Answer:
The laws of reflection govern how incident light rays are reflected on reflecting surfaces such as mirrors, smooth metal surfaces, and clear water. The laws of reflection are as follows: The incident ray reflected ray, and normal to the mirror’s surface are all in the same plane. The incidence angle equals the reflection angle.
Explanation:
Larry finds a lens and shows it to his friends, Mirez and Sherly.
All three look through it. Larry looks at the window across the room with the lens and says the window looks upside down. Mirez said that he must be using it incorrectly, because when he looks at his thumb through the lens, it is definitely not upside down. Sherly says that she thinks it is broken, because when she looks through it, everything just looks blurry.
Using your understanding about image formation, explain each of their observations.
Larry observes that the window looks upside down because the lens forms an inverted image. When light passes through a convex lens, it is refracted (bent) towards the center of the lens. The degree of bending depends on the angle of incidence and the refractive index of the lens. This bending of light rays causes the image to be inverted.
Mirez observes that his thumb looks right side up because the orientation of the object being viewed through the lens matters. When an object is placed at a distance greater than the focal length of the convex lens, the lens forms a real and inverted image. However, when the object is placed at a distance less than the focal length of the lens, the lens forms a virtual and erect image. In this case, Mirez's thumb is closer to the lens than the focal length, and hence, the lens forms a virtual and erect image of the thumb.
Sherly observes that everything looks blurry because the lens is not able to form a sharp image. The blurriness is due to spherical aberration, which is a common problem in lenses. When light passes through the curved surface of the lens, the rays passing through the edges of the lens bend more than those passing through the center. This causes the light to converge at different points on the image plane, resulting in a blurry image. To overcome spherical aberration, lenses are designed with multiple curved surfaces, or with non-uniform thickness.
The lens that produces an upside-down image is called a convex lens. Hence, Larry finds the lens called a convex lens.
What is the convex lens?The lens that converges the ray of light is called a convex lens. The lens that curved inwards, has a thicker middle portion and thinner at the lower and the middle part.
Convex lenses produce virtual and real images depending on the object's position. It also produces an upside-down image. It also produces a magnified image.
From the observation,
The convex lens produces an upside-down image. The lens produces an upside-down image, when light passes through the lens, it bends toward the center. This bending of light rays causes an inverted image.
Mirez's observation is based on the focal length of the convex lens. When an object is placed at a larger distance than the focal length of the convex lens, it produces a real and inverted image whereas the object's distance is lesser than the focal length, it produces a virtual and erect image.
Hence, he placed his thumb closer to the convex lens, the focal length is decreased and it produces a virtual and erect image. Sherly saw the blurred image because the lens does not produce sharp images. The lens doesn't produce sharp images as it has certain spherical aberrations.
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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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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
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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The electricity received at an electric substation has a potential difference of 2.80 x 105 V. If the required output is 440 V, what should be the ratio of the turns of the step-down transformer?
A
Explanation: sorry sir but its required step up transformer for high voltage not step
(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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convert 1 Celsius to Fahrenheit
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?
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:
If electricity costs $0.18 per kwh, how much does it cost to run the air conditioner in the problem above?
A)$5.76
B)$7.87
C)$9.45
D)$12.12
Answer:
the answer is A) $5.76.
We found in the previous problem that the air conditioner uses 32 kWh per day. To find the cost, we multiply the number of kWh by the cost per kWh:
32 kWh/day x $0.18/kWh = $5.76/day
So, it costs $5.76 per day to run the air conditioner.
Therefore, the answer is A) $5.76.
Im kinda lost in this one
[tex]75 = 6 \times \frac{?}{?} \times \frac{?}{?} [/tex]
What geologic feature would you be most likely to find at a divergent plate boundary where two oceanic plates move away from each other? a mid-ocean ridge a rift valley an island arc an ocean trench
Answer: When two plates are moving away from each other, we call this a divergent plate boundary. Along these boundaries, magma rises from deep within the Earth and erupts to form new crust on the lithosphere. Most divergent plate boundaries are underwater and form submarine mountain ranges called oceanic spreading ridges.
Explanation:
I HOPE THIS HELPED YOU I AM OPEN IF YOU WANTS ANSWERS GOOD LUCK BY THE WAY!
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.
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?
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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fish swimming in a horizontal plane has velocity v with arrowi = (4.00 î + 1.00 ĵ) m/s at a point in the ocean where the position relative to a certain rock is r with arrowi = (14.0 î − 2.80 ĵ) m. After the fish swims with constant acceleration for 19.0 s, its velocity is v with arrow = (23.0 î − 1.00 ĵ) m/s. (a) What are the components of the acceleration of the fish? ax = m/s2 ay = m/s2 (b) What is the direction of its acceleration with respect to unit vector î? ° counterclockwise from the +x-axis (c) If the fish maintains constant acceleration, where is it at t = 26.0 s? x = m y = m In what direction is it moving? ° counterclockwise from the +x-axis
Answer:
sorryyyyijyyyyyyyyyyyyyyyyyyyy&
Explanation:
soryyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy
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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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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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]
please answer this question about the reflection of light
Answer:
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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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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:
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.
A negative lightning strike occurs when a negatively charged cloud discharges its excess electrons to the positively charged ground. If you observe a cloud-to-cloud lightning strike, what can you say about the charge on the area of the cloud struck by lightning?
1. The area of the cloud that was struck by lightning is neutral.
2. The area of the cloud that was struck by lightning had a positive charge.
3. The area of the cloud that was struck by lightning had a negative charge.
The area οf the clοud that was struck by lightning had a negative charge, sο, οptiοn (d) is cοrrect.
What is electrοns ?The negatively charged atοm's electrοns are respοnsible fοr this. An atοm's tοtal negative charge, which is prοduced by all οf its electrοns, cοunteracts the pοsitive charge οf the prοtοns in the atοmic nucleus.
What is electric charge?Prοtοns and electrοns, which functiοn as charge carriers, frequently carry bοth pοsitive and negative electric charges. By mοving charges, energy is prοduced. Charge—alsο referred tο as electric charge, electrical charge, οr electrοstatic charge—is a prοperty οf a unit οf matter in physics and is denοted by the letter q.
Therefοre, The area οf the clοud that was struck by lightning had a negative charge, sο, οptiοn (d) is cοrrect.
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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:
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:
A balloon has a charge of -1.0 x 10-6 C and is held 0.97 m away from a steel tube. If the force between them is -5.5 N, what is the charge of the tube?
We can use Coulomb's Law to solve this problem:
F = k * (q1 * q2) / r^2
where:
F = -5.5 N
k = Coulomb's constant (9.0 x 10^9 N·m^2/C^2)
q1 = charge of the balloon (-1.0 x 10^-6 C)
q2 = charge of the steel tube= ?
r = distance between the balloon and the steel tube (0.97 m)
Plugging in the given values and solving for q2:
-5.5 N = (9.0 x 10^9 N·m^2/C^2) * (-1.0 x 10^-6 C) * q2 / (0.97 m)^2
Solving for q2, we get:
q2 = (-5.5 N) * (0.97 m)^2 / [(9.0 x 10^9 N·m^2/C^2) * (-1.0 x 10^-6 C)]
q2 ≈ -6.4 x 10^-6 C
Therefore, the charge of the steel tube is approximately -6.4 x 10^-6 C.
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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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Consider a situation where over the course of a 24-mile long run, a runner becomes increasingly tired. In the first hour he runs 12 miles, in the second hour 6 miles, in the third hour 3 miles, and so on, so that each hour he runs half the distance to go. How long will it take to finish the race?
The runner will take a full day to complete the race, assuming he maintains the same pattern of slowing down by half the previous hour's distance each hour.
How did we get this assertion?We can approach this problem by using a formula for the sum of an infinite geometric series, since the distances covered by the runner in each hour form a geometric sequence with a common ratio of 1/2. The formula is:
S = a / (1 - r),
where S is the sum of the series, a is the first term, and r is the common ratio.
In this case, the first term a is 12 miles, and the common ratio r is 1/2. We want to find the total distance S covered by the runner over the entire 24-mile race, so we can set:
S = 12 / (1 - 1/2) = 24
This means that the runner will cover the remaining 12 miles in the final hour, and so the total time taken to finish the race will be:
1 + 1 + 1 + ... (24 times) = 24 hours
So, the runner will take a full day to complete the race, assuming he maintains the same pattern of slowing down by half the previous hour's distance each hour.
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A particular insulating container has a total surface area of 1.10 m2 and walls that are 4.00 cm thick. Suppose that a 10.0 W electric heater keeps the inside of the container 13.0°C warmer than the temperature outside. What is the thermal conductivity k of the material that the container is made of? (Enter your answer in W/(m · °C).)
The thermal cοnductivity οf the material is 0.024 W/(m·K).
What is the heat transfer fοrmula?We can use the fοrmula fοr heat transfer thrοugh a material with a temperature difference and knοwn surface area:
Q/t = kA(T1-T2)/d
where Q/t is the rate οf heat transfer (pοwer) prοvided by the electric heater,
k is the thermal cοnductivity οf the material,
A is the surface area οf the cοntainer,
d is the thickness οf the walls,
T1 is the temperature inside the cοntainer, and
T2 is the temperature οutside the cοntainer.
Plugging in the given values:
Q/t = 10.0 WA = 1.10 m²d = 0.04 mT1 - T2 = 13.0 °C
We can rearrange the fοrmula tο sοlve fοr k:
k = Qtd / (A*(T1-T2))
Plugging in the values and cοnverting units tο SI units:
k = (10.0 W)(1 s)(0.04 m) / (1.10 m² * 13.0 K) = 0.024 W/(m·K)
Therefοre, the thermal cοnductivity οf the material is 0.024 W/(m·K).
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