Answer:
First, let's calculate the potential energy stored in the spring:
PE = (1/2)kx²
where k is the spring constant and x is the distance the spring is compressed. Plugging in the given values, we get:
PE = (1/2)(600.0 N/m)(7.5 m)² = 16875 J
This potential energy is converted into kinetic energy as the roller coaster moves along the track. At the horizontal section, all of the potential energy has been converted into kinetic energy:
KE = (1/2)mv²
where m is the mass of the roller coaster and v is its velocity. Plugging in the given values, we get:
16875 J = (1/2)(205.0 kg)(6.0 m/s)²
Simplifying and solving for the vertical displacement, we get:
Δy = (KE/mg) - 7.5 m
where g is the acceleration due to gravity. Plugging in the values, we get:
Δy = [(1/2)(205.0 kg)(6.0 m/s)²/(205.0 kg)(9.81 m/s²)] - 7.5 m
Δy = 8.47 m
Therefore, the roller coaster is 8.47 meters above the starting level at the second (flat) level.
Explanation:
Assume that an average student in your physics class can load into a van forty 12.7 kg boxes of copy paper in 5.0 min . The van has a loading height of 0.70 m . Assume also that the magnitude of the work done on each bag by the student equals the magnitude of the work done on the bag by gravity when the box is lifted into the van.
What is the average power output of the student in watts?
Express your answer in watts.
The average power output of the student in watts, given that the student can load into a van forty 12.7 kg boxes of copy paper in 5.0 mins is 11.62 Watts
How do i determine the average power output?First, we shall obtain the work done by the student in loading the forty 12.7 kg boxes of copy paper. Details below:
Total mass of box (m) = 40 × 12.7 = 508 KgHeight (h) = 0.7 mAcceleration due to gravity (g) = 9.8 m/s² Work done (Wd) = ?Wd = mgh
Wd = 508 × 9.8 × 0.7
Wd = 3484.88 J
Now, we shall determine the average power output of the student. Details below:
Time (t) = 5.0 mins = 5 × 60 = 300 secondsWork done (Wd) = 3484.88 JAverage power output (P) = ?P = Wd / t
P = 3484.88 / 300
P = 11.62 Watts
Thus, the average power output is 11.62 Watts
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For the simple harmonic oscillation where k = 19.6
N/m, A = 0.100 m, x = -(0.100 m) cos 8.08t, and v =
(0.808 m/s) sin 8.08t, determine (a) the total energy, (b)
the kinetic and potential energies as a function of time,
(c) the velocity when the mass is 0.050 m from
equilibrium, (d) the kinetic and potential energies at
half amplitude (x = A/2).
a. Total energy is 0.098 J
b. Potential and Kinetic Energies is 0.032 sin^2(8.08t) J
c. Velocity at x is -0.808 sin(8.08t) m/s
d. Potential and Kinetic Energies at x is 0.016 sin^2(8.08t) J
Step by step explanationWe can use the following formulas for the energy, velocity, and potential and kinetic energies of a simple harmonic oscillator:
Total Energy: E = 1/2 k A^2Velocity: v = -ωA sin(ωt)Potential Energy: U = 1/2 k x^2Kinetic Energy: K = 1/2 m v^2where ω = √(k/m) is the angular frequency.
Given that k = 19.6 N/m, A = 0.100 m, x = -(0.100 m) cos 8.08t, and v = (0.808 m/s) sin 8.08t, we can find the values of E, U, and K as follows:
(a) Total Energy:
E = 1/2 k A^2 = 1/2 * 19.6 * 0.1^2 = 0.098 J
(b) Potential and Kinetic Energies:
U = 1/2 k x^2 = 1/2 * 19.6 * (-0.1 cos(8.08t))^2 = 0.098 cos^2(8.08t) J
K = 1/2 m v^2 = 1/2 * (0.1) * (0.808 sin(8.08t))^2 = 0.032 sin^2(8.08t) J
(c) Velocity at x = 0.050 m:
When x = 0.050 m, cos(8.08t) = -0.5, so we have:
v = -ωA sin(ωt) = -ω(0.1) sin(8.08t) = -0.808 sin(8.08t) m/s
(d) Potential and Kinetic Energies at x = A/2:
When x = A/2 = 0.050 m, cos(8.08t) = -0.5, so we have:
U = 1/2 k x^2 = 1/2 * 19.6 * (0.050)^2 = 0.0245 J
K = 1/2 m v^2 = 1/2 * (0.1) * (0.808 sin(8.08t))^2 = 0.016 sin^2(8.08t) J
Note that the sum of potential and kinetic energies at any point in time is equal to the total energy, which is constant.
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When an object speeds up, it has a? 7._______
When an object speeds up, it has a positive acceleration
What is Positive acceleration?Positive acceleration is the rate at which an object's speed increases over time. It is measured in distance units per time squared (m/s2) and is the result of a net force being applied to an object.
Positive acceleration indicates that an object is accelerating in the same direction as the applied force. When a net force is applied to an object, it changes the velocity of the object in the same direction as the force. The object's velocity will continue to increase until the net force is equal to zero.
At this point, the object is said to be moving at a constant velocity. Positive acceleration occurs when the net force acting on an object is greater than zero, resulting in an increase in the object's speed. This increase in speed is known as a positive acceleration.
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A frog is riding on the top of a cylindrical piece of wood floating in still water. Half of the wood, with a diameter of 4 cm and length 20 cm, is immersed in water. The density of water is 1 gm/cc. a) What is the mass of the wood along with the frog? b) After the frog slowly goes into the water only one third of the wood remains immersed in water. Calculate the mass of the frog. c) Calculate x, the distance between the water level and the center of the circular end of the wooden piece. d) Briefly describe the motion of the wood after the instance the frog moves into the water. Give a rough sketch of x as a function of time.
The total mass of the wood along with the frog is 120π gm.
The mass of the frog is (160/3)π gm.
How to calculate the MassThe volume of the wood that is immersed in water is given by the volume of a cylinder with a radius of 2 cm and a height of 10 cm, which is V1 = π(2cm)²(10cm) = 40π cm³. The mass of the water displaced by this volume of wood is m1 = V1ρ = 40π gm. The mass of the remaining part of the wood above water is m2 = ρV2 = ρ(π(2cm)²(10cm)) = 80π gm.
mTherefore, the total mass of the wood along with the frog is m1 + m2 = 120π gm.
b) After the frog goes into the water, the volume of the wood that is immersed decreases to V3 = (1/3)π(2cm)^2(20cm) = (80/3)π cm^3. The mass of the water displaced by this volume of wood is m3 = V3ρ = (80/3)π gm. Therefore, the mass of the frog is (m1 + m2) - m3 = (120π - (80/3)π) gm = (240/3)π - (80/3)π = (160/3)π gm.
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2. This diagram shows an electric bell ringing in a sealed glass chamber containing air. to vacuum pump 5655 bell A student hears the bell ringing. The air is then removed from the chamber. State and explain any change in the sound heard by the student.
When the air is removed from the chamber using a vacuum pump, the sound heard by the student will become quieter.
What is Vacuum?
Vacuum is typically created by removing gases and other matter from a closed container, using methods such as mechanical pumps, diffusion pumps, or cryopumps. In the absence of matter, there is no medium for sound waves to propagate, which is why sound cannot travel through a vacuum.
This is because sound waves require a medium to travel through, such as air. When the air is present in the chamber, the sound waves from the vibrating bell can travel through the air and reach the student's ear. However, when the air is removed, there is no medium for the sound waves to travel through, so they cannot reach the student's ear as effectively.
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A baseball projected with an initial velocity of 212 m/s
at an angle of 45∘
follows a parabolic path and hits a balloon at the top of its trajectory.
Neglecting air resistance, find the speed that the ball hits the balloon. V=
The speed that the ball hits the balloon is approximately 214.43 m/s.
Which of the following three formulae of motion apply?The velocity-time connection refers to the first motion equation, v = u + it. On the other hand, the position-time connection is denoted by the second equation of motion, s = ut + 1 / 2at2.
The following equation can be used to determine the ball's ultimate velocity:
v_f = sqrt(v_x² + v_y²)
where v_x is the horizontal component of the velocity and v_y is the vertical component of the velocity at the point of impact.
Substituting the given values, we get:
v_i_x = v_i_y = 212 / √(2) = 150.13 m/s
t = v_y / a_y = 150.13/9.8 = 15.31 s
y = v_i_y * t + 0.5 * a_y * t² = 150.13 * 15.31 + 0.5 * (-9.8) * (15.31)² = 1149.59 m
x = v_i_x * t = 150.13 * 15.31 = 2298.52 m
v_f = √(v_x² + v_y²) = √((212/√(2))² + (-9.8 * 15.31)²)
= 214.43 m/s
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Marina was immunized against chicken pox when she was young. Which of the following statements is true?
Since she was immunized, it is impossible for Marina to contract chicken pox.
Marina was exposed to a weak form of chicken pox antigen.
The immunization provided Marina with passive immunity.
Marina needs to be immunized again because antibodies do not last long in the body.
Answer:
see below
Explanation:
In chickenpox vaccine , weakened/killed pathogens are introduced into the body to generate immune response. The first response is slow and is called primary response while the subsequent exposure with the same pathogen generates a highly intensified immune response which is known as secondary response .
This type of immunity which generates antibody against the virus particles by introducing them into the body is called active immunity . It lasts forever in the body as the immune system has the memory of first exposure with the pathogen and after coming in contact with the same pathogen it recognises it and generates immune response.
So the correct option would be,
Marina was exposed to a weak form of chicken pox antigen.[tex]\rule{200}2[/tex]
Related information:-
Passive immunity:-
It is the type of immunity when performed antibodies are introduced in the body . Like in case of smallpox. This doesn't last long in the body and requires repeated infusions in the body after coming in contact with the same pathogen again.
Also , it is helpful when quick reponse is required against the antigen and we don't have time to wait for generating immune response like in case of snake bites .
Need help with these two please!! Thank you in advance.
Answer:
I agree with Erikson stages of development that all adolescents and young adults pass through the stage
How high would a 8 kg mass need to be lifted to have a potential energy of 400 J?
Explanation:
Potential Energy = m g h
400 J = 8 kg * 9.81 m/s^2 * h
400 / (8 *9.81) = h = 5.1 m
Suppose that two equally charged spheres attract each other with a force of -0.492 N ("-" means attractive) when placed a distance of 29.1 cm from each other. Determine the charge of the spheres.
Each sphere has a charge of 2.00 x 10^-7 C.
The electric force between two charged objects is given by Coulomb's law:
F = k(q1q2/r^2),
where F is the force, k is Coulomb's constant (9.0 x 10^9 N m^2/C^2), q1 and q2 are the charges of the two objects, and r is the distance between them.
In this case, we know that the force is -0.492 N (attractive), the distance is 29.1 cm (0.291 m), and the two spheres have the same charge, so q1 = q2 = q
Substituting these values into Coulomb's law, we get:
-0.492 N = k(q^2 / (0.291 m)^2)
Solving for q, we get:
q = sqrt((-0.492 N * (0.291 m)^2) / k)
q = sqrt((-0.492 N * (0.291 m)^2) / (9.0 x 10^9 N m^2/C^2))
q = 2.00 x 10^-7 C
Therefore, each sphere has a charge of 2.00 x 10^-7 C.
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1. a) Find the diffusion coefficient of copper-silver penetration at 500°C. b) For this system, what time is required to achieve the same results (the same size at the same distance) of the diffusion process at 500°C for 10 hours at 600°C? ? 2. The iron-carbon alloy with FCC structure initially content, and its surface was exposed to an environment with C = 1.0% carbon content and carbonization treatment was carried out by increasing the ambient temperature. If after 49.5 hours the alloy has a carbon content of 0.35%C at a depth of 2 = 4.0mm from the surface, at what temperature was this heat treatment carried out? C = 0,20% C 334
The time required to achieve the same diffusion results at 500°C for 10 hours at 600°C is approximately 1.1 minutes.
What is Diffusion?
Diffusion is a physical process where molecules or particles move from an area of high concentration to an area of lower concentration. This movement is driven by the natural tendency of molecules to spread out and achieve a state of equilibrium, where the concentration is the same throughout the system. Diffusion occurs in gases, liquids, and solids, and is responsible for a wide range of phenomena, from the movement of oxygen and carbon dioxide in the lungs to the mixing of chemicals in a beaker.
a) The diffusion coefficient of copper-silver penetration at 500°C can be calculated using Fick's first law:
J = -D*(dc/dx)
where J is the diffusion flux, D is the diffusion coefficient, dc/dx is the concentration gradient.
Assuming that copper and silver diffuse independently and the concentration gradient is constant, we can write:
J = -Dc*(dc/dx)
where Dc is the effective diffusion coefficient for copper in silver.
At 500°C, the value of Dc for copper in silver is approximately 2.7 x 10^-11 m^2/s.
b) To determine the time required to achieve the same diffusion results at 500°C for 10 hours at 600°C, we can use the Arrhenius equation:
D2/D1 = exp(-Q/R)*exp((1/T1) - (1/T2))
where D1 and T1 are the diffusion coefficient and temperature at 500°C, D2 and T2 are the diffusion coefficient and temperature at 600°C, Q is the activation energy for diffusion, and R is the gas constant.
Assuming that the activation energy for diffusion is 100 kJ/mol, we can calculate the diffusion coefficient at 600°C:
D2 = D1exp(-Q/R)exp((1/T1) - (1/T2))
= 2.7 x 10^-11 m^2/s * exp(-100000/(8.314500))(1/773 - 1/873)
= 1.3 x 10^-9 m^2/s
Now, we can use Fick's second law to determine the distance traveled by diffusion in 10 hours at 600°C:
x = sqrt(4Dt)
= sqrt(4*(1.3 x 10^-9 m^2/s)*36000 s)
= 0.016 m
To achieve the same diffusion results at 500°C, the same distance must be traveled. Therefore, we can calculate the time required at 500°C:
t = x^2/(4D1)
= (0.016 m)^2/(4*(2.7 x 10^-11 m^2/s))
= 0.019 hours
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A bungee jumping company wants to set up a bungee
jumping location on the top of a bridge that is 300 m above
the ground. For safety reasons, the company wants to
select a bungee cord spring constant such that a jumper
with a mass of 115 kg will reach his lowest point that is,
the point when the change in gravitational potential energy
equals the amount of energy stored in the bungee cord at
the bottom of the jump - at 50 m above the ground. What
is the approximate spring constant the company should
choose, assuming that air resistance, friction, and the
weight of the cord can be ignored and that the cord
immediately begins to stretch as soon as the jumper
begins to fall? (Recall that g = 9.8 m/s²)
cord mg
A. 23 N/m
B. 9 N/m
C. 4 N/m
D. 15 N/m
Answer:
Approximately [tex]9\; {\rm N \cdot m^{-1}}[/tex].
Explanation:
Change in the gravitational potential energy (GPE) of the system:
[tex](\text{change in GPE}) = m\, g\, \Delta h[/tex], where:
[tex]m = 115\; {\rm kg}[/tex] is the mass of the jumper.[tex]g = 9.8\; {\rm m\cdot s^{-2}} = 9.8\; {\rm N\cdot kg^{-1}}[/tex] is the gravitational field strength.[tex]\Delta h = (300 - 50)\; {\rm m} = 250\; {\rm m}[/tex] is the absolute value of the change in height.Change in the elastic potential energy (EPE) of the system:
[tex]\text{(change in EPE)} = (1/2)\, k\, x^{2}[/tex], where:
[tex]k[/tex] is the spring constant and needs to be found.[tex]x = (250 - 0)\; {\rm m} = 250\; {\rm m}[/tex] is the change in the length of the cord. Note that since the cord started stretching immediately, that initial length of the cord would be [tex]0\; {\rm m}[/tex] .Set [tex]\text{(change in GPE)} = \text{(change in EPE)}[/tex] and solve for the spring constant [tex]k[/tex]:
[tex]\displaystyle m\, g\, \Delta h = \frac{1}{2}\, k\, x^{2}[/tex].
[tex]\begin{aligned}k &= \frac{m\, g\, \Delta h}{(1/2)\, x^{2}} \\ &= \frac{(115)\, (9.8)\, (250)}{(1/2)\, (250)^{2}}\; {\rm N\cdot m^{-1}} \\ &\approx 9\; {\rm N\cdot m^{-1}}\end{aligned}[/tex].
what is the turns ratio of a primary transformer with 208 volts and the secondary with 24 volts
By dividing the number of turns on the primary (Np) by the number of turns on the secondary (Ns), one can determine a transformer's turns ratio (Np/Ns) (Ns). As a result, Np/Ns = 8.66 is roughly the turns ratio.
What is the ratio of a transformer's main to secondary turns?Using the turns ratio method is a simpler method. By dividing the higher number of turns by the smaller number of turns, you can find a ratio. For instance: A transformer with a turns ratio of 2:1 will have 100 primary turns and 50 secondary turns.
We can instead apply the following formula:
Vs/Vp = Ns/Np Plugging in the values given:
Vs = 24 V
Vp = 208 V
Vs/Vp = Ns/Np
24/208 = Ns/Np
Simplifying:
0.1154 = Ns/Np
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match the perspective in column 1 to the corresponding question in column 2
The matching perspective to the corresponding questions are:
A. Developmental psychologyB. Developmental psychologyC. Positive psychologyD. Social psychologyE. Social psychologyWhat is psychology?Psychology is the scientific study of the human mind and behavior, exploring topics such as perception, cognition, attention, emotion, motivation, personality, brain function, and social interaction. It encompasses a range of approaches, from studying the biological and neurological underpinnings of behavior to investigating the social and cultural factors that shape our experiences and interactions.
Psychology seeks to understand and explain a wide range of phenomena related to human thought, feeling, and behavior, and to use that understanding to promote individual and collective well-being.
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The complete question:
Match the perspective in Column 1 to the corresponding question in Column 2.
A. Positive psychology At what age do children begin to use language?
B. Biopsychology How do adolescent brains develop?
C. Cognitive psychology How can I lead a happier life?
D. Social psychology How do our thoughts affect our self-concept?
E. Developmental psychology How can we reduce prejudice?
Write a synthetic route for the conversion of cyclopropane to cyclopropanecarboxylic acid via Grignard reagent.
Here is a synthesis method for using the Grignard reagent to change cyclopropane into cyclopropanecarboxylic acid: Make cyclopropane into cyclopropanone using ozonolysis or another appropriate process.
What is a cyclopropanation example?Dichlorocarbene is one illustration. The formation of cyclopropanes from these halogenated carbenes is similar to that of methylene, with the intriguing addition of two halogen atoms in lieu of the hydrogen atoms. Although they do not strictly qualify as carbenes, carbeneoids are substances that combine to form cyclopropanes.
What is alkene cyclopropanation?Since the addition of carbene and carbenoids to alkenes is a type of cheletropic reaction and occurs in a syn way, cyclopropanation also exhibits stereospecificity.
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A ray diagram shows that an object is placed in front of a plane mirror. What are the characteristics of the image produced by the object?
inverted, larger than object, real
upright, smaller than object, virtual(this is not the answer)
inverted, same size as object, real
upright, same size as object, virtual
The image created when an object is placed in front of a plane mirror is virtual, hence it cannot be projected onto a screen. The right response is: virtual, upright, and of the same size as the object.
Does an object's image emerge when it is placed in front of a flat mirror?A virtual picture is created when an object is placed in front of a plane mirror. The distance between the image and the mirror is equal to the distance between the item and the mirror, and the size of the image is the same as the size of the object.
When the object is flipped over in relation to the mirror's planar image?The left side of an object appears to be the right side of its image when it is placed in front of a plane mirror, and the opposite is true for the right side of the object. Lateral inversion is the term for this phenomena.
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What is formula of force
Answer:
Hey Buddy!
Explanation:
This is ur answer....
F = m × aHope it helps!
Brainliest pls!
Have a good day!
Answer:
The formula for force is Force = Mass x Acceleration (F = m x a).What do non count? As apples and oranges
Non-count nouns, such as substances or concepts, are often things that are difficult to count or quantify. Like with count nouns like apples or oranges, you cannot count them in discrete units.
Which nouns are countable and uncountable?Nouns may or may not be countable. One apple, two apples, three apples, etc. are all examples of countable nouns. Uncountable nouns, such as air, rice, water, etc., cannot be tallied. When learning a new word, it is important to determine if it is countable or uncountable and to take note of its placement in a sentence.
How does fruit not have a count?It is okay to say "I love fruit" instead of "I love fruits" because "fruit" is generally considered to be an uncountable noun. But, if you refer to a specific kind of fruit, then this word becomes countable: for instance, This region is suitable for citrus fruit cultivation.
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Ronaldo has two pots of water. Pot 1 has a large number of particles, moving slowly on average. Pot 2 has a smaller number of particles, but they are moving faster on average.
Match the pot with its description.
Pot 1
Pot 2
[ Choose ]
I Choose I
Has a higher kinetic energy
Has a hicher kinetic energy and a higher temperature
Does not have a higher kinetic energy or temperature
Has a higher temperature
The kinetic theory of matter, which holds that all matter is made up of microscopic particles that are always in motion, can be used to explain this situation.
What happens as the particle velocity increases to an object's temperature?When the average kinetic energy of the object's particles increases, so does its thermal energy. The thermal energy of an object therefore increases as its temperature does.
Which example has the most kinetic energy for the water molecules?Water molecules usually have the highest kinetic energy in the steam phase. Since the gaseous phase of a substance always has the highest kinetic energy of the three states of matter, steam is a gaseous state in which water molecules have the highest kinetic energy.
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PLEASE HELP! I AM SO LOST! BRAINLIEST AND 40 PTS!
Answer:
R (total) = 14 Ω
V1 = 68,58 V
V2 = 68,58 V
V3 = 51,42 V
I (total) ≈ 8,57 A
I1 ≈ 4,29 A
I2 = 4,28 A
I3 ≈ 8,57 A
Explanation:
Given:
R1 and R2 are connected in parallel
R3 with (R1 and R2) are connected in series
V (total) = 120,0 V
R1 = 16,0 Ω
R2 = 16,0 Ω
R3 = 6,0 Ω
R (total) = R1 + R2 + R3
First, let's find the resistance in (R1 and R2) part
Since R1 = R2, we can use this formula:
R = R1/n (n is the number of resistors, in this case it's 2)
R = 16/2 = 8 Ω
Now, we add this number to R3 and we'll get the total resistance in this circuit:
R (total) = 8 + 6 = 14 Ω
I (total) = V (total) / R (total)
I (total) = 120/14 ≈ 8,57 A
I3 = I ≈ 8,57 A, since it's connected in series with the current source
V3 = I3 × R3
V3 = 8,57 × 6 = 51,42 V
V1 = V2 = V (total) - V3, since it's a parallel connection
V1 = V2 = 120 - 51,42 = 68,58 V
I1 = V1/R1
I1 = 68,58/16 ≈ 4,29 A
I2 = I (total) - I1
I2 = 8,57 - 4,29 = 4,28 A
I hope I did everything correct
Consider the diagram of a pendulum's motion shown above. A pendulum can be used to model the change from potential energy to kinetic energy and back to potential energy. If you pull the bob back to point A and release it, potential energy is converted to kinetic energy. What do you think happens to the energy at point C?
Responses
A Potential energy is converted to kinetic energy.
B Potential energy decreases.
C Kinetic energy increases.
D Kinetic energy is converted to potential energy.
D. Kinetic energy is converted to potential energy.
How Kinetic energy is converted to potential energy.At point C, the pendulum is at its highest point, and the kinetic energy it has accumulated from the initial release at point A has been fully converted to potential energy. As the pendulum swings back toward point A, it will lose potential energy and gain kinetic energy until it reaches point A once again.
At point A, potential energy is converted to kinetic energy. At point C, the pendulum is at its highest point, and the kinetic energy has been fully converted to potential energy. As the pendulum swings back toward point A, it will lose potential energy and gain kinetic energy until it reaches point A once again.
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5. Determine the friction a car that has a mass of 320kg would experience traveling 20 m/s going around a curve if
the radius of the curve is 200m.
The frictional force acting on the car is equal to the centripetal force, therefore the frictional force = 3200 N.
What is frictional force?The force produced when two surfaces slide against and touch each other is called frictional force.
To determine the friction that a car would experience, we need to use the formula for centripetal force:
F = m * (v² / r)
where F is the force required to keep the car moving in a circular path, m is the mass of the car, v is the velocity of the car, and r is the radius of the curve.
In this case, we can substitute the given values to find the required force:
F = 320 kg * (20 m/s)² / 200 m
F = 3200 N
This force is the centripetal force required to keep the car moving in a circular path around the curve. This force is provided by the friction between the car's tires and the road surface. Therefore, the frictional force acting on the car is equal to the centripetal force:
Frictional force = 3200 N
Note that this calculation assumes that the car is traveling at a constant speed around the curve. If the car is accelerating or decelerating, additional forces (such as the force due to braking or acceleration) would need to be considered in the calculation of the frictional force.
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John and Mary are skating at an ice rink. John skates at a constant speed of 6.5 m/s, with respect to the ice surface, directly south. Mary skates at a constant speed of 10.5 m/s in a direction of 27° west of south, with respect to the ice. What are the magnitude and direction of Mary's velocity with respect to John? Give the magnitude in m/s, and give the direction as measured relative to due south.
Mary's velocity with respect to John has a magnitude of approximately 5.459 m/s and a direction of approximately 120.7° relative to due south.
What is velocity?A vector quantity that describes the rate of change of any object's position with respect to the time is called velocity.
Component of Mary's velocity vector in the south direction is given by:
[tex]\rm v_{south[/tex] = 10.5 cos(27°) = 9.373 m/s
Component of Mary's velocity vector in the west direction is: [tex]\rm v_{west[/tex] = 10.5 sin(27°) = 4.642 m/s
Mary's velocity vector with respect to the ice can be written as: [tex]\rm v_M/Ice[/tex] = -9.373 m/s (in the south direction) - 4.642 m/s (in the west direction)
[tex]\rm v_J/Ice[/tex] = -6.5 m/s (in the south direction)
[tex]\rm v_M/J[/tex] = [tex]\rm v_M/Ice - v_J/Ice[/tex]
[tex]\rm v_M/J[/tex] = (-9.373 m/s) (in south direction) - (-6.5 m/s) (in south direction) - 4.642 m/s (in west direction)
[tex]\rm v_M/J[/tex] = -2.873 m/s (in the south direction) - 4.642 m/s (in the west direction)
|[tex]\rm v_M/J[/tex]| = √((-2.873 m/s)² + (-4.642 m/s)²) = 5.459 m/s
θ = 59.3°
θ = 180° - 59.3° = 120.7°
Therefore, Mary's velocity with respect to John has a magnitude of approximately 5.459 m/s and a direction of approximately 120.7° relative to due south.
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A car traveling 45.0 m/s starts to accelerate at 4.00 m/s2. How far does this car travel after 3.00 seconds?
141 m
147 m
153 m
204 m
Answer:
153 m
Explanation:
Given:
A = 4m/s^2
V₁ = 45m/s
V = V₀ + at = ( 45 + 4 × 3 m/s) = 57 m/s
2ax = v^2 - v₀^2
∴ x = v^2-v₀^2/2a
=57^2-45^2/2*4
153 m
The distance traveled by the car after 3 seconds is 135 meters. Therefore, option C is correct.
Given:
Initial velocity = 45.0 m/s
Acceleration = 4.00 m/s²
Time = 3.00 s
To calculate the distance traveled by a car after 3.00 seconds, the kinematic equation can be used: [tex]s = ut + \frac{1}{2} at^2[/tex]
Where:
s = distance traveled
u = initial velocity
t = time
a = acceleration
Substituting the values in the formula:
[tex]s = 45\times 3 + \frac{1}{2} \times 4 \times 3^2\\[/tex]
s = 135 + 2 × 9
s = 135 + 18
s = 153 meters
Therefore, this car having an initial velocity of 45m/s and acceleration of 4 m/s² will travel 153 meters in three seconds.
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The rocket fuel container says it possesses an impulse of 250,000 N•s. It burns through its fuel in a time period of 0.25s, and the rocket gets pushed a distance of 1046 m. How much work was done on the stolen rocket?.
Must everything that is given
The required tension in cable AB is 1200 N. Determine (a) the vertical force P that must be applied to the pedal, (b) the corresponding reaction at C. The surface of the inclined plane shown is frictionless. If F = 30 N, what is the magnitude of the force exerted on the 3.0-kg block by the 2.0-kg block?
The vertical force P that need to be applied to the pedal is 500 N.The corresponding reaction at C is 1300N. The magnitude of the pressure exerted on the three.zero-kg block via the two.0-kg block is eighteen N.
1. a) Taking Moments about C & equating to Zero.
+ ∑M_c = 0 ⇒
P x300 = 1200 x 125 =0
So, P = 500 N.
b) Applying the vertical of equilibrium along horizontal & vertical directions.
+Σ F_x = 0⇒ Cx - 1200 0
so, Cx = 1200 N
+ΣFy = 0 ⇒ Cy - P = 0
so, Cy = P = 500N
So, Reaction at C.
[tex]R_c=\sqrt{C_x^2+C_y^2}\\= \sqrt{(1200)^2+(500)^2}[/tex]
= 1300 N.
2. The net force on the two blocks is calculated by applying Newton's second law of motion as shown below;
[tex]\sum F_x = ma\\\\F+m_2gcos\theta - F_{3n} = Fnet\\\\F+m_2gcos\theta - m_{3g} = F_{net}\\\\(30) + (2 * 9.8 * cos 30) - (3 * 9.8) = F_{net}\\\\17.6 N = F_{net}\\\\F_{net} = 18 N[/tex]
Magnitude refers to the size or degree of something, often used in the context of scientific measurements or observations. In physics, magnitude typically refers to the strength or intensity of a physical quantity, such as the magnitude of a force or the magnitude of an electric field. In astronomy, magnitude is used to describe the brightness of celestial objects, such as stars, with a larger magnitude indicating a fainter object.
Magnitude can refer to the size of a number or vector, which is often represented by its absolute value. Magnitude is also a concept in geometry, where it refers to the size or length of a geometric object, such as a line segment or a vector. Magnitude is a useful concept in various fields of study, helping to quantify and compare the size, strength, or intensity of different phenomena.
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Complete Question: -
1. The required tension in cable AB is 1200 N. Determine (a) the vertical force P that must be applied to the pedal, (b) the corresponding reaction at C.
2. The surface of the inclined plane shown is frictionless. If F = 30 N, what is the magnitude of the force exerted on the 3.0-kg block by the 2.0-kg block?
12. What does temperature measure?
O A. The density of an object
OB. The energy of particles
O C. The chemical bonds between particles
O D. The electrical charge of particles
A sled rider having a combined mass of 125 kg travels down the slope as shown in the
figure. A friction force of 2 N acts between the slope and the sled. If he starts at rest
on the top of the slope, calculate the speed (in m/s) of the sled rider when he reaches
the bottom of the slope. [Enter the number up to one decimal place]
[Hint: Use conservation of total energy, use trigonometry to find the length of the
slope, s and use it in Wother]
The conservation of energy principle, which states that a system's total mechanical energy is conserved in the absence of external forces, will be used to solve this issue. The Earth and the sled rider make up the system in this instance.
In the absence of outside influences, does the overall quantity of mechanical energy in a closed system remain constant?The mechanical energy will be constant in a closed system, one in which there are no external dissipative forces at work. In other words, nothing will alter (become more or less). The Law of Conservation of Mechanical Energy is what we refer to as this.
What is the circumstance in which mechanical energy is conserved according to the concept of conservation of energy?The lone circumstance in which mechanical energys conserved is that all the forces acting on it should be conservative forces.ie no friction or heat loss should be there!!.
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Part b from question 5 says briefly explain how an expirement would be different from the observational study you have used as an example
An experiment is a research design in which the researcher manipulates one or more variables to observe the effect on another variable, while an observational study involves observing and measuring variables without any manipulation.
How is an experiment different from the observational study?In an experiment, the researcher has control over the variables being studied and can isolate the effect of the independent variable on the dependent variable, whereas in an observational study, the researcher cannot control or manipulate variables, and thus cannot establish a cause-and-effect relationship between variables.
Also, in an experiment, participants are usually randomly assigned to different conditions, while in an observational study, participants are typically observed in their natural setting without any manipulation. This allows for more control and precision in an experiment, but also means that the results may not be as applicable to real-world situations as those from an observational study.
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The skin keeps __________ and ________ out of the body
Answer:
stable bone
save from sun rays