 78 km/h over a distance of 50 m. What is the average acceleration of the motorcycle over this distance?
Answers
The average acceleration of the motorcycle over the given distance is approximately 9.39 m/s².
To calculate the average acceleration of the motorcycle, we can use the formula:
Average acceleration = (final velocity - initial velocity) / time
First, let's convert the final velocity from km/h to m/s since the distance is given in meters. We know that 1 km/h is equal to 0.2778 m/s.
Converting the final velocity:
Final velocity = 78 km/h * 0.2778 m/s = 21.67 m/s
Since the motorcycle starts from rest (initial velocity is zero), the formula becomes:
Average acceleration = (21.67 m/s - 0 m/s) / time
To find the time taken to reach this velocity, we need to use the formula for average speed:
Average speed = total distance/time
Rearranging the formula:
time = total distance / average speed
Plugging in the values:
time = 50 m / 21.67 m/s ≈ 2.31 seconds
Now we can calculate the average acceleration:
Average acceleration = (21.67 m/s - 0 m/s) / 2.31 s ≈ 9.39 m/s²
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Internal energy is affected by two properties of the particles which make up a substance. Identify the two properties. A. Motion and position B. Acceleration and mass C. Specific heat capacity and volume D. State of matter and potential energy
Answers
The two properties of particles which make up a substance that affect its internal energy are:
A. Motion and position
The internal energy of a substance depends on the kinetic energy (motion) and potential energy (position) of its constituent particles. The kinetic energy of the particles determines the temperature of the substance, while the potential energy depends on the intermolecular forces between the particles.
Therefore, option A is the correct answer.
Hans figures out one math problem easily and then applies that solution to the rest of the problems on the page; however, he gets the rest of the answers wrong. Hans has encountered a common problem with:
Answers
Answer:
Explanation:
overgeneralization or applying a single solution to a variety of problems without considering their unique characteristics. This is a common issue in math and other problem-solving situations where individuals may rely too heavily on past successful solutions without adjusting for the specific details of each new problem.
A 340 kg piano slides 2.8 m down a 27∘ incline and is kept from accelerating by a man who is pushing back on it parallel to the incline
Part A: Determine the force exerted by the man.
Express your answer to two significant figures and include the appropriate units.
Part B: Determine the work done on the piano by the man.
Express your answer to two significant figures and include the appropriate units.
Part C: Determine the work done on the piano by the force of gravity.
Express your answer to two significant figures and include the appropriate units.
Answers
The force exerted by the man is 1500 N
The work done is given as - 4200 J
The work done on the piano by gravity is 4200 J
How to solve for the work doneThe force exerted by the man
= mgsinθ
= 340 * 9.8 * sin 27
= 1512.7 N
= 1500 N in two significant figures
b. The work done is given as - Fs
= - 1512.7 N * 2.8 m
= - 4235.56
= - 4200 J in two significant figures
c. The work done on the piano by gravity
Wg = -W
= 4200 J
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how often the earth magnetism change
Answers
Why is it advised not to hold the thermometer by its bulb while reading it?
Answers
Describe and explain motion due to uniform velocity in one direction and uniform acceleration in a perpendicular direction
Answers
Answer: you have to divide and multiple fam
Explanation:
Scientists seek to acquire knowledge and understanding of the real world through the formulation, testing, and evaluation of what?
A. technology
B. scientific method
C. scientific hypothesis
D. deductive reasoning
Answers
Scientists seek to acquire knowledge and understanding of the real world through the formulation, testing, and evaluation of scientific hypotheses (Option C).
What are scientific hypotheses?Scientific hypotheses are explanations about questions of the real world that can be used to test them by using the scientific method, i.e., by testing them to confirm or reject their assumptions through experimental and observation procedures.
Therefore, with this data, we can see that a scientific hypothesis is formulated and tested by using the scientific method in order to confirm or reject its assumptions and thus build scientific knowledge.
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Answer:
Scientific hypothesis
Explanation:
With what minimum speed must athlete leave the ground in order to lift his center of mass 2.00 m and cross the bar with a speed of 0.95 m/s
Answers
The athlete must leave the ground with a speed of 6.33m/s.
Kinect and potential energyTo calculate the initial speed, with the information of height and final speed, we can use the following expression that uses the kinetic energy and potential energy:
\(mgh_1 + \frac{1}{2}mv_1^{2}= mgh_2 + \frac{1}{2}mv_2^{2}\)
Applying the values given by the statement we have:
\(9.81\times 0 + \frac{1}{2}v_1^{2} = 9.81 \times 2 + \frac{1}{2}(0.95)^{2}\)
\(v_1 = 6.33m/s\)
So, the athlete must leave the ground with a speed of 6.33m/s.
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No no no no. no no no no
Answers
a box of mass 8.0 kg rests on a horizontal rough surface. a string attached to the box passes over a smooth pulley and supports a 2.0 kg mass at its other end, when the box is released, a frictional force of 6.0 n acts on it. (a) draw free-body diagrams of the 8.0 kg box and the 2.0 kg mass. (b) determine the (i) acceleration of the system, (in) tension in the string.
Answers
a. The free-body diagrams of the 8.0 kg box and the 2.0 kg mass is attached below.
bi) the acceleration of the system is 0.4 m/s^2
bii) the tension in the string is 0.8 N.
How do we calculate?Net force = ma
Net force = T - F_friction
where T is the tension force and F_friction is the frictional force.
Substituting the given values, we have:
T - F_friction = ma
T - 6.0 N = (8.0 kg + 2.0 kg) a (since the tension force acts on both masses)
T - 6.0 N = 10.0 kg a
(ii) To find the tension in the string, we can apply Newton's second law of motion to the 2.0 kg mass:
Net force = ma
where m is the mass of the mass and a is the acceleration of the system. The net force on the mass is the tension force:
Net force = T
Substituting the given values, we get:
T = ma
T = 2.0 kg x a
To solve for T, we need to find the acceleration of the system.
To find both a and T, we can use the equations we derived above and solve them simultaneously:
T - 6.0 N = 10.0 kg a (equation 1)
T = 2.0 kg x a (equation 2)
Substituting equation 2 into equation 1, we get:
2.0 kg x a - 6.0 N = 10.0 kg a
Solving for a, we get:
a = 0.4 m/s^2
Substituting a into equation 2, we get:
T = 2.0 kg x 0.4 m/s^2 = 0.8 N
Therefore, the acceleration of the system is 0.4 m/s^2 and the tension in the string is 0.8 N. of the system is 0.4 m/s^2 and the tension in the string is 0.8 N.
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When an element ejects an alpha particle, the mass number of that element
A.reduce by 4.
B.remains unchanged.
C.increase by 1.
D. reduce by 1.
Answers
Answer:
A.reduce by 4.
Explanation:
In Chemistry, an alpha particle which is typically a helium nucleus has an atomic mass (number of nucleons) of four (4). Therefore, the ejection of an alpha particle by any chemical element simply means that, the mass number of that particular chemical element would be reduced by four (4).
Basically, this process is referred to as an alpha decay and can be defined as a radioactive disintegration of a chemical element that causes it to emit an alpha particle and as a result reducing its mass number by four (4).
Hence, when an element ejects an alpha particle, the mass number of that element reduces by 4.
A body of mass 1 kg is pushed at a constant speed against a vertically placed wall, with a constant force F, which forms an angle of 45 degrees with the horizontal, as in the picture. The sliding friction coefficient is 0.2. What is the intensity of the force F? For the acceleration of the heavier force, take g=10 m/s2.
Answers
The intensity of the force F is calculated to be approximately 2.83 N.
What is sliding friction coefficient?Coefficient of sliding friction is a value that measures force of sliding friction for particular surface type.
Weight = mg = 1 kg x 10 m/s² = 10 N (acting downwards)
F_vertical - Weight = 0
F_vertical = 10 N
As Frictional force = coefficient of friction x normal force
Frictional force = 0.2 x 10 N = 2 N (acting to the left)
F_horizontal = F x cos(45) = F / √2
F_horizontal - frictional force = 0
F_horizontal = frictional force = 2 N
F / √2 = 2 N
F = 2 N x √2
F ≈ 2.83 N
Therefore, the intensity of the force F is approximately 2.83 N.
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***ECONOMICS***
A government that wants to increase its GDP would most likely take which
action?
A. Increase the money supply to make it easier to borrow money
Ο Ο
B. Decrease the money supply to slow the growth of inflation
C. Increase taxes on businesses that operate outside the country
O O
D. Decrease taxes on citizens who are poor or unemployed
Answers
Answer:
The correct answer is A. A government that wants to increase its GDP would most likely increase the money supply to make it easier to borrow money.
Explanation:
If the government wanted to increase its GDP, the most appropriate way to do so would be to increase the money supply both through issuance and through a reduction in bank reserve requirements, thereby increasing the circulating money in the hands of society.
This, in turn, would make citizens reinvest that money, increasing economic production and, therefore, the national GDP.
Answer: A. Increase the money supply to make it easier to borrow money
Explanation: I just took the test on Ap ex
ANSWER THIS! Which of these statements about the Sun is the result of its closeness to Earth? A) It is the only star with a gravitational pull. B) It is the largest star in the Milky Way Galaxy. C) It appears (from Earth) to be the brightest star. D) It has the lowest temperature of any star seen from Earth.
Answers
Answer:
C) It appears (from Earth) to be the brightest star.
Explanation:
This is because due to sun's brightness we can predict its distance.
What is the maximum speed your car can go around a flat 300m radius turn. Assume a coefficient of static friction of 0.9.
Answers
Answer:
vmax = 51.4 m/s
Explanation:
If the turn is flat, this means that the car is not accelerated in the vertical direction, so the normal force and the force of gravity are equal each other in magnitude, as follows:\(F_{n} = F_{g} = m*g (1)\)
At the same time there exists a single force that keeps the car turning, which is the centripetal force, aiming to the center of the turn.This force is not a different force, is just the net force acting on the car in the horizontal direction, which is the friction force.This friction reaches to a maximum value, when the friction force is equal to the static friction force.This force can be expressed as follows:\(F_{fs} = \mu_{s} *F_{n} = \mu_{s} * m*g (2)\)
This force must be equal to the maximum centripetal force, which can be written as follows:\(F_{c} = m*\frac{v^{2}}{r} (3)\)
Since the left sides of (2) and (3) are equal each other, right sides must be equal too:\(\mu_{s} * m*g = m*\frac{v^{2}}{r} (4)\)
Rearranging, and solving for v, we get the maximum speed that the car can go around the turn without sliding:\(v_{max} =\sqrt{\mu_{s} *g*r} =\sqrt{0.9*9.8m/s2*300m} = 51.4 m/s (5)\)
Given the following information, what is the magnitude of the sum of the three
vectors?
Vector A: [13, 8, 0]
Vector B: [13, 0, 8]
Vector C: [0, 1, 8]
Express your answer to two decimals
Answers
Answer:
31.84
Explanation:
To find the magnitude of the sum of the three vectors, first, we need to add the vectors component-wise. Then, we can find the magnitude of the resulting vector.
Add the vectors component-wise:
Vector A + Vector B + Vector C = [13+13+0, 8+0+1, 0+8+8] = [26, 9, 16]
Find the magnitude of the resulting vector:
The magnitude of a vector [x, y, z] is given by the formula:
magnitude = sqrt(x^2 + y^2 + z^2)
Plugging in the values from the resulting vector:
magnitude = sqrt(26^2 + 9^2 + 16^2)
magnitude = sqrt(676 + 81 + 256)
magnitude = sqrt(1013)
magnitude ≈ 31.84
The magnitude of the sum of the three vectors is approximately 31.84.
Hope this helps!