The acceleration of mass m2 to the right is 3.125 m/s².
Let's denote the compression of the spring by x, the acceleration of m1 by a1 to the left, and the acceleration of m2 by a2 to the right.
According to Newton's second law, the force exerted on an object is equal to its mass times its acceleration:
F = ma. In this case, the forces acting on the two masses are the force of the compressed spring and the force of friction between the masses.
For mass m1, the net force is given by:
F1 = -kx - f
where k is the spring constant, x is the compression of the spring, and f is the force of friction. The negative sign in front of kx indicates that the force of the spring is acting to the left. Using Newton's second law, we have:
m1a1 = -kx - f
For mass m2, the net force is given by:
F2 = kx - f
where the force of the spring is now acting to the right. Using Newton's second law, we have:
m2a2 = kx - f
We want to find the acceleration of mass m2, which is given by a2. To do this, we need to eliminate the force of friction f from the above two equations.
To eliminate f, we can add the two equations:
m1a1 + m2a2 = -kx + kx - 2f
Simplifying and substituting the given values, we get:
(2.5 kg)(2.0 m/s²) + (1.6 kg)a2 = 0
Solving for a2, we get:
a2 = -(2.5 kg)(2.0 m/s²)/(1.6 kg) = -3.125 m/s²
Therefore, the acceleration of mass m2 to the right is 3.125 m/s².
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PLS HELP ASAP!!!
Examine two items that use more than one battery, such as a flashlight, a 2-way radio, or a battery operated toy. Look at the arrangement of the batteries in the item. Are they connected in series? For each item, state the number and type of batteries, the voltage of each battery and the total voltage
produced.
Flashlight: The flashlight typically uses multiple batteries, arranged in series to provide a higher voltage output.
What is the battery about?In continuation, The number and type of batteries used in a flashlight can vary depending on the model, but a common arrangement is to use two or three 1.5V AA batteries. The batteries are connected in series, with the positive end of one battery connected to the negative end of the next battery, and so on.
For example, if the flashlight uses three 1.5V AA batteries, the total voltage produced would be 4.5V (1.5V x 3).Secondly, 2-way radio:
A 2-way radio also typically uses multiple batteries, arranged in series to provide a higher voltage output. Again, the number and type of batteries used can vary depending on the model, but a common arrangement is to use four or six 1.5V AA batteries. The batteries are connected in series, with the positive end of one battery connected to the negative end of the next battery, and so on.
For example, if the 2-way radio uses six 1.5V AA batteries, the total voltage produced would be 9V (1.5V x 6).Therefore, Note that the arrangement of batteries in series increases the total voltage produced by the batteries.
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(a) Find
A + B
graphically.
magnitude
m
direction
° counterclockwise from the +x axis
(b) Find
A − B
graphically.
magnitude
m
direction
° counterclockwise from the +x axis
(c) Find
B − A
graphically.
magnitude
m
direction
° counterclockwise from the +x axis
(d) Find
A − 2B
graphically.
magnitude
m
direction
° counterclockwise from the +x axis
The displacement vector for a is given below:
a. tan^-1(6.0/3.7) = 58.34o counterclockwise from +X axisb. tan^-1 = 328.1o…….counterclockwise from +X axisc. tan^-1 = 148.1o…….counterclockwise from +X axisd. tan^-1 = 229.84o…….counterclockwise from +X axisHow to solveA=4.15m, θA=26.5o
Ax=AcosθA = 4.15cos26.5 = 3.7 m
Ay=AsinθA = 4.15sin26.5 = 1.85 m
B= 4.15m, θB =26.5o
Bx=BcosθB = 4.15cos90= 0.0 m
By=BsinθB = 4.15sin90= 4.15 m
a)
(A+B)x= Ax+ Bx= 3.7 – 0.0 = 3.7 m
(A+B)y = Ay+ By= 1.85 + 4.15 = 6.0 m
(A+B)=sqrt[(3.7)^2+(6.0)^2] = 7.05 m
Φ= tan^-1[((A+B)y)/( (A+B)x)] = tan^-1(6.0/3.7) = 58.34o…….counterclockwise from +X axis
b)
(A-B)x= Ax- Bx= 3.7 – 0.0 = 3.7 m
(A-B)y = Ay- By= 1.85 - 4.15 = -2.3 m
(A-B)=sqrt[(3.7)^2+(2.3)^2] = 4.36 m
Φ= tan^-1[((A-B)y)/( (A-B)x)] = tan^-1(-2.3/3.7) = -31.9o = 360-31.9 = 328.1o…….counterclockwise from +X axis
c)
(B-A)x= Bx- Ax= 0.0-3.7 = -3.7 m
(B-A)y = By- Ay= 4.15-1.85 = 2.3 m
(B-A)=sqrt[(-3.7)^2+(-2.3)^2] = 4.36 m
Φ= tan^-1[((B-A)y)/( (B-A)x)] = tan^-1(2.3/-3.7) = -31.9o = 180-31.9 = 148.1o…….counterclockwise from +X axis
d)
(A-2B)x= Ax- 2Bx= 3.7 – 2*0.0 = 3.7 m
(A-2B)y = Ay- 2By= 1.85 – 2*4.15 = -6.45 m
(A-2B)=sqrt[(3.7)^2+(-6.45)^2] = 7.44 m
Φ= tan^-1[((A-2B)y)/( (A-2B)x)] = tan^-1(-6.45/3.7) = -60.16o = = 360-60.16 = 229.84o…….counterclockwise from +X axis
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Im kinda lost in this one
[tex]75 = 6 \times \frac{?}{?} \times \frac{?}{?} [/tex]
Science
help
anwer all
Answer:
True
False
True
True
True
Explanation:
Light is measured by its wavelength (in nanometers). It is usually characterized by the Greek symbol λ. Visible light is usually defined as having wavelengths in the range of 400–700 nanometers (nm) or one billionth of a meter.
Light travels faster in vacuum than any other medium. This is because there is no obstruction in vacuum for the propagation of light and thus, the refractive index of vacuum is the lowest.
Brightness is used to describe how bright somthing is
The shorter the wavelengths and higher the frequency corresponds with greater energy. So the longer the wavelengths and lower the frequency results in lower energy.
In order from highest to lowest energy, the sections of the EM spectrum are named: gamma rays, X-rays, ultraviolet radiation, visible light, infrared radiation, and radio waves.
Drag each label to the correct location on the image.
Match the government activities to the different fiscal policies.
government is spending
less than what it earns
budget indicates a surplus
budget indicates a deficit
government is spending
more than what it earns
Contractionary Fiscal Policy
government is spending more
on infrastructure development
Expansionary Fiscal Policy
Matching the government activities to the different fiscal policies.
Contractionary Fiscal Policy:
budget indicates a surplus
government is spending less than what it earns
Expansionary Fiscal Policy:
government is spending more on infrastructure development
budget indicates a deficit
government is spending more than what it earns
When the government is spending less than what it earns, it has a budget surplus. This indicates that the government is collecting more revenue than it is spending. This is an example of a contractionary fiscal policy because it reduces the amount of money circulating in the economy, which can help control inflation.
When the government is spending more than what it earns, it has a budget deficit. This indicates that the government is spending more money than it is collecting in revenue. This is an example of an expansionary fiscal policy because it injects more money into the economy, which can stimulate economic growth.
When the government is spending more on infrastructure development, it is an example of an expansionary fiscal policy because it increases government spending and stimulates economic growth.
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Set the charged object in motion by dragging it and releasing it. What do you observe about the behavior of the field lines in the vicinity of the object
When a charged object is at rest, the electric field lines emanating from it are radially symmetric and point outward in all directions, forming a pattern that depends on the magnitude and sign of the charge. If the charged object is set in motion, it creates a changing electric field that propagates outward from the object at the speed of light.
How is the direction of the magnetic field line depicted?The direction of magnetic field lines is depicted using arrows or lines that indicate the direction of the magnetic field at each point in space. The convention for drawing magnetic field lines is that they always form closed loops, and the direction of the field is tangential to the bar at each point.
Does the electric field affect the magnetic field?Yes, electric fields can affect magnetic fields and vice versa. Electric and magnetic fields are intimately related and form two sides of the same coin, as described by Maxwell's equation of electromagnetism.
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An ideal spring with a constant of 200 N/m is acted upon by a 600 N force directed in the positive direction, what is the magnitude and direction of the displacement?
The displacement has a 3 m magnitude and is moving in the opposite direction as the external force, which is pushing backwards.
How do you determine the spring's maximum stretch?With the provided information for the 4 kilogramme mass, we can get the spring constant. The displacement of a 1.5 kg mass is then determined using the formula x = F/k. The work needed to stretch a spring x distances from its equilibrium position is W = 12kx2.
We can use the following formula to determine the force a spring exerts:
F = -kx
The magnitude of the force exerted by the spring is:
F = -kx
-600 N = -200 N/m * x
Solving for x, we get:
x = 3 m
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State the first law of thermodynamics and apply this to the system/surrounding model.
Answer:
The first law of thermodynamics, also known as the law of conservation of energy, states that energy cannot be created or destroyed, only transferred or transformed from one form to another. In other words, the total energy of a closed system and its surroundings remains constant.
When applying this law to a system/surrounding model, the energy exchanged between the system and its surroundings can take different forms, such as heat, work, or a combination of both. For example, if a gas is compressed in a piston, work is done on the gas by the surroundings, increasing the internal energy of the gas. Alternatively, if a gas is heated, energy is transferred to the gas from the surroundings, increasing the internal energy of the gas.
Overall, the first law of thermodynamics serves as a fundamental principle in the study of thermodynamics, allowing us to analyze and predict energy transfers and transformations in various physical and chemical systems.
Explanation:
If the average kinetic energy of the molecules in an ideal gas initially at 36°C doubles, what is the final temperature of the gas?
Answer: 345.15°C
Explanation:
The average kinetic energy of the molecules in an ideal gas is proportional to its temperature in Kelvin scale. So, if the average kinetic energy doubles, then the temperature must also double.
The initial temperature of the gas is 36°C = 36 + 273.15 = 309.15 K.
Doubling the temperature, we get:
Final temperature = 2 × 309.15 K = 618.3 K
Converting back to Celsius scale, we get:
Final temperature = 618.3 - 273.15 = 345.15°C
Therefore, the final temperature of the gas is 345.15°C.
An amplifier operating from a ± 20 V power supply is fed with sinusoidal voltage having 1.5 V peak and delivers a sinusoidal output voltage of 18 V peak to a 100 Ω load. The amplifier draw a current of 0.1 A from each of its power supplies. The input current of the amplifier is in a sinusoidal form with 1 mA peak ,find voltage gain
Answer:
the voltage gain of the amplifier is approximately 416.9.
Explanation:
We can use the voltage gain formula of the amplifier to determine its voltage gain:
Voltage Gain = (Output Voltage Amplitude) / (Input Voltage Amplitude)
The output voltage amplitude is given as 18 V peak, and the input voltage amplitude is 1.5 V peak.
To calculate the input voltage in terms of RMS, we can use the formula:
Vrms = Vpeak / sqrt(2)
Therefore, the input voltage amplitude in RMS is:
Vrms = 1.5 Vpeak / sqrt(2) = 1.06 Vrms
The input current amplitude is given as 1 mA peak, and we can similarly calculate the input current amplitude in RMS:
Irms = 1 mA peak / sqrt(2) = 0.707 mA RMS
Now we can use the given information to determine the voltage gain of the amplifier:
Output Voltage Amplitude = 18 V peak
Input Voltage Amplitude = 1.06 Vrms
Input Current Amplitude = 0.707 mA RMS
The current drawn by the amplifier from each of its power supplies is 0.1 A, and since there are two power supplies, the total power consumed by the amplifier is:
P = (2 * 0.1 A) * (± 20 V) = 4 W
We can now use the power gain formula to determine the voltage gain of the amplifier:
Power Gain = (Output Power) / (Input Power)
The output power can be calculated as:
Pout = (Vout^2) / Rload = (18 V peak)^2 / 100 Ω = 3.24 W
The input power can be calculated as:
Pin = (Vrms^2 / Rin) + (Irms^2 * Rin)
where Rin is the input resistance of the amplifier.
Assuming the input impedance of the amplifier is much larger than 100 Ω, we can neglect the first term in the above equation, and we get:
Pin = (Irms^2 * Rin)
Solving for Rin, we get:
Rin = (Pin / Irms^2) = (4 W / (0.707 mA RMS)^2) = 80.4 kΩ
Now we can calculate the input power as:
Pin = (Vrms^2 / Rin) + (Irms^2 * Rin) = (1.06 Vrms)^2 / (80.4 kΩ) + (0.707 mA RMS)^2 * (80.4 kΩ) = 7.77 mW
Therefore, the voltage gain of the amplifier can be calculated as:
Voltage Gain = (Output Power) / (Input Power) = (3.24 W) / (7.77 mW) = 416.9
Therefore, the voltage gain of the amplifier is approximately 416.9.
Answer:
To find the voltage gain of the amplifier, we need to first determine the output voltage in relation to the input voltage. From the information given, we know that the input voltage is 1.5 V peak, and the output voltage is 18 V peak. Therefore, the voltage gain can be calculated as:
Voltage gain = output voltage / input voltage
Voltage gain = (18 V peak) / (1.5 V peak) = 12
This means that the output voltage is 12 times greater than the input voltage.
Next, we need to determine the input impedance of the amplifier. From the information given, we know that the input current is in sinusoidal form with 1 mA peak, and that the amplifier draws a current of 0.1 A from each of its power supplies. Therefore, the input impedance can be calculated as:
Input impedance = input voltage / input current
Input impedance = (1.5 V peak) / (1 mA peak) = 1500 Ω
Now, we can use Ohm's law to determine the power consumed by the amplifier from each of its power supplies:
Power supply current = 0.1 A
Power supply voltage = ± 20 V
Power supply power = (Power supply voltage) x (Power supply current)
Power supply power = (20 V) x (0.1 A) = 2 W
Therefore, the amplifier consumes 2 W from each of its power supplies.
In summary, the voltage gain of the amplifier is 12, the input impedance is 1500 Ω, and the amplifier consumes 2 W from each of its power supplies.
(Please could you kindly mark my answer as brainliest)
Two model cars collide and then move together. Car 1 has a mass of 2 kg and has an initial velocity of -5m/s. Car 2 has a mass of 1.0kg and an initial velocity of 4m/s immediately before the two model cars have a perfectly inelastic collision.
What is their final velocity immediately after the collision?
The initial momentum of the system before the collision can be calculated as: p1 = m1v1 + m2v2 = -6 kgm/s
After the collision, the two objects stick together and move with a final velocity of v. The final momentum of the system can be calculated as:
p2 = (m1 + m2)v
p2 = 3v
Since momentum is conserved, we can equate p1 and p2 to get:
p1 = p2
-6 kgm/s = 3v
v = -2 m/s
Therefore, the final velocity of the combined object after the collision is -2 m/s.
What is momentum conservation?Momentum conservation is a fundamental principle in physics that states that the total momentum of a closed system remains constant in the absence of external forces. In other words, the rate of an object or a system of things cannot change unless an external force acts on it.
Is momentum a vector quantity?Yes, momentum is a vector quantity that represents the product of an object's mass and velocity, and it describes the tendency of an object to continue moving in the same direction and at the same speed unless acted upon by an external force.
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How would you interpret the graphs? Did the subject respond only to the tone they were conditioned on? Were trials 1-10 the same or different from trials 11-20? If so, how?
Answer:
Trials 1-10 were bigger than 11-20, so it is different.
Explanation:
brainlyist pls
A vertical wire carrics an electric current out of the page, so the direction of the
magnetic field at point (P) which located at the west of the wire is
(A) to the west.
N
(B) to the south.
(C) to the north.
D) to the east.
W
S
www.
E
.P OI
The direction of the magnetic field at point P, West of the wire, would be to the South.
The right-hand ruleThe right-hand rule can be used to determine the direction of the magnetic field around a current-carrying wire.
If the thumb of the right hand is pointed in the direction of the current (out of the page), and the fingers wrap around the wire in the direction of the magnetic field, then the palm of the right-hand points in the direction of the magnetic field.
Using this rule, we can determine that the magnetic field at point (P), located west of the wire, will be directed to the south.
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Why cant an object become positively charged by gaining protons?
Answer:
An object can become positively charged by losing electrons, but it cannot become positively charged by gaining protons. This is because the charge on an object depends on the balance of protons and electrons it has. Protons have a positive charge, while electrons have a negative charge. So, when an object gains electrons, it becomes negatively charged because it now has more negative charges than positive charges. On the other hand, when an object loses electrons, it becomes positively charged because it now has more positive charges than negative charges.
However, protons cannot be gained or lost easily because they are tightly bound within the atomic nucleus of an atom, and they are not free to move around like electrons. Therefore, the only way for an object to become positively charged is to lose electrons, not by gaining protons.
Explanation:
1. An object of mass 4 kg has 200 J of kinetic energy. An external force does
- 50 J of work on the object. How much kinetic energy does the object
have now?
f=ma
55=10a
a=55/10
now we know the constant acceleration
now we just use the formula
v^2=u^2+2as
now, the kinetic energy formula is 1/2 * m * v^2
1/2 * 10 * (√47.3)^2
1/2 * 10 * 47.3
=236.5 J of kinetic energy
In physics, what exactly is kinetic energy?kinetic energy is the energy a moving item has. To accelerate an item, we must apply force. Using force needs us to perform labor. Once the work is completed, energy is transferred to the item, and the thing moves at a new constant speed.
Kinetic energy (KE) is defined in classical mechanics as half of an object's mass (1/2*m) multiplied by velocity squared. For example, if a 10 kilogram item moves at a velocity of 5 meters per second (v = 5 m/s), the kinetic energy is 125 Joules, or (1/2 * 10 kg) * 5 m/s2.
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Suppose a volcano threw so much ash into the air that it blocked much of the sunlight. How might this affect the ability of animals to obtain energy to live?
they would be affected because herbivores and omnivores which rely on plants to survive would not recieve the nutrition necessary because for the plant to create food it would need sunlight
What is the wavelength of water waves which have a frequency of 0.60 Hz and a speed of 4.0 m/s?
Answer:
1.9 m/s
Explanation:
2. What are the benefits of a normative approach to lifespan development?
A normative approach to lifespan development involves studying and comparing the typical patterns of development and behavior across different individuals or groups of people at various ages. Here are some benefits of using this approach:
Identifying developmental milestones: A normative approach helps to identify the typical milestones and achievements that people reach at different ages, such as crawling, walking, talking, and reading. This can help parents, educators, and healthcare professionals to monitor and assess a child's development and provide appropriate support and interventions when necessary.
Understanding individual differences: While a normative approach focuses on typical patterns of development, it also recognizes that there are individual differences in development and behavior. By comparing people's development to the norm, we can better understand how and why some individuals may differ from the norm, such as in terms of their physical, cognitive, or socioemotional development.
Informing public policies and interventions: A normative approach can help to inform public policies and interventions that support healthy development across the lifespan. For example, knowledge about the typical milestones of development can inform early childhood education programs, while information about the typical age-related changes in cognition and memory can inform policies related to employment and retirement.
If a person steps on a scale in an elevator that is accelerating at a rate -1.100 m/s^2 (negative means downward while positive means upwards) and sees a scale reading of 598.900 Newtons what would the scale read if the elevator were not moving?
The scale reading when the elevator is accelerating can be found using the following formula:
Weight in Elevator = Mass × (Acceleration of Gravity + Acceleration of Elevator)
where Weight in Elevator is the scale reading, Mass is the mass of the person, Acceleration of Gravity is the acceleration due to gravity (9.81 m/s^2), and Acceleration of Elevator is the acceleration of the elevator.
What would the scale read if the elevator were not moving?Using this formula, we can solve for the mass of the person:
Weight in Elevator = Mass × (Acceleration of Gravity + Acceleration of Elevator)
598.9 N = Mass × (9.81 m/s^2 - 1.1 m/s^2)
Mass = 65 kg
Now, when the elevator is not moving, the weight of the person will be equal to their mass multiplied by the acceleration due to gravity, which is:
Weight on Ground = Mass × Acceleration of Gravity
Weight on Ground = 65 kg × 9.81 m/s^2
Weight on Ground = 637.65 N
Therefore, the scale reading when the elevator is not moving would be 637.65 Newtons.
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Two piloted satellites approach one another at a relative speed of 0.25 m/s, intending to dock. The
first has a mass of 4.00 × 103 kg, and the second a mass of 7.50 × 103 kg. If the two satellites collide
elastically rather than dock, what is their final relative velocity?
please answer this question about the reflection of light
Answer:
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Explanation:
2. The term fluids refers to.....
Answer:
In physics, the term "fluids" refers to substances that have no fixed shape and are capable of flowing. Fluids can be categorized into two main types: liquids and gases. Both liquids and gases are considered fluids because they can flow and take the shape of their container. Examples of liquids include water, oil, and blood, while examples of gases include air, helium, and carbon dioxide. The study of fluids is known as fluid mechanics and is an important field in physics and engineering.
Explanation:
PLEASEEEEEEEEE HELP!!!!!!!!!!!!!!!!!!!!! (I will give a brainlist)
1. What does a spring scale measure? Include the units for the measurements. (2 points)
2. Summarize how to use a spring scale to measure a pull and how to use it to apply a push with a specific force. (4 points)
3. Compare the strengths and directions of the forces acting on the model car when it is motionless. (2 points)
4. Are these forces balanced or unbalanced? What is the net force on the car? Explain. (4 points)
5. How does the inertia of the model car compare with the inertia of a real car? (2 points)
6. Was a 0.5 N push enough to move the model car? What about the 1.0 N push? (2 points)
7. How does the size of each push compare with the force of friction on the car? Explain your answer in terms of the net force on the car. (4 points)
8. How does the inertia of car 2 (carrying 210 g) compare with the inertia of the empty car 1? (2 points)
9. How does the force needed to make car 2 move compare with the force needed to make car 1 move? (2 points)
10. Use Newton's first law to explain why the forces needed to move car 1 and car 2 were different. (4 points)
11. Why did both car 1 and car 2 slow down and come to a stop after they were pushed? (2 points)
12. Consider this question: If the mass of the car is kept constant, how will increasing the applied force affect the distance the car travels?
Write a hypothesis based on this question. (2 points)
13. Identify the dependent variable, independent variable, and constant for this experiment. (2 points)
15. Use the data to complete the graph. For any data that are uncertain, round to the nearest ten. (8 points)
16. Does the trend in your data shown in the graph support your hypothesis? What conclusion can you draw about force and the change in motion of the car? (4 points)
Answer:
A spring scale measures weight or force when an object is hung from its hook.
Explanation:
Draw a block diagram of a closedloop and Open loop control system; identify with function, Six of its components.
In closed Loop Control System,the input to the system is the desired set-point or reference value.In oen Loop Control System,the input to the system is the desired set-point or reference value.
What is value ?Value is the importance, worth, or usefulness of something. It is the importance an individual or group places on an object, service, or idea. Value is determined by how much an individual or group is willing to give up to obtain that object, service, or idea. Value can also refer to the monetary worth of an object, service, or idea.
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A rocket accelerates upwards at 6.20 ft/s/s. How far will the rocket travel in 2 minutes?
Answer:
44,640 ft
Explanation:
assuming the rocket started from rest, then v₀ = 0
2 min = 120 s
Δx = v₀t + 1/2at²
Δx = 0 + 1/2(6.2 ft/s²)(120 s)² = 44,640 ft ≈ 8.45 mi
A horizontal net force F is exerted on an object at rest. The object starts at x = 0m and has a speed of 8.0m/s after moving 6.0m along a horizontal frictionless surface. The net force. F as a function of the object's position x is shown below.
What is the mass of the object?
Answer:
i'm going to go with 5
Explanation:
In the figure below, m₁ = 11.0 kg and m₂ = 4.5 kg. The coefficient of static friction between m, and the horizontal surface it
1711
M₂
(a) If the system is released from rest, what will its acceleration be?
m/s²
(b) If the system is set in motion with m₂ moving downward, what will be the acceleration of the system?
m/s²
17. [0/5 Points] DETAILS
PREVIOUS ANSWERS SERCP9 4.P.047.WI.
The coefficient of static friction between the m = 3.15-kg crate and the 35.00 in
Answer:
See below.
Explanation:
The list of given we have:
[tex]m_1=11.0Kg[/tex][tex]m_2=4.5Kg[/tex][tex]u_s=0.60[/tex][tex]u_k=0.30[/tex](a) We are asked to find the acceleration of the system if the system is released from rest.
We can simply distinguish between the forces operating on the two masses to provide an answer. We must first determine the force affecting the masses. Hence, the only force acting on mass 2 is the gravitational force since it is suspended from the cord.
[tex]Fg=m_2g[/tex]
[tex]F_g=(4.5Kg)(9.8m/s^2)[/tex]
[tex]F_g=44.1N[/tex]
while for the mass 1 we have the static frictional force,
[tex]f_s=u_sN[/tex]
[tex]f_s=(0.60)(11.0Kg)(9.8m/s^2)[/tex]
[tex]f_s=64.68N[/tex]
We may infer that if the system is released from rest, it does not move at all since the static frictional force acting on mass 1 was greater than the gravitational force acting on mass 2, which means the system's acceleration must be equal to [tex]a=0m/s^2[/tex].
(b) We are asked to find the acceleration of the system if the mass 2 moves downward.
For this question, we must draw a free-body diagram (attachment #1).
Since we are able to draw a free-body diagram and identify the force(s) acting on the masses, we can find the acceleration of the system using the equation of Newton's second law, so we have:
[tex]F_\text{net}=m_{sys} a[/tex]
[tex]a=\frac{F_{net}}{m_{sys}}[/tex]
where the [tex]F_{net}[/tex] is the sum of force(s) acting on the system and [tex]m_{sys}[/tex] is the total mass of the system,
[tex]a=\frac{Fg_2-T+T-f_k}{m_1+m_2}[/tex]
[tex]a=\frac{F_g2 - f_k}{m_1+m_2}[/tex]
[tex]a=\frac{m_2g-u_km_1g}{m_1+m_2}[/tex]
substituting all of the given
[tex]a=\frac{(4.5Kg)(9.8m/s^2)-(0.30)(11.0Kg)}{11.0Kg-4.5Kg}[/tex]
[tex]a=\frac{40.8Kgm/s^2}{6.5Kg}[/tex]
[tex]a=6.2769[/tex]
We can conclude that if the mass 2 is going downward then the acceleration of the system would be [tex]6.2769m/s^2.[/tex]
A 6.00-kg block is sent up a ramp inclined at an angle =27.0∘ from the horizontal. It is given an initial velocity 0=15.0 m/s up the ramp. Between the block and the ramp, the coefficient of kinetic friction is k=0.40 and the coefficient of static friction is s=0.70.
What distance along the ramp's surface does the block travel before it comes to a stop?
Answer:
X = 8.2 m
Explanation:
m = 4.25 kg, v0 = 15.0 m/s, v = 0 m/s
Since you have to push the block to overcome the static friction to start moving, the force required to set it in motion must be greater than the difference between the component of weight along the ramp and the static frictional force. This force with a minimum magnitude equal to the kinetic friction is required to keep the block in a constant motion. The normal force is N = mg cosθ
F ≥ μkN + μsN - mg sinθ = μk mg cosθ + μs mg cosθ - mg sinθ
=mg[( μk + μs)cosθ + sinθ]
=4.25 kgx9.8 m/s2[(0.368+0.663)cos31.5+sin31.5]
= 58.3754 N
Fnet = ma
ma = 58.3754, a = 13.735 m/s2
v2 = v02 - 2aX
02 = (15.0 m/s)2 -2(13.735m/s2)X
X = 8.2 m
What type of energy is demonstrated when a marble is in position at the top of a rent before it begins to move
The kinetic energy is related to the motion of the marble, but the potential energy is related to its position. The marble's potential energy is transformed into kinetic energy as it slides down the ramp from the top.
While the stone is in this position before it starts to move, what kind of energy is being shown?The stone has potential energy when it is at the top of the ramp because gravity will lead it to fall. The term for this is gravitational potential energy. The stone is freed, and the potential energy transforms into kinetic energy as it moves. Kinetic energy is the term used to describe a moving object.
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A frictionless roller coaster with an initial speed of
The final speed of the roller coaster is 454.6 m/s.
How to determine final speed?To determine the behavior of the roller coaster, we can use the conservation of energy principle, which states that the total energy of a closed system remains constant. The initial energy of the roller coaster is potential energy (due to its height) and kinetic energy (due to its initial speed), and the final energy is potential energy (due to its final height) and kinetic energy (due to its final speed). Assuming no energy losses due to friction or other factors, the initial energy must equal the final energy.
The potential energy of the roller coaster at height h is given by:
Ep = mgh
where m is the mass of the roller coaster, g is the acceleration due to gravity (9.81 m/s²), and h is the height of the roller coaster.
At the top of the roller coaster (where h = 100 m), the potential energy of the roller coaster is:
Ep = (1000.0 kg)(9.81 m/s²)(100.00 m) = 981000 J
The kinetic energy of the roller coaster at the initial speed vi is given by:
Ek = (1/2)mv²
where m is the mass of the roller coaster, and v is its speed.
At the beginning of the roller coaster (where vi = 10.00 m/s), the kinetic energy of the roller coaster is:
Ek = (1/2)(1000.0 kg)(10.00 m/s)² = 50000 J
The total energy of the roller coaster at the beginning of the ride is:
Etotal = Ep + Ek = 981000 J + 50000 J = 1031000 J
At the bottom of the roller coaster, all of the potential energy has been converted to kinetic energy, and the roller coaster has reached its maximum speed. Therefore, the kinetic energy at the bottom of the roller coaster is:
Ek = Etotal - Ep = 1031000 J - 0 J = 1031000 J
The final speed of the roller coaster, vf, is found using the equation:
Ek = (1/2)mv²
Solving for vf:
vf = √(2Ek/m) = √(2(1031000 J)/(1000.0 kg)) = 454.6 m/s
Therefore, the final speed of the roller coaster is approximately 454.6 m/s.
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The complete question is:
a frictionless roller coaster is given an initial speed of vi=10.00m/s , at the initial height h=100:00m,has a mass m=1000.0kg. what is the roller coaster's final speed?