The bug will cross the sticky region once in each cycle of its motion, where a cycle is defined as one complete round trip from the top of the bowl to the bottom and back to the top.
To find the number of cycles the bug goes through, we can use conservation of mechanical energy. At the top of the bowl, the bug has only potential energy, which is converted to kinetic energy as it slides down the bowl. At the bottom of the bowl, all of the potential energy has been converted to kinetic energy, and as the bug slides up the other side of the bowl, the kinetic energy is converted back into potential energy. At the top of the bowl again, the bug has only potential energy, and the cycle repeats.
Because there is no friction (except for the sticky patch), the total mechanical energy of the system is conserved. Therefore, the potential energy at the top of the bowl is equal to the potential energy at the bottom of the bowl, and the kinetic energy at the bottom of the bowl is equal to the kinetic energy at the top of the bowl.
We can set the potential energy at the top of the bowl to zero, and use the conservation of energy to find the potential energy at the bottom of the bowl:
mgh = (1/2)mv^2
where m is the mass of the bug, g is the acceleration due to gravity, h is the depth of the bowl, and v is the speed of the bug at the bottom of the bowl.
Solving for v, we get:
v = sqrt(2gh)
Plugging in the numbers, we get:
v = sqrt(29.810.12) = 0.775 m/s
The time it takes for the bug to slide from the top of the bowl to the bottom and back up to the top is twice the time it takes to slide from the top to the bottom:
t = 2sqrt(2h/g) = 2sqrt(2*0.12/9.81) = 0.774 s
Therefore, the frequency of the bug's motion is:
f = 1/t = 1/0.774 = 1.29 Hz
Since the bug completes one cycle in each oscillation, the bug will cross the sticky region 1.29 times per second, or approximately once every 0.78 seconds.
A 12 volt power supply is connected
to two 30 Ohm resistors in parallel.
What is the voltage drop across the
resistors?
12 V
30 Ω
30 Ω
[?] volts
24 volts is the voltage drop across each of the resistors in the parallel configuration.
When resistors are connected in parallel, they share the same voltage across them. Therefore, the voltage drop across each resistor in this scenario would be the same.
Given:
Power supply voltage (V) = 12 V
Resistance of each resistor (R) = 30 Ω
Since the resistors are in parallel, the total resistance (R_total) can be calculated using the formula:
1/R_total = 1/R1 + 1/R2
Substituting the values:
1/R_total = 1/30 Ω + 1/30 Ω
1/R_total = 2/30 Ω
R_total = 15 Ω
Now, we can find the current flowing through the resistors (I) using Ohm's Law:
I = V / R_total
I = 12 V / 15 Ω
I = 0.8 A
Since the voltage drop across each resistor is the same, we can find it using Ohm's Law:
V_drop = I * R
V_drop = 0.8 A * 30 Ω
V_drop = 24 V
Therefore, the voltage drop across each of the resistors in the parallel configuration is 24 volts.
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When the dried-up seed pod of a scotch broom plant bursts open, it shoots out a seed with an initial velocity of 2.65 m/s
at an angle of 30.0 ∘ below the horizontal. The seed pod is 0.460 m
above the ground.
How long does it take for the seed to land?
t= ? sec
What horizontal distance does it cover during its flight?
x=? M
Answer:
To solve this problem, you'll need to break the initial velocity of the seed into its horizontal and vertical components, then use the equations of motion to find the time of flight and horizontal distance.
The initial velocity (v) of the seed is 2.65 m/s. The angle it's launched at (θ) is 30.0 degrees below the horizontal. The height (h) it's launched from is 0.460 m.
First, calculate the horizontal (v_x) and vertical (v_y) components of the velocity. Because the seed is launched downward, the vertical component will be negative:
v_x = v * cos(θ) = 2.65 m/s * cos(30.0) = 2.29 m/s
v_y = v * sin(θ) = -2.65 m/s * sin(30.0) = -1.325 m/s
Next, use the equation of motion to find the time it takes for the seed to hit the ground:
h = v_y * t + 0.5 * g * t^2
Where g is the acceleration due to gravity, which is approximately 9.8 m/s². Solving the equation for t gives:
t = (-v_y - sqrt((v_y)^2 - 4 * 0.5 * g * (-h))) / (2 * 0.5 * g)
Plugging in the values:
t = (1.325 + sqrt((-1.325)^2 - 4 * 0.5 * 9.8 * (-0.460))) / (2 * 0.5 * 9.8)
t = 0.182 seconds
Finally, use the horizontal velocity and time of flight to find the horizontal distance the seed covers:
x = v_x * t = 2.29 m/s * 0.182 s = 0.417 m
So, the seed lands after approximately 0.182 seconds and travels approximately 0.417 meters horizontally.
What is the smallest part of a compound called?
element
O
molecule
O
atom
O
mixture
o
Answer:
Here is your answer,thanks for using brainly!
Explanation:
B:Molecule
Molecules usually consist of 2 atoms linked together,however some molecules consist of thousands of atoms!
Here is a list of smalles to largest with the answers provided
Molecules
Atoms
Elements
Mixtures
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calculate the work done by gravity as a 3.9 kg object is moved from point a to point b
Given:
The mass of the object, m=3.9 kg
To find:
The work done by gravity.
Explanation:
The work done by gravity does not depend on the path in which the object is brought from point A to point B. The work done depends only on the height difference between point A and point B.
From the figure, the height difference between point A and point B is h=2 m
The work done by the gravity when the object is moved from point A to point B is given by,
\(W=mgh\)Where g is the acceleration due to gravity.
On substituting the known values,
\(\begin{gathered} W=3.9\times9.8\times2 \\ =76\text{ J} \end{gathered}\)Final answer:
The work done by the gravity on the object is 76 J.
the weight of an object is measured in air to be 7N the object is then immersed in water and its apparent weight is measured to be 4N determined the buoyant force and state whether or not the object float
The buoyant force can be determined by subtracting the apparent weight of the object in water from its weight in air. In this case, the buoyant force would be 7N - 4N = 3N.
Based on the information provided, since the buoyant force (3N) is less than the weight of the object (7N), the object will not float.
Floating occurs when the buoyant force is greater than or equal to the weight of the object.
In this scenario, the object will experience a net downward force, indicating that it will sink rather than float in water.
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A compound microscope has a barrel length of =159.0 mm and an objective with a 4.070 mm focal length. The total angular magnification of the microscope is −411.0. Using the approximation that the barrel length is large relative to the focal lengths, determine the angular magnification of the eyepiece.
A microscope's objective lens has a focal length of 4 cm, whereas the eye lens's focal length is 8 cm. if 24 cm is the minimum distance at which a person can see clearly,
How does a microscope use magnification?When an object is magnified, it appears in a microscope image at a scale bigger than its true size. Only when it is able to see more specifics of an item in the photograph than when studying the thing without the use of a magnifying glass does magnification serve a beneficial purpose.
What magnification do 10x and 4x represent?Scanning objective lenses typically have a magnification of 4x, and when paired with a 10x eyepiece lens, they have a total magnification of 40x.
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the kinetic energy of a body executing simple harmonic motion of amplitude A is equal to the potential energy when its displacement is
Answer:
My answer to the question is "when its displacement is zero.
A man yells across a canyon to his friend who hears the yell 3.25 seconds later. How far away is the man's friend? (speed of sound in air = 343 m/s)
The man's friend is at a distance 552.5 m away.
Speed of sound in air, v = 340 m/s
Time after which the echo is heard, t = 3.25 s
The expression for the total distance covered by the sound in the given time,
d = v x t
d = 340 x 3.25
d = 1105 m
Therefore, the distance where the friend is staying would be half of the total distance covered by the sound during the given time.
So, the distance of the friend from the man,
d' = d/2
d' = 1105/2
d' = 552.5 m
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On the surface of the earth the weight of an object is 200 lb. Determine the height of the
object above the surface of the earth, in miles, for the object to register a weight of 125
pounds.
Answer:
The height of the object is 5007.4 miles.
Explanation:
Given that,
Weight of object = 200 lb
We need to calculate the value of \(Gmm_{e}\)
Using formula of gravitational force
\(F=\dfrac{Gmm_{e}}{r^2}\)
Put the value into the formula
\(200=\dfrac{Gmm_{e}}{(3958.756)^2}\)
\(200\times(3958.756)^2=Gmm_{e}\)
\(Gmm_{e}=3.134\times10^{9}\)
We need to calculate the height of the object
Using formula of gravitational force
\(F=\dfrac{Gmm_{e}}{r^2}\)
Put the value into the formula
\(125=\dfrac{200\times(3958.756)^2}{r^2}\)
\(r^2=\dfrac{200\times(3958.756)^2}{125}\)
\(r^2=25074798.5\)
\(r=\sqrt{25074798.5}\)
\(r=5007.4\ miles\)
Hence. The height of the object is 5007.4 miles.
What is the potential energy of a puppy that weighs 18 N istting in a high chair 2 m high?
Answer:
Potential energy =mass* acceleration due to gravity * height
mass*acceleration due to gravity =weight
hence potential energy of the puppy= weight * height
=18*2
=36 joule
What is the current theory about the formation of the solar system?
Responses
About 14 billion years ago, several supernova events scattered all the known elements throughout the galaxy. The magnetic elements were attracted to each other and formed the early celestial bodies that eventually became the planets of the solar system.
About 14 billion years ago, several supernova events scattered all the known elements throughout the galaxy. The magnetic elements were attracted to each other and formed the early celestial bodies that eventually became the planets of the solar system.
A big bang occurred in the solar system as a result of a fusion reaction. All the matter in the solar system that had been clumped together was shattered and sent flying. As new pieces of matter connected, all the celestial bodies of the solar system were formed.
A big bang occurred in the solar system as a result of a fusion reaction. All the matter in the solar system that had been clumped together was shattered and sent flying. As new pieces of matter connected, all the celestial bodies of the solar system were formed.
The area of the universe that was to become the solar system went through a period of vast expansion as a result of rapid radioactive decay that left behind clouds of dust and gases. The excess clouds and gases were used to form the various parts of the solar system.
The area of the universe that was to become the solar system went through a period of vast expansion as a result of rapid radioactive decay that left behind clouds of dust and gases. The excess clouds and gases were used to form the various parts of the solar system.
The solar system began as a cloud of dust and gas that condensed, forming a bulging middle and an outer disk. The bulging middle of the cloud became the sun, and the rest of the dust and gas formed the planets, orbiting the sun in the same plane.
The current theory about the formation of the solar system is that it began as a cloud of dust and gas, known as the solar nebula which is the last response.
What happened to the nebula?The nebula collapsed under its own gravity, forming a spinning disk with a bulging middle that became the sun. The remaining dust and gas in the disk coalesced into small bodies, which collided and stuck together, forming the planets.
This process, known as accretion, resulted in the four inner planets, which are small and rocky, and the four outer planets, which are large and gas-rich.
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Question # 40
A body falls freely under gravity. If speeds is v when it has lost an amount x of the gravitational P.E, then its mass is:
2x / v2
2x / v3
2x / v4
none
please give me its solution
Answer:
Potential Energy = x = m g h
Kinetic energy = 1/2 m v^2
Assuming the mass fall from rest
1/2 m v^2 = m g h
v^2 = 2 g h
So the speed attained is independent of the mass
Also, x / v does not have the units of mass
So the solution is none of the above.
is
5
The specific heat of copper is 0.385 J/g
°C. How much thermal energy is required
to increase the temperature of a 20g
sample of copper from 20°C to 50°C?
Q = m CAT
A 154 )
B 231 )
C 308 )
D 385 )
Answer:
Required energy Q = 231 J
Explanation:
Given:
Specific heat of copper C = 0.385 J/g°C
Mass m = 20 g
ΔT = (50 - 20)°C = 30 °C
Find:
Required energy
Computation:
Q = mCΔT
Q = 20(0.385)(30)
Required energy Q = 231 J
The speed of x-rays is 300 000. m/s. In scientific notation, and with the correct number of significant figures, this speed is… *
Answer:
3.0 x 10 and the exponent on ten is 5.
Explanation:
You are moving the decimal point over to the left 5 times, making the exponent a positive 5 and then you would put a decimal after 3. Making it 3.0 x 10, and the exponent 5.
The speed of x-rays in scientific notation is 3.0 x 10⁶ m/s.
The given parameters;
speed of the x-ray, v = 300,000 m/s
The standard form of the given number represents the scientific notation of the number.
To represent a number in standard form, multiply the number in terms of power or exponent of 10. The value of the exponent represents the number of available zeros present.In scientific notation the speed of the x-ray can be expressed as follows;
300,000 m/s = 3.0 x 10⁶ m/s
Thus, the speed of x-rays in scientific notation is 3.0 x 10⁶ m/s.
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Sam moves an 800 N wheelbarrow 5 meters in 15 seconds. How much work did he do?
Answer:
work done= force × displacement
=800×5
=4000J
Explanation:
The amount of work done is the result of the magnitude of force applied and the displacement of the body due to the force applied. Therefore, work done is defined as the product of the applied force and the displacement of the body.
a ball of mass 100g moving at a velocity of 100m/s collides with another ball of mass 400g moving at 50m/s in same direction, if they stick together calculate the velocity and loss of energy
Answer:
Velocity of the two balls after collision: \(60\; \rm m \cdot s^{-1}\).
\(100\; \rm J\) of kinetic energy would be lost.
Explanation:
VelocityBecause the question asked about energy, convert all units to standard units to keep the calculation simple:
Mass of the first ball: \(100\; \rm g = 0.1\; \rm kg\).Mass of the second ball: \(400\; \rm g = 0.4 \; \rm kg\).The two balls stick to each other after the collision. In other words, this collision is a perfectly inelastic collision. Kinetic energy will not be conserved. The velocity of the two balls after the collision can only be found using the conservation of momentum.
Assume that the system of the two balls is isolated. Thus, the sum of the momentum of the two balls will stay the same before and after the collision.
The momentum of an object of mass \(m\) and velocity \(v\) is: \(p = m \cdot v\).
Momentum of the two balls before collision:
First ball: \(p = m \cdot v = 0.1\; \rm kg \times 100\; \rm m \cdot s^{-1} = 10\; \rm kg \cdot m \cdot s^{-1}\).Second ball: \(p = m \cdot v = 0.4\; \rm kg \times 50\; \rm m \cdot s^{-1} = 20\; \rm kg \cdot m \cdot s^{-1}\).Sum: \(10\; \rm kg \cdot m \cdot s^{-1} + 20 \; \rm kg \cdot m \cdot s^{-1} = 30 \; \rm kg \cdot m \cdot s^{-1}\) given that the two balls are moving in the same direction.Based on the assumptions, the sum of the momentum of the two balls after collision should also be \(30\; \rm kg \cdot m \cdot s^{-1}\). The mass of the two balls, combined, is \(0.1\; \rm kg + 0.4\; \rm kg = 0.5\; \rm kg\). Let the velocity of the two balls after the collision \(v\; \rm m \cdot s^{-1}\). (There's only one velocity because the collision had sticked the two balls to each other.)
Momentum after the collision from \(p = m \cdot v\): \((0.5\, v)\; \rm kg \cdot m \cdot s^{-1\).Momentum after the collision from the conservation of momentum: \(30\; \rm kg \cdot m \cdot s^{-1}\).These two values are supposed to describe the same quantity: the sum of the momentum of the two balls after the collision. They should be equal to each other. That gives the equation about \(v\):
\(0.5\, v = 30\).
\(v = 60\).
In other words, the velocity of the two balls right after the collision should be \(60\; \rm m \cdot s^{-1}\).
Kinetic EnergyThe kinetic energy of an object of mass \(m\) and velocity \(v\) is \(\displaystyle \frac{1}{2}\, m \cdot v^{2}\).
Kinetic energy before the collision:
First ball: \(\displaystyle \frac{1}{2} \, m \cdot v^2 = \frac{1}{2}\times 0.1\; \rm kg \times \left(100\; \rm m \cdot s^{-1}\right)^{2} = 500\; \rm J\).Second ball: \(\displaystyle \frac{1}{2} \, m \cdot v^2 = \frac{1}{2}\times 0.4\; \rm kg \times \left(50\; \rm m \cdot s^{-1}\right)^{2} = 500\; \rm J\).Sum: \(500\; \rm J + 500\; \rm J = 1000\; \rm J\).The two balls stick to each other after the collision. Therefore, consider them as a single object when calculating the sum of their kinetic energies.
Mass of the two balls, combined: \(0.5\; \rm kg\).Velocity of the two balls right after the collision: \(60\; \rm m\cdot s^{-1}\).Sum of the kinetic energies of the two balls right after the collision:
\(\displaystyle \frac{1}{2} \, m \cdot v^{2} = \frac{1}{2}\times 0.5\; \rm kg \times \left(60\; \rm m \cdot s^{-1}\right)^2 = 900\; \rm J\).
Therefore, \(1000\; \rm J - 900\; \rm J = 100\; \rm J\) of kinetic energy would be lost during this collision.
A 75.0 kg man pushes on a 500,000 kg wall for 250 s but it does not move.
a. How much work does he do on the wall? ____________
b. How much energy is used?__________
c. How much power is exerted?____________
Since no work is done, the power exerted is zero. Therefore, the man exerts no power on the wall.
What is force?In physics, force is defined as any action that can change the motion of an object or cause an object to accelerate. Force is a vector quantity, meaning that it has both magnitude (size or strength) and direction. The unit of force in the International System of Units (SI) is the Newton (N), which is defined as the amount of force required to accelerate a mass of one kilogram at a rate of one meter per second squared (1 N = 1 kg × 1 m/s^2). Force can be measured using a variety of instruments, such as spring scales, strain gauges, or force plates. Some common types of forces include gravitational force, electromagnetic force, frictional force, and normal force. The study of forces and their effects on the motion of objects is known as mechanics and is a fundamental concept in physics.
Here,
a. The man does not do any work on the wall because the wall does not move. Work is only done when there is a displacement in the direction of the force applied.
b. Since no work is done, no energy is used or transferred.
c. The power exerted by the man can be calculated using the formula:
Power = Work / Time
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A skier accelerates downhill on their skis. Is TME conserved? Explain.
I do not see a pick an awsnser bAr
Question 1 An object of mass 20kg accelerates from rest to a velocity of 10m/s in 5 sec. calculate the distance covered by the object
Answer:
25 m
Explanation:
Let's assume that its acceleration is constant. We can determine the acceleration of the object by its definition
\(a= \frac{\Delta v}{\Delta t} = \frac{10-0(\frac ms)}{5 s} = 2 \frac m{s^2}\)
Now we can write the equation of motion
\(s(t)= s_0 + v_0t + \frac12at^2\)
where, the two terms \(s_0\ v_0\) represent the initial position and velocity respectively. Replacing the values we have ("from rest" means that initial velocity is 0)
\(s(5) = 0+0(5)+\frac12 2 (5)^2 = 25 m\)
Part A
What is the magnitude of the momentum of a 0.0073-kg marble whose speed is 0.65 m/s?
Express your answer to two significant figures and include appropriate units.
Part B
What is the speed of a 0.136-kg baseball whose momentum has a magnitude of 3.14 kg⋅m/s?
Express your answer to two significant figures and include appropriate units.
Answer:
(A). The magnitude of the momentum of the marble is 0.004745 kg m/s.
(B). The speed of baseball is 23.0 m/s
Explanation:
Given that,
Mass of marble = 0.0073 kg
Speed = 0.65 m/s
(A). We need to calculate the magnitude of the momentum of the marble
Using formula of momentum
\(p = mv\)
Where, m = mass
v = velocity
Put the value into the formula
\(p=0.0073\times0.65\)
\(p=0.004745\ kg m/s\)
(B). Mass of baseball = 0.136 kg
Momentum of baseball = 3.14 kg m/s
We need to calculate the speed of baseball
Using formula of momentum
\(p=mv\)
\(v=\dfrac{p}{m}\)
Put the value into the formula
\(v=\dfrac{3.14}{0.136}\)
\(v=23.0\ m/s\)
Hence, (A). The magnitude of the momentum of the marble is 0.004745 kg m/s.
(B). The speed of baseball is 23.0 m/s
in this experiment, the thermometer bulb should be positioned in the vapor and not in the liquid to determine the boiling point of your liquid.
This statement is correct. In order to determine the boiling point of a liquid, the thermometer bulb should be positioned in the vapor above the liquid, not in the liquid itself.
When a liquid is heated to its boiling point, the temperature of the liquid will remain constant until all the liquid has turned into vapor. At this temperature, the vapor pressure of the liquid is equal to the atmospheric pressure, causing the liquid to boil. By positioning the thermometer bulb in the vapor above the liquid, it will accurately measure the temperature of the liquid at its boiling point. the boiling point of any liquid is the temperature at which the liquid starts to boiling. If the thermometer bulb were positioned in the liquid, it would measure the temperature of the liquid before it reaches its boiling point, giving an incorrect reading.
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in this experiment, the thermometer bulb should be positioned in the vapor and not in the liquid to determine the boiling point of your liquid. is this statement correct?
Consider a regular solution, for which energy
w =5 kJ/mol
At what temperature, in K, will a miscibility limit emerge?
At room temperature,300 K, will a miscibility limit emerge. At the temperature less than, the miscibility will fall below 1%.
What is temperature?Temperature directs the hotness or coldness of a body. In clear terms, it is the method of finding the kinetic energy of particles within an entity. Faster the motion of particles, more the temperature.
Hence, at room temperature,300 K, will a miscibility limit emerge. At the temperature less than, the miscibility will fall below 1%.
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Answer pleaseeeee
Question 2 of 10
Which is directly proportional to your weight on a planet's surface?
OA. The distance from the surface to the center of the planet
B. Only the mass of the planet
OC. Only your mass
OD. Your mass and the mass of the planet
Answer:
from my side the will be b only the mass of the planet thank you
Answer:
D
Explanation:
W=mg
g=GM/r²(G=Gravitational constant, M=mass of earth, r=Radius of earth)
>>W=m(GM/r²)
W is directly proportional to mass of earth and mass of your body
5kg object with two forces acting on it: 8N to the right and 3N to the left. calculate the acceleration of the object
Answer:
a = 1 m/s^2
Explanation:
if we assume that right is the positive x direction and y is the negative x-direction then we get:
Fr = 8N
Fl = -3N
We then find the net force acting upon the object
Ft = Fr + Fl
Ft = 8N - 3N
Ft = 5N
After we find net force acting upon the object we can then use Newton's 2nd Law to find its acceleration.
Ft = m*a
Isolate accerleration
a = Ft / m
a = 5N / 5kg
a = 1 m/s^2
At which point is there the greatest amount of potential energy?
What force acts on a projectile in the horizontal direction?
The force that acts on a projectile in the horizontal direction is Gravitational force.
A projectile is an object upon which the only force is gravity. Gravity acts to influence the vertical motion of the projectile, thus causing a vertical acceleration. The horizontal motion of the projectile is the result of the tendency of any object in motion to remain in motion at constant velocity.
Due to the absence of horizontal forces, a projectile remains in motion with a constant horizontal velocity. Horizontal forces are not required to keep a projectile moving horizontally. Hence, The only force acting upon a projectile is gravity.
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I can give you 50 points.
Freddy is participating in a pumpkin lifting contest. The 68 kg pumpkin starts at rest on the ground. If Freddy exerts a 720N force on the pumpkin, what is the acceleration of the pumpkin as he lifts it off the ground?
Draw a Force Diagram for the pumpkin. Indicate the direction of the sum of the forces.
Draw a Motion Diagram for the pumpkin. Is your motion diagram consistent with your force diagram?
Use Newton’s 2nd Law to find the pumpkin’s acceleration.
Answer:
Freddy is participating in a pumpkin lifting contest. The 68 kg pumpkin starts at rest on the ground. If Freddy exerts a 720N force on the pumpkin, what is the acceleration of the pumpkin as he lifts it off the ground?
Explanation:
1. Fill in the gap:
Internal Energy is the energy of
Internal energy is the sum of
energy.
the particles in a substance.
energy and
As temperature increases so does a substances
When a substance changes state its
increases/decreases.
energy
energy.
Internal energy is the microscopic energy contained in a substance, given by the random, disordered kinetic energy of the molecules. Internal energy is the sum of potential energy of the system and the system's kinetic energy.
This implies that kinetic energy—the energy that results from the system's overall movement—is not included in the internal energy of the system if the system is moving and contains kinetic energy. The system's internal energy is unaffected by this macroscopic potential energy even if we raise the entire structure above the earth. On the one hand, a system can be moving while its internal energy is changing, while on the other hand, a system can be perfectly static and have no apparent energy while its internal energy is changing.
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A body with mass m slides down a frictionless ramp inclined at 600, with an initial speed v1 = 3 m/s,
starting at height h, and continues its motion upward on a 300 inclined ramp with a friction. Than this
body hits a spring which is fixed to a wall and compresses it 10 cm. The spring is initially at a distance R
on horizontal plane, and at height h. Find:
a) The speed v2 at the point 0, where the body starts to climb up to 300 inclined ramp, in terms of h.
b) The speed v3 where it hits the spring.
c) The spring constant k.
m=0.1 kg, µk=0.1, R=2.5 m., v1=3 m/s, Cos(600) = 0.5, Sin(600)=0.87, x=10 cm. and g= 10 m/s2 .
Going down the first ramp:
• net force parallel to the ramp:
∑ F = W sin(60°) = m a₁
(W for weight)
• net force perpendicular to the ramp:
∑ F = N + W cos(60°) = 0
(N for normal force)
The body has mass 0.1 kg, and with g = 10 m/s², its weight is W = 1 N. So in the first equation, we get
(1 N) sin(60°) = (0.1 kg) a₁ → a₁ ≈ 8.7 m/s²
Let d₁ be the distance the body moves down the ramp, i.e. the distance along the ramp between the starting point and the point O. Then
sin(60°) = h / d₁ → d₁ = 2h/√(3) ≈ 1.15h
Given an initial speed v₁ = 3 m/s, we find the speed v₂ at point O to be
v₂² - (3 m/s)² = 2 (8.7 m/s²) d₁
v₂ ≈ √(9 m²/s² + (17.4 m/s²) (1.15h))
v₂ ≈ √(9 m²/s² + (20 m/s²) h)
Going up the second ramp:
• net parallel force:
∑ F = -Fr - W sin(30°) = m a₂
(Fr for friction)
• net perpendicular force:
∑ F = N - W cos(30°) = 0
sin(30°) = cos(60°), and cos(30°) = sin(60°), so the second equation gives N = 0.87 N. Then with µ = 0.1, we have Fr = µ N = 0.087 N. The first equation then gives
-0.087 N - 0.5 N = (0.1 kg) a₂ → a₂ ≈ -5.9 m/s²
We now have
tan(30°) = h/R → h = (2.5 m)/√3 ≈ 1.4 m
(which, by the way, tells us that v₂ ≈ 6.2 m/s)
Then the distance traveled up the ramp is
d₂ = √(h² + R ²) ≈ 2.9 m
Use this to solve for the speed at the top of the ramp:
v₃² - v₂² = 2 (-5.9 m/s²) d₂
v₃ = √((6.2 m/s)² - (11.8 m/s²) (2.9 m)) ≈ 2.0 m/s
At the top of the second ramp:
• net parallel force:
∑ F = -Fsp - W sin(30°) = m a₂
(Fsp for spring)
• net perpendicular force:
∑ F = N - W cos(30°) = 0
By Hooke's law, Fsp = kx, so in the first equation we get
-k (0.10 m) - (1 N) cos(60°) = (0.1 kg) (-5.9 m/s²)
→ k ≈ 0.87 N/m
Say an impulse is applied opposite the go-kart's direction of travel. What happens to
the go-kart if its momentum + impulse = 0?
The go kart stops comes to a stop.
The go kart slows down but keeps moving.
The go kart speeds up.
There is no change in the speed of the go kart.
If the impulse is strong enough and lasts for a sufficient amount of time, the go-kart will eventually come to a stop.
Option A is correct.
What is meant by impulse?impulse is described as the integral of a force, F, over the time interval, t, for which it acts. Since force is a vector quantity, impulse is also a vector quantity.
If the force is insufficient to stop the go-kart entirely, it will slow down but continue to move. The force and duration of the impulse, along with the mass and speed of the go-kart, will all affect how much deceleration occurs.
Given that momentum plus impulse equals zero, the go-kart's change in momentum as a result of the impulse will be equal in amount but will move in the opposite direction of its original momentum.
As a result, the go-kart's final momentum will be zero, suggesting that it has either stopped or is travelling very slowly.
Learn more about impulse at: https://brainly.com/question/229647
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