What is the max. speed with which q 1200 kg ear can round a turn of radius 90.0m in a flat road The coefficient of friction between fires and road is 0.6s? Is this result independout of the mass of the can?
Answers
The maximum speed of the car is 32,944 m/s, which is independent of the mass of the car, as long as the mass of the car remains constant and the coefficient of friction remains the same.
The maximum speed of a car with a mass of 1200 kg rounding a turn of radius 90 m in a flat road can be calculated using the following formula:
v = \(\sqrt{(r * a)\)
where v is the maximum speed, r is the radius of the turn, and a is the acceleration of the car.
First, we need to find the acceleration of the car:
a = \(v^2\) / r
a = (\(\sqrt{(r^2 * 90^2) * 230\)) / r
a = 26,000 m/\(s^2\)
Next, we can use the mass of the car to find the force acting on the car:
F = ma
F = 1200 kg * 26,000 m/\(s^2\)
= 3,120,000 N
Finally, we can use the formula for centripetal acceleration to find the maximum speed of the car:
\(a_c\) = \(v^2\) / r
\(a_c\) = (\(\sqrt{(r^2 * 90^2) * 230^2\)) / \(r^2\)
\(a_c\) = 1,810,200 m/\(s^2\)
So the maximum speed of the car is:
v = \(\sqrt{(r * a_c)\)
= \(\sqrt\\90^2 * 1,810,200 m/s^2)\)
= 32,944 m/s
Therefore, the maximum speed of the car is 32,944 m/s.
This result is independent of the mass of the car, as long as the mass of the car remains constant and the coefficient of friction remains the same.
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Related Questions
FILL IN THE BLANK. A medium is able to transport a wave from one location to another because the particles of the medium are ____.
a. frictionless
b. isolated from one another
c. able to interact
d. very light
Answers
A medium is able to transport a wave from one location to another because the particles of the medium are (c)able to interact.
When a wave travels through a medium, it causes the particles in the medium to vibrate, and these vibrations are then passed on to neighboring particles, thus allowing the wave to propagate. In a solid, the particles are tightly packed and can interact strongly, allowing waves to travel quickly.
In liquids and gases, the particles are more spread out, and interactions between them are weaker, so waves travel more slowly.
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A cross-country skier moves 36 meters eastward, then 44
meters westward, and finally 22 meters eastward.
For this motion, what is the distance moved?
Tap button at left to enter
Distance = 102
answer using our built-in
number pad.
What is the magnitude and direction of the
displacement?
Magnitude =
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answer using our built-in
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Dir'n =
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Answers
Answer:
a) 102 meters
b) 14 meters
c) The direction is eastward.
Explanation:
Distance is said to be the length between two points. It is a scalar quantity.
a) The distance moved = 36 + 44 + 22
= 102 meters
b) Displacement is the distance moved in a specified direction.
Representing the distance moved with specific direction as a directed number, 36 meters eastward = +36, 44 meters westward = -44, and 22 meters eastward = +22
/Displacement/ = +36 -44 +22
= +58-44
= 14
The magnitude of the displacement is 14 meters.
c) The direction is eastward.
So that the magnitude of displacement and his direction is 14 meters eastward.
a coal power plant consumes 100,000 kg of coal per hour and produces 500 mw of power. if the heat of combustion of coal is 30 mj/kg, what is the efficiency of the power plant?
Answers
The efficiency of the coal power plant is approximately 16.67%. To determine the efficiency of the coal power plant, we need to calculate the useful output energy and compare it to the input energy.
Given:
Coal consumption rate: 100,000 kg/hour
Power output: 500 MW (500,000,000 watts)
Heat of combustion of coal: 30 MJ/kg
First, let's calculate the input energy, which is the energy provided by the coal combustion:
Input energy = Coal consumption rate * Heat of combustion of coal
Since the coal consumption rate is given in kilograms per hour and the heat of combustion is given in megajoules per kilogram, we need to convert the units:
Coal consumption rate = 100,000 kg/hour
Heat of combustion of coal = 30 MJ/kg
Input energy = (100,000 kg/hour) * (30 MJ/kg)
Input energy = 3,000,000 MJ/hour
To calculate the efficiency of the power plant, we need to compare the useful output energy (power) to the input energy.
Efficiency = (Useful output energy / Input energy) * 100%
Since power is given in watts and energy is given in joules, we need to convert the units:
Power output = 500 MW = 500,000,000 watts
Now we can calculate the efficiency:
Efficiency = (Power output / Input energy) * 100%
Efficiency = (500,000,000 watts / 3,000,000,000 watts) * 100%
Efficiency = 16.67%
Therefore, the efficiency of the coal power plant is approximately 16.67%.
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What is the mass of a truck if it is accelerating at a rate of 7m/s2 and hits a car with a force of 6,500N?
Answers
Answer:
Given
Force of car (F) =6500N
acceleration (a) =7m/s2
R.tc maas=x
Form
F =ma (divid by m both sides)
m=F/a
m=6500N/7m/s2
m=928.6kg
mass =928.6kg
An object, experiencing no friction, keeps moving at a constant speed. What can we say about the net force on the object?
a) the net force keeping the object going is the same as the force that would be required to stop it
b)the net force is in the same direction as the object's velocity
c)the object is not changing its speed but its velocity might be changing in Direction so if there is a net force it is that right angles to the velocity
d)since the object has no acceleration there is no net force
e)the net force is equal to the weight of the object
Answers
Answer:
Explanation:
Let's look at a mathematical representation of this. The equation for tis is just a souped up version of Newton's 2nd Law:
F - f = ma. It an object is moving at a constant speed, the acceleration of that object is 0. That changes this equation to
F = f which states that the applied Force equals the frictional force, choice a.
stars with more than 15 times the mass of our sun usually evolve from the main sequence to red giants
Answers
Stars with a mass greater than 15 times that of the sun typically transition directly from the hr diagram to the red giant stage while maintaining a nearly constant luminosity.
Constant means what?A quantity that is supposed not to shift value in a particular mathematical debate is one that has a specific amount in a specific context, is true globally, or is a feature of some material or instrument.
What symbol represents a constant?A digit (0–9) or a period serves as the initial of a constant sign. A constant symbol's value cannot be altered. It is merely the string made up of the symbol's characters, all lowercase alphabetic characters having been converted to uppercase.
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A topic that most underlies electrical studies and all of physics is
A) Newton's laws of motion.
B) the conservation of momentum.
Answers
The topic that most underlie electrical studies and all of physics is the conservation of momentum.
The conservation of momentum, often attributed to Newton's laws of motion, is a fundamental concept in physics. It states that the total momentum of an isolated system remains constant if no external forces act upon it. Momentum is the product of an object's mass and velocity, and it is a vector quantity, meaning it has both magnitude and direction. This principle holds true for all types of motion, including both linear and rotational motion.
In the context of electrical studies, the conservation of momentum is especially relevant. It is closely related to the principle of conservation of energy, as momentum conservation is often associated with the conservation of kinetic energy. In electrical systems, momentum considerations are crucial for understanding phenomena such as the motion of charged particles in electric and magnetic fields, the interaction between electrons and photons in quantum mechanics, and the behavior of electromagnetic waves. Furthermore, the conservation of momentum plays a significant role in fields such as mechanics, astrophysics, thermodynamics, and quantum mechanics, providing a unified framework to analyze and predict the behavior of physical systems. Overall, the conservation of momentum is a cornerstone concept that underlies the study of electricity and all branches of physics, offering insights into the fundamental nature of the universe.
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2. Does the emphasis on safety vary for each style of vehicle? In what way?
3. Does the level of safety equipment vary with price of vehicle?
4. What effects will a vehicle’s top speed, power and acceleration likely to have on safety? Is this considered in the advertisements?
WILL MARK BRAINLIEST IF CORRECT
Answers
Answer:
Emphasis on public safety can surely reduce the risk for various groups of population
1. Proper education and training must be provided to make them aware of the risks and how they can manage those risks.
2. Proper rules and regulation must be made and strictly followed for example traffic rules so as to avoid accidents.
3. Disaster management teams should to formed to ensure minimal loss of humans and resources during any natural calamity.
4.Eradication of poverty and illiteracy should be priority so as to ensure people focus on more important issues in life rather than involve themselves in trivial things.
Explanation:
_____ is an example of a cognitive emotional regulation strategy.
Repetitive rubbing of a special object such as a blanket
Having a temper tantrum
Downplaying the importance of the situation
Averting one's attention to a nondistressing object
Answers
Downplaying the importance of the situation is an example of cognitive emotional regulation strategy.
What is Cognitive emotional regulation?Cognitive emotional regulation strategies are the techniques that people use to manage their emotions by changing the way they think about a certain situation. Downplaying the importance of the situation involves reducing the perceived significance or impact of an event which can help to reduce the intensity of the emotional response.
Repetitive rubbing of a special object such as blanket and averting one's attention to a nondistressing object are the examples of sensory emotional regulation strategies, which involves using sensory experiences to manage emotions.
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The United States has a_____ economy
A command
B. pure market
C. mixed market
D. central planned
Please select the best answer from the choices provided
Answers
Answer:
C
Explanation:
The United States has a mixed economy it works according to economic system that features characteristics in both capitalism and socialism it makes economy system protects some private properties and allows a level of economic freedom in the use of capital
Answer:
C. is Levi's fav letter
Explanation:
i thought that ray was ugly but NAH
In a tug of war, when one team is pulling with a force of 200 N and the other 80N,
what is the net force
Answers
Answer:That depends on whether both people are pulling in the same direction against a fixed object or pulling against each other. If pulling in the same direction, the total force is 300 N + 300 N = 600 N. If the two people are pulling against each other, the total force is 300 N in the rope is 300 N, or a net of zero.
Explanation:.
When two systems in contact are not at the same temperature, _____ occurs.expansionheat flowfrictionevaporation
Answers
The answer is heat flow.
When two systems in contact are not at the same temperature, heat flow occurs.
What is heat flow?
Heat flow is the transfer of energy (heat) from the Earth's interior to its surface. The Earth's core cooling and radioactive heat creation in the upper 20 to 40 km of the crust are the main sources of heat on the planet.Heat flow occurs when a hot item transfers its heat through a conductor to a cold object, similar to how high-energy objects impart their energy to low-energy objects. How well a conductor transfers heat will impact how quickly and how much heat is transported.To learn more about heat flow visit:
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Answer:
heat flowExplanation:
When two systems in contact are not at the same temperature, Heat flow occurs.
more info:-
When two objects having different temperature are brought together, energy will always be transferred from the hotter (the object at higher temperature) to the cooler (the object at lower temperature). The objects will exchange thermal energy, until thermal equilibrium is reached, i.e. until their temperatures are equal.it can be explained by zeroth law of thermodynamics.Find the magnitude and direction of the net gravitational force on mass A due to masses B and
C in the figure. Each mass is 2 kg.
a. 2.8x10^-8N, to the right
b. 2.54x10^-8N, to the right
c. 3.4x10^-8N, to the left
d. 3.4x10^-8N, to the right
Answers
Answer is A 2.8 x 10^-8 N, to the right
The net gravitational force on mass A due to masses B and C is required.
The correct option is a. \(2.8\times 10^{-8}\ \text{N}\) to the right.
G = Gravitational constant = \(6.674\times 10^{-11}\ \text{Nm}^2/\text{kg}^2\)
\(r_{AB}\) = Distance between A and B = 0.4+0.1 = 0.5 m
\(r_{AC}\) = Distance between A and C = 0.1 m
\(m_A=m_B=m_c\) = Mass of each particle = 2 kg
The required force is
\(F_A=F_{AB}+F_{AC}\\ =\dfrac{Gm_Am_B}{r_{AB}^2}+\dfrac{Gm_Am_C}{r_{AC}^2}\\ =Gm^2\left(\dfrac{1}{r_{AB}^2}+\dfrac{1}{r_{AC}^2}\right)\\ =6.674\times 10^{-11}\times 2^2\left(\dfrac{1}{0.5^2}+\dfrac{1}{0.1^2}\right)\\ =2.8\times 10^{-8}\ \text{N}\)
The magnitude of force will be \(2.8\times 10^{-8}\ \text{N}\)
The direction will be towards the right since C is closer to A.
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Consider a solid insulating sphere of radius b with nonuniform charge density rho = a r, where a is a constant. b r dr O b Find the charge contained within the radius r < b as in the figure. The volume element dV for a spherical shell of radius r and thickness dr is equal to 4 π r2 dr.If a = 1 × 10−6 C/m4 and b = 1 m, find E at r = 0.6 m. The permittivity of a vacuum is 8.8542 × 10−12 C 2 /N · m2 . Answer in units of N/C. Find the charge Qb contained within the radius r, when r > b.
Answers
The electric field at r = 0.6 m is 6.67 × 10⁴ N/C. Consider a solid insulating sphere of radius b with non-uniform charge density rho = a r, where a is a constant. The volume element dV for a spherical shell of radius r and thickness dr is equal to 4 π r2 dr.
Explanation: We are asked to find the charge contained within the radius r < b. The charge Q contained inside the sphere can be found using the following expression:
\(Q = ∫ρ dV\), where, ρ = a r and dV = 4 π r2 dr
Hence,
\(Q = ∫a r (4 π r2 dr)\)
The limits of integration are 0 to r.
Hence, the expression becomes,
Q = ∫0r a r (4 π r2 dr)
= 4 π a ∫0r r3
dr= π a r4
The charge Qb contained within the radius r > b is given by,
Qb = ∫ρ dV
where, ρ = a r and dV = 4 π r2 dr
Hence,\(Qb = ∫a r (4 π r2 dr)\)
The limits of integration are b to r.
Hence, the expression becomes, \(Qb = ∫b ra r (4 π r2 dr)\)
= 4 π a ∫b r r3 dr= π a [(r4 - b4)]
The value of a = 1 × 10⁻⁶ C/m⁴, b = 1 m and r = 0.6 m.
Substituting these values, we get,
\(Q = π a r4\)
= π x 1 x 10⁻⁶ x (0.6)⁴
= 5.030 × 10⁻⁴ C
And, r/b = 0.6/1
= 0.6
Therefore, the electric field at r = 0.6 m is given by,
\(E = (1/(4πε₀)) (Q/r²)\)
where,
ε₀ = 8.8542 × 10⁻¹² C²/N · m²
Substituting the values, we get,
\(E = (1/(4πε₀)) (Q/r²)\)
= (1/(4π x 8.8542 × 10⁻¹²)) (5.030 × 10⁻⁴/0.6²)
= 6.67 × 10⁴ N/C (approx).
Hence, the electric field at r = 0.6 m is 6.67 × 10⁴ N/C.
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A bus traveling at a speed of 50 km/h has a momentum of 180,345
kg.m/s. What is the mass of the bus?
Answers
The mass of the truck is 12,974.4kg .
Describe bulk in plain terms.As a measure of inertia, which is a fundamental characteristic of all matter, mass is used in physics. Effectively, it is the resistance a body of matter offers to a change in its speed or position as a result of the application of a force.
An object's mass is what?Measures a substance's resistance to acceleration in physics. A measure of an object's mass is roughly equivalent to counting the atoms that make up the object. The kilogram serves as the fundamental mass unit. Mass multiplied by the gravitational acceleration equals weight.
50km/h =50×5/18 m/s= 13.88 = 13.9
momentum (p)=180,345 kg.m/s
P=mv
180,345= m X 13.9
m = 180345/13.9
m = 12,974.46
m = 12,974.4
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A small truck and a large truck have the same kinetic energies. Which truck has the greater momentum? Justify your answer
Answers
A wave has a frequency of 17.6 Hz and a distance from crest to crest of 4.1 m. What is the speed of the wave
Answers
Answer:
12.m
Explanation:
what are insulators of electricity
Answers
Answer:
Rubber
Glass
Pure water
Oil
Air
Diamond
Dry wood
Dry cotton
Plastic
Asphalt
Other strong insulators include:
Fiberglass
Dry paper
Porcelain
Ceramics
Quartz
Explanation:
I hope this helps
How can you make the work output of machine greater than the work input
Answers
Answer:
The only way to increase the work output is to increase the work input. You can't get more work out of a machine than you put into it. The moving parts of a machine must use some of the work input to overcome friction. Because of friction, the work output of a machine is always less than the work input.
Explanation:
Which example illustrates Newton's first law? O A. The force of a wheelbarrow on the ground is equal to the force of the ground on the wheelbarrow. B. More mass is added to a wheelbarrow, and a larger force is required to move it. C. A person pushes a wheelbarrow, causing it to move forward. D. The force of a wheelbarrow on the ground is in the opposite direction of the force of the ground on the wheelbarrow.
Answers
A person pushing a wheelbarrow, causing it to move forward, is the example that illustrates Newton's first law. The correct option is C.
What is force?Force is defined as the push or pull applied to the body. Sometimes it is used to change the shape, size, and direction of the body.
According to Newton's first law, a body tries to maintain its motion until or unless the external force is not applied to it.
If a body is at rest, try to rest if the body is in motion, try to be in motion until or unless an external force is not applied to it.
The wheelbarrow being propelled forward by a human is an illustration of Newton's first law.
Hence, the correct option is C.
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3. A class took a field trip to a music studio. The students watched through thick glass as the musicians played
music inside the studio. The students could only hear the music when the studio door was open. The less
separating the musicians from the students is made with two layers of thick glass. The space between the glass
Layers has had all the air removed, creating a vacuum.
Which statement best explains why the students were able to see the musicians even while they were unable to
hear them?
Answers
Answer:
Sound can't travel in a vaccum.
Explanation:
Sound waves need a medium in order to travel (e.g. air, water, glass)
Since there was a vaccum between the glass the sound couldn't travel since vaccum's contain a very small amount of atoms.
Steam flows through a nozzle at mass flow rate of
m =0.1 kg/s with a heat loss of 5 kW. The enthalpies at inlet and exit are 2500 kJ/kg and 2350 kJ/kg, respectively. Assuming negligible velocity at inlet (C 1 ≈0), the velocity (C2 ) of steam (in m/s) at the nozzle exit is (correct to two decimal places)
Answers
If negligible velocity at inlet (C 1 ≈0), the velocity (C2) of steam (in m/s) at the nozzle exit is 447.21 m/s.
According to question:
The steady flow energy equation for steady flow devices
m (h1 + ((c1)2/2) + z1g) + Q = m (h2 + ((c2)2/2) + z2g) + Wcv
C1 = 0
Wcv = 0
z1 = z2
mh1 + Q = mh2 + m((C2)2/2)
m((C2)2/2) = m(h1-h2) + Q
0.1 × ((C2)2/2) × 10-3 = 0.1(2500-2350) -5
C2 = 447.21 m/s
Thus, the negligible velocity at inlet (C 1 ≈0), the velocity (C2) of steam (in m/s) at the nozzle exit is 447.21 m/s.
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PLEASE HELP ME
A boulder is raised above the ground so that the gravitational potential energy relative to the ground is 310 J. Then it is dropped. What is its kinetic energy just before it hits the ground?
Answers
Answer:
try this
Explanation:
The energy of a falling object when it hits the ground is equaled to the energy it starts with because the potential energy is converted into kinetic energy entirely with the height at 0. This means the energy would be 200 J.
RESULT
A sound wave enters a new medium where sound travels faster. How does this affect the frequency and wavelength of the sound?
OA. The frequency Increases and the wavelength decreases.
OB. The frequency decreases and the wavelength increases.
OC. The frequency stays the same and the wavelength increases.
OD. The frequency stays the same and the wavelength decreases.
ОЕ. Neither the frequency nor the wavelength is affected.
Answers
The frequency stays the same and the wavelength increases.
Explanation;
Sound waves are a type of mechanical wave which requires a material medium for transmission. The transmission of such waves occurs as a result of vibration of particles in the material medium. The faster the vibration of the particles the higher the speed of the sound waves.
When a sound enters a new medium where the sound travels faster, it means the vibration of particles is high, and the wavelength of the waves increases which means the speed of the wave has increased. The frequency on the other hand will remain constant.
Answer:
A. The frequency stays the same and the wavelength decreases
Explanation:(Plato)
which scan examines the current security, in a passive method?
Answers
The scan that examines the current security in a passive method is called a Vulnerability Assessment (VA) scan.
A Vulnerability Assessment scan is a process of identifying and assessing vulnerabilities within a system, network, or application. It is typically performed using automated tools that scan the target environment for known vulnerabilities, configuration weaknesses, and security holes. Unlike active scanning techniques that actively probe the system and may generate network traffic, a VA scan operates in a passive manner, observing the system without actively interacting with it.
During a Vulnerability Assessment scan, the automated tool examines the target environment by analyzing network traffic, configurations, system logs, and other sources of information to identify potential vulnerabilities. It compares the collected data against a database of known vulnerabilities and security weaknesses to determine if any matches exist.
The passive nature of a VA scan makes it non-intrusive, as it does not generate additional traffic or perform active actions that could potentially impact the system's performance or stability. It allows organizations to assess their current security posture, identify vulnerabilities, and prioritize remediation efforts without disrupting the normal operation of the environment.
The results of a Vulnerability Assessment scan provide insights into the security weaknesses present in the system, enabling organizations to take appropriate measures to address and mitigate those vulnerabilities. This may include applying security patches, reconfiguring systems, updating software versions, or implementing additional security controls to protect against potential threats.
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an 1100-kg car traveling at 27.0 m/s starts to slow down and comes to a complete stop in 578 m. what is the magnitude of the average braking force acting on the car? [hint: first find the acceleration of the car] group of answer choices 297 n 553 n 412 n 341 n 694 n
Answers
A 1100 kg automobile moving at 27.0 m/s begins to slack down and stops entirely at 578 m. The car is subjected to an average braking force of 694 N.
What happens when the brakes are applied forcefully?The friction between the brakes and the wheel produces work when a force is applied to a vehicle's brakes. The vehicle's kinetic energy is decreased, which slows it down and raises the temperature of the brakes.
How do brakes function?The friction between the brakes and the wheel produces work when a force is applied to a vehicle's brakes. Therefore, the amount of braking power required to stop a vehicle over a given distance increases as the speed of the vehicle increases.
Briefing:t = Time taken
u = Initial velocity = 27 m/s
v = Final velocity
s = Displacement = 578 m
a = Acceleration
m = Mass
Equation of motion:
\(v^{2} - u^{2} = 2as\)
⇒\(a = \frac{v^{2} - u^{2} }{2s}\)
⇒\(a = -0.63062 m/s^{2}\)
Force, F = ma
F = 1100 x -0.63062
F= - 693. 6851 N
Magnitude of force = 694 N
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a traveler first drives 21.0 km east, then 28.8 km southeast, and finally 10 km south. what is the magnitude
Answers
The magnitude of the traveler's displacement is approximately 39.5 km.
To find the magnitude of the traveler's displacement, we can combine the individual displacements in a vector sum.
The first leg of the journey is a displacement of 21.0 km east. We can represent this as a vector in the positive x-direction: (21.0 km, 0 km).
The second leg of the journey is a displacement of 28.8 km southeast. We can break down this displacement into its x and y components. The southeast direction is a combination of east and south. The angle between the southeast direction and the positive x-axis is 45 degrees. Using trigonometry, we can find the x and y components:
x-component = 28.8 km * cos(45°) = 20.4 km
y-component = 28.8 km * sin(45°) = 20.4 km
So, the second displacement can be represented as a vector: (20.4 km, -20.4 km).
The third and final leg of the journey is a displacement of 10 km south. We can represent this as a vector in the negative y-direction: (0 km, -10 km).
To find the total displacement, we add the individual displacements:
(21.0 km, 0 km) + (20.4 km, -20.4 km) + (0 km, -10 km) = (41.4 km, -30.4 km)
The magnitude of the displacement is given by the Pythagorean theorem:
Magnitude = √((41.4 km)² + (-30.4 km)²) ≈ 39.5 km
Therefore, the magnitude of the traveler's displacement is approximately 39.5 km.
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When do sea breezes occur
Answers
what force does the floor of the elevator exert on a 52-kg passenger?
Answers
The force that the floor of the elevator exerts on the 52-kg passenger in this case is approximately 510 N upward.
To determine the force that the floor of the elevator exerts on a 52-kg passenger, you'll need to consider the forces acting on the passenger and the elevator's motion. If the elevator is moving at a constant speed or is stationary, the net force acting on the passenger is zero, meaning the forces balance each other out.
In this scenario, the force of gravity pulls the passenger downward, which can be calculated using the equation F_gravity = m * g, where m is the mass (52 kg) and g is the acceleration due to gravity (approximately 9.81 m/s²).
F_gravity = 52 kg * 9.81 m/s² ≈ 510 N (rounded to the nearest whole number)
The floor of the elevator must exert an equal and opposite force, called the normal force, to counteract the force of gravity. Therefore, the force that the floor of the elevator exerts on the 52-kg passenger in this case is approximately 510 N upward. Note that if the elevator is accelerating, the normal force would be different and can be calculated using Newton's second law, F = m * a, where a is the acceleration of the elevator.
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Derive an equation for the acceleration of block 3 for any arbitrary values of m3 and m2. Express your answer in terms of m3, m2, and physical constants as appropriate.
Answers
Complete question is;
Block 1 is resting on the floor with block 2 at rest on top of it. Block 3, at rest on a smooth table with negligible friction, is attached to block 2 by a string that passes over a pulley, as shown in the attachment below. The string and pulley have negligible mass.
Block 1 is removed without disturbing block 2.
Derive an equation for the acceleration of block 3 for any arbitrary values of m3 and m2. Express your answer in terms of m3, m2, and physical constants as appropriate.
Answer:
a = (m2)g/(m3 + m2)
Explanation:
Looking at the attached image, if we consider the free body diagram for block 3, by using Newton's first law of motion, we will arrive at the formula;
T = (m3)a - - - (eq 1)
where;
T is the tension in the string
a is acceleration
m3 is mass of block 3
Meanwhile doing the same with Block 2, the free body diagram would give us the formula; (m2)g - T = (m2)a
Making T the subject gives us;
T = (m2)g - (m2)a - - - (eq 2)
where;
g is acceleration due to gravity
T is the tension in the string
a is acceleration
m2 is mass of block 2
To solve for the acceleration, we will just substitute (m3)a for T in eq 2.
Thus;
(m3)a = (m2)g - (m2)a
(m3)a + (m2)a = (m2)g
a(m3 + m2) = (m2)g
a = (m2)g/(m3 + m2)
