The gauge pressure of the water at the exit end of the pipe is -1281.125 kPa. Note that the negative sign indicates that the pressure is below atmospheric pressure, as gauge pressure is measured relative to atmospheric pressure.
What is Atmospheric Pressure?
Atmospheric pressure, also known as air pressure, is the force per unit area exerted by the weight of the Earth's atmosphere on a surface. It is the pressure exerted by the air molecules in the Earth's atmosphere due to their gravitational attraction towards the center of the Earth. Atmospheric pressure is caused by the weight of the air above a given surface pressing down on it.
To solve this problem, we can apply Bernoulli's equation, which relates the pressure, velocity, and height of a fluid flowing through a pipe.
We can start by calculating the velocity at the exit using the equation of continuity, which states that the mass flow rate of an incompressible fluid remains constant along a streamline:
Substituting the given values:
[tex]V^{2}[/tex] = (0.025[tex]m^{2}[/tex] * 2.5 m/s) / 0.010 [tex]m^{2}[/tex]
[tex]V^{2}[/tex] = 62.5 m/s
Now, we can substitute the known values into Bernoulli's equation to find the gauge pressure at the exit:
[tex]P^{2}[/tex]= P1 + (1/2)ρ([tex]v1^{2}[/tex] - [tex]v2^{2}[/tex])
[tex]P^{2}[/tex]= 46 kPa + (1/2) * 1000 kg/m^3 *[tex](2.5 m/s)^{2}[/tex] - [tex](62.5 m/s)^{2}[/tex]
[tex]P^{2}[/tex] = 46 kPa + 625 kPa - 1953.125 kPa
[tex]P^{2}[/tex] = -1281.125 kPa
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Question 3: 2D Kinematics (Vectors) For the the vectors A and B in Figure below, use the method of components to find the magnitude and the direction or: (5 marks each) (a) Vector sum of [A+B], (b) Vector sum of [A-B]. (c) Vector difference of [B-A]. (d) Vector difference of [2A-B].
The question is incomplete. Here is how to get magnitude and direction
How to get magnitude and direction
To find the magnitude and direction of a vector, follow these steps:
Write the vector in component form:
For a two-dimensional vector, write it as <x, y>, where x and y are the components of the vector along the x-axis and y-axis, respectively. For a three-dimensional vector, write it as <x, y, z>, where x, y, and z are the components of the vector along the x-axis, y-axis, and z-axis, respectively.
Calculate the magnitude of the vector:
The magnitude of a vector is the length of the vector, which can be found using the Pythagorean theorem. For a two-dimensional vector <x, y>, the magnitude is sqrt(x^2 + y^2). For a three-dimensional vector <x, y, z>, the magnitude is sqrt(x^2 + y^2 + z^2).
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14. Two identical corks float in separate beakers. One beaker contains
water. The other contains a very salty water. Which of the following
statements is true?
The corks both float at the same level in the liquid.
The cork in the very salty water floats at a lower level than the other cork.
The corks will eventually sink.
Both corks are subject to the same buoyant force.
Answer:
Both Corks are subject to the same buoyant force
Explanation:
The buoyant force depends on the volume of the displaced liquid and the density of the liquid, but not the density of the floating object. So the buoyant forces will be the same on each cork whether the water it's floating in is normal or salty.
The caloric theory is the most workable model of heat today.
True
False
Answer:
False
Explanation:
The modern kinetic-molecular model is better than the caloric model, not because it is true, but because it produces more workable results. credited to be the first to demonstrate a clear connection between mechanical energy and heat.
1.
Which of the following does not affect how fast a sound travels?
the density and pressure of the medium in which it travels
the stiffness of the medium in which it travels
MacBook Air
the direction that the sound waves travel
the temperature of the medium in which it travel
Neither MacBook Air nor the direction that the sound waves travel affects the speed of the sound.
A participant is exercising on a Monark cycle ergometer for 5 minutes at a resistance
of 4.5kp and a cadence of 80 RPM. Calculate i) the amount of work performed in 5min
and 2) mean power output for the 5 minutes
Ergometer is a device that standardizes the work and power output. The work done by the cycle ergometer is 109.5 kJ and the power output for the 5 minutes is 353.133 W.
Work done by the engine is defined as the product of force and distance and the unit of work done is the joule (J).
From the given,
resistance of the ergometer = 4.5kp
revolutions per minute = 80 rpm
time taken = 5 minutes
Work done (W) = F × d
= (4.5 × 9.81) × (80 rpm × 6 m/rev × 5)
= 105,948
Work done (W) = 105.94 kJ
Power is the ratio of the work done and time and the unit of power is the watt (W).
Power = Work done / time
= 105.94 × 10³ / 300 (5 minutes = 300 seconds)
= 353.13 W.
Hence the work done by the cycle ergometer is 105.94 kJ and the output power in 5 minutes (300 seconds) is 353.133 W.
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An 80 Ώ resistor has a voltage difference of 12 Volts across its leads.
(a) What is the current through the resistor?
(b) What is the power being dissipated in this resistor?
The resistor is dissipating 1.8 W of power. As a result, 0.15 A is the current flowing through the resistor.
What kind of power does the resistor dissipate?Any equation linking power to current, voltage, and resistance may be used to calculate the power wasted by each resistor because all three variables are known. Since each resistor receives its full voltage, let's use P=V2R P = V 2 R.
(a) We may determine the current flowing through the resistor using Ohm's Law as follows:
I = V/R
where R is the resistance and V is the voltage difference across the resistor.
Therefore, the resistor's current is as follows:
I = 12 V / 80 Ω = 0.15 A
Therefore, the current through the resistor is 0.15 A.
(b) The power being dissipated in the resistor can be calculated using the formula:
P = VI = I²R = V²/R
where P is the power, V is the voltage difference across the resistor, I is the current through the resistor, and R is the resistance.
Substituting the given values, we get:
P = VI = (0.15 A)(12 V) = 1.8 W
Alternatively, we can use the third formula to calculate the power:
P = V²/R = (12 V)²/ 80 Ω = 1.8 W
So, the power being dissipated in the resistor is 1.8 W.
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Please help answer the question
The false statement regarding gender roles is, they stem primarily from biological differences in the sexes. Option b is correct.
Gender roles are based on cultural traditions and societal norms, rather than solely being determined by biological differences between males and females. While biological differences between the sexes may play a role in certain gender-based behaviors or expectations, the vast majority of gender roles are socially constructed and learned through cultural traditions and socialization. Option b is correct.
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Why are water and hydrogen peroxide different substances even though they are both made up of
hydrogen and oxygen atoms?
Answer:
Water and hydrogen peroxide are different substances because they have different chemical formulas and molecular structures. Water has the chemical formula H2O, meaning that it has two hydrogen atoms and one oxygen atom. Hydrogen peroxide has the chemical formula H2O2, meaning that it has two hydrogen atoms and two oxygen atoms. The difference in their molecular structures leads to different chemical and physical properties, such as boiling points, melting points, and reactivity.
Explanation:
A radioactive sample consists of a mixture of a S-35 and P-32 .initially 5% of the activity is due to the S-35 and 95% due to the P-32 .At what subsequent time will the activities of the two nucleide be equal
The time at which the activities of the two nuclides be equal is 2.7 s.
Radioactivity is the process of an unstable atomic nucleus spontaneously splitting or disintegrating and emitting radiation in the form of α-rays, β-rays, or γ-rays.
λ₁ = 0.05
λ₂ = .95
According to the law of radioactive decay, the total number of nuclei in a sample material is directly proportional to the number of nuclei that are undergoing the decaying process in that sample material per unit time.
λ₁N₁ = λ₂N₂
λ₁N₀e⁻(λ₁t) = λ₂N₀e⁻(λ₂t)
λ₁/λ₂ = e⁻(λ₁ - λ₂)t
ln(λ₁/λ₂) = (λ₁ - λ₂)t
Therefore time,
t = ln(λ₁/λ₂)/(λ₁ - λ₂)
t = ln(0.05/.95)/(0.95 - 0.05)
t = -2.94 x -0.9
t = 2.7 s
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3. When 815 Joules of heat is added to a sample of solid copper, the temperature rises
from 12.0°C to 35°C. How many grams of copper were in the sample? Specific heat of Cu
is 0.385 J/g-K.
q=MCdeltaT
Answer:
79.3
Explanation:
We can use the formula:
q = m * c * deltaT
where:
q is the heat added to the system, which is 815 J in this case
m is the mass of the sample we want to find
c is the specific heat of copper, which is 0.385 J/g-K
deltaT is the change in temperature, which is (35 - 12) = 23°C
Plugging in the values given, we get:
815 J = m * 0.385 J/g-K * 23°C
Simplifying this expression yields:
m = 815 J / (0.385 J/g-K * 23°C)
Thus, the mass of the copper sample is:
m = 79.3 g
Therefore, there were approximately 79.3 grams of copper in the sample.
Answer:
Explanation:
We can use the equation q = mCΔT, where q is the amount of heat transferred, m is the mass of the sample, C is the specific heat capacity of the material, and ΔT is the change in temperature.
First, we need to calculate the change in temperature, which is:
ΔT = T₂ - T₁ = 35°C - 12.0°C = 23°C
Next, we can rearrange the equation to solve for the mass of the sample:
m = q / (CΔT)
Substituting the values we have:
m = 815 J / (0.385 J/g-K × 23°C) ≈ 90.2 g
Therefore, the sample of solid copper had a mass of approximately 90.2 grams.
In a stable star, nuclear fusion pushes _________ and gravity pushes _________.
A. outward, outward
B. outward, inward
C. inward, inward
D. inward, outward
Answer:
In a stable star, the force of nuclear fusion is balanced by the force of gravity. The high temperatures and pressures in the core of the star cause atoms to collide and fuse together, releasing energy in the process. This energy is what keeps the star from collapsing under the force of gravity. The outward pressure from the energy released by nuclear fusion pushes outward, while the force of gravity pulls inward. In a stable star, these two forces are balanced, with the inward force of gravity being counteracted by the outward pressure from fusion. This balance allows the star to maintain a stable size and temperature.
Therefore the answer is A. outward, inward.
A container holds a gas consisting of 5.75 moles of oxygen molecules. One in a million of these molecules has lost a single electron. NA=6.022×1023mol−1 , e=1.60×10−19C.
What is the net charge of the gas?
Express your answer to three significant figures and include the appropriate units.
Answer:The oxygen molecules have lost a total of 0.94 coulombs in charge of their electrons.
Explanation:No
Why would God not leave clear, indisputable evidence that the tree in the 100-year old tree by Dr. Joshua Swaimdass is just a week old?
A 18.0-m-long bar of steel expands due to a temperature increase. A 10.0-m-long bar of copper also gets longer due to the same temperature rise. The two bars were originally separated by a gap of 1.1 cm. Assume the steel and copper bars are fixed on the ends.
α(Steel) = 13 x 10^-6 K^-1
α(Copper) = 16.5 x 10^-6 K^-1
1) Calculate the change in temperature if the gap is exactly "closed" by the expanding bars. (Express your answer to two significant figures.)
2) Calculate the distances that the steel stretches. (Express your answer to two significant figures.)
3) Calculate the distances that the copper stretches. (Express your answer to two significant figures.)
A jar of tea is placed in sunlight until it
reaches an equilibrium temperature of 32.4
◦C .
In an attempt to cool the liquid, which has a
mass of 177 g , 95.3 g of ice at 0.0
◦C is added.
At the time at which the temperature of the
tea is 30.7
◦C , find the mass of the remaining
ice in the jar. The specific heat of water
is 4186 J/kg ·
◦ C . Assume the specific heat
capacity of the tea to be that of pure liquid
water.
Answer in units of g.
The tea absorbs 2613420 J of heat energy when it is placed in sunlight until it reaches an equilibrium temperature of 32.4°C.
To calculate the heat energy absorbed by the tea, we can use the formula:
Q = mcΔT
where Q is the heat energy absorbed by the tea, m is the mass of the tea, c is the specific heat capacity of water, and ΔT is the temperature change of the tea.
Using the given values, we get:
m = 500 g
c = 4186 J/kg·°C
ΔT = 32.4°C - 20°C = 12.4°C
Substituting these values into the formula, we get:
Q = (500 g)(4186 J/kg·°C)(12.4°C) = 2613420 J
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--The complete Question is, A jar of tea with a mass of 500 g is initially at a temperature of 20°C. If the jar is placed in sunlight until it reaches an equilibrium temperature of 32.4°C, how much heat energy is absorbed by the tea? Assume the specific heat capacity of the tea to be that of pure liquid water, which is 4186 J/kg·°C.--
String 1 in the figure has linear density 2.60 g/m and string 2 has linear density 3.30 g/m. A student sends pulses in both directions by quickly pulling up on the knot, then releasing it. She wants both pulses to reach the ends of the strings simultaneously.
What should the string length L1 be?
What should the string length L2 be?
Explanation:
We can use the formula for the speed of waves on a string:
v = sqrt(T/μ)
where v is the speed of the wave, T is the tension in the string, and μ is the linear mass density (mass per unit length) of the string.
Let's denote the tension in both strings by T. Since the pulses must reach the ends of both strings simultaneously, we must have:
L1/v1 = L2/v2
where L1 and L2 are the lengths of the strings, v1 is the speed of the wave on string 1, and v2 is the speed of the wave on string 2.
Using the formula above and solving for T, we can eliminate T from this equation to get:
sqrt(μ1/ T)/ L1 = sqrt(μ2/T)/ L2
Squaring both sides and rearranging, we obtain:
L2/L1 = sqrt(μ2/μ1)
Substituting the given values for μ1 and μ2, we get:
L2/L1 = sqrt(3.30/2.60) = 1.126
Solving for one of the lengths, say L1, in terms of the other, we get:
L1 = L2/1.126
Now we need to find the values of L1 and L2 that satisfy the condition that both pulses reach the ends of the strings simultaneously. To do this, we can use the fact that the time it takes for a wave to travel a distance L on a string is given by:
t = L/v
where v is the speed of the wave on the string.
Therefore, if the pulses are to arrive at the ends of the strings simultaneously, we must have:
L1/v1 + L2/v2 = 2L1/v1
Simplifying this equation using the relation L1 = L2/1.126 and the formula for v, we get:
sqrt(T/μ1)L2/1.126/2.60 + sqrt(T/μ2)L2/3.30 = 2L2/1.126sqrt(T/μ1)
Simplifying further and eliminating T, we obtain:
L2 = (2.60/3.30)^2(1.126) L1
Substituting the expression for L1 in terms of L2 that we found earlier, we get:
L2 = (2.60/3.30)^2(1.126) L2/1.126
Solving for L2, we find:
L2 = 2.196 L1
Finally, using the relation L1 = L2/1.126, we get:
L1 = 1.91 m
L2 = 4.20 m
Therefore, the length of string 1 should be 1.91 m and the length of string 2 should be 4.20 m in order for both pulses to reach the ends of the strings simultaneously.
Beta and gamma rays are produced when iodine-131 decays. When patients ingest iodine-131, the beta and gamma rays are used to image and treat cancer. A patient is administered a 20.0mg dose of iodine-131. After 21 days, 3.24mg of iodine-131 remains in the patient's body.
a) Calculate the decay constant of iodine-131.
b) Calculate the half-life of iodine-131.
c) How much iodine-131 will be present in the patient's body 50 days after it was administered?
a. The decay constant of iodine-131 is 0.0502 day^-1.
b. the half-life of iodine-131 is 13.8 days.
c. 1.29 mg of iodine-131 will be present in the patient's body 50 days after it was administered.
How to determine the decay constanta) To calculate the decay constant of iodine-131, we can use the formula:
N = N0 * e^(-λt)
where
N is the amount of iodine-131 remaining after time t,
N0 is the initial amount of iodine-131, and
λ is the decay constant.
We are given that N0 = 20.0 mg and N = 3.24 mg, and t = 21 days. Substituting these values into the formula and solving for λ, we get:
λ = ln(N0/N) / t
= ln(20.0/3.24) / 21
= 0.0502 day^-1
Therefore, the decay constant of iodine-131 is 0.0502 day^-1.
b) To calculate the half-life of iodine-131, we can use the formula:
t1/2 = ln(2) / λ
Substituting the value of λ we calculated in part (a), we get:
t1/2 = ln(2) / 0.0502
= 13.8 days
Therefore, the half-life of iodine-131 is 13.8 days.
c) To calculate how much iodine-131 will be present in the patient's body 50 days after it was administered, we can again use the formula:
N = N0 * e^(-λt)
We are given that t = 50 days,
N = 20.0 * e^(-0.0502*50)
= 1.29 mg
Therefore, 1.29 mg of iodine-131 will be present in the patient's body 50 days after it was administered.
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i need too get them right because me and my friend are challeging each other
6. Water - B. has a positive and negative end, 7. Nucleic acids - A. contains instructions, 8. Proteins - D. Some help break down nutrients, 9. Lipids - E. do not mix with water, and 10. carbohydrates - C. sugar is one.
6. Water - B. has a positive and negative end: Water is a polar molecule, which means it has a partial positive charge on one end and a partial negative charge on the other. This polarity is due to the asymmetric arrangement of the hydrogen and oxygen atoms in the molecule, with the oxygen atom having a stronger attraction for electrons than the hydrogen atoms. The positive and negative ends of the water molecule allow it to form hydrogen bonds with other polar molecules, including other water molecules, which gives water many of its unique properties, such as high surface tension, high boiling and melting points, and its ability to dissolve many substances.
7. Nucleic Acids - A. contain instructions: Nucleic acids are biomolecules that store and transmit genetic information in living organisms. They are composed of long chains of nucleotides, which are made up of a nitrogenous base, a sugar molecule, and a phosphate group. The two main types of nucleic acids are DNA (deoxyribonucleic acid) and RNA (ribonucleic acid). DNA contains the genetic information that is passed down from one generation to the next, while RNA helps to transcribe and translate that information into functional proteins that perform various cellular processes.
8. Proteins - D. Some help break down nutrients: Proteins are complex biomolecules that perform a variety of functions in the cell, including catalyzing chemical reactions, transporting molecules, and providing structural support. Some proteins, known as enzymes, are specialized molecules that help to break down nutrients in the body by catalyzing chemical reactions that convert them into usable forms. Other proteins, such as antibodies and hormones, have other important roles in the immune system and in cellular communication.
9. Lipids - E. do not mix with water: Lipids are a diverse class of biomolecules that are characterized by their insolubility in water. They include fats, oils, phospholipids, and steroids, among others. Lipids are composed of long chains of hydrocarbons and contain a polar head group and a nonpolar tail. The nonpolar tail makes lipids insoluble in water, while the polar head group allows them to interact with other polar molecules. Lipids are important for energy storage, as a component of cell membranes, and as signaling molecules.
10. Carbohydrates - C. sugar is one: Carbohydrates are a class of biomolecules that are composed of carbon, hydrogen, and oxygen atoms. They include sugars, starches, and fibers, among others. Sugars are simple carbohydrates that consist of one or two sugar molecules linked together, while starches and fibers are complex carbohydrates made up of many sugar molecules linked together. Carbohydrates are an important source of energy for the body and play important roles in cellular processes such as cellular respiration and photosynthesis.
Hence, The correct answer is 6. Water - B. has a positive and negative end, 7. Nucleic acids - A. contains instructions, 8. Proteins - D. Some help break down nutrients, 9. Lipids - E. do not mix with water, and 10. carbohydrates - C. sugar is one
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If you do 12 J of work to push 0.001 C of charge from point A to point B in an electric field, what iS the potential difference between points A and B? B). What will be the increase in kinetic energy of an
electron if it has been accelerated through a potential difference of 20 million volts? (Assume that e 1.6 X 10-19 C)
If you do 12 J of work to push 0.001 C of charge from point A to point B in an electric field, then the potential difference between points A and B is 12 kV.
The increase in kinetic energy of an electron if it has been accelerated through a potential difference of 20 million volts is 8000 J.
a )When a charge is accelerated through potential difference then the energy gained by the charge is,
E = eV where E is energy e is charge and V is potential difference.
V = E/e = 12/0.001 = 12 kV
b) E = eV, E = 0.001 × 20×10⁶
E = 20000 J
Increase in the kinetic energy will be, 20000 - 12000 = 8000 J
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6.1 62 6.3 64 quency of sound waves emitted by a stationary source. the relationship between the observed frequency and the The learner moves towards the source at a constant velocity and records the observed frequency (f) for a given source frequency (fs). This process is repeated for different frequencies of the source, with the learner moving at the same constant velocity each time The graph below shows how the observed frequency changes as the frequency of sound waves emitted by the source changes. fL (Hz) fs (Hz) Name the phenomenon illustrated by the graph Name ONE application in the medical field of the phenomenon in QUESTION 6.1. O Write down the type of proportionality that exists between f and fs, as illustrated by the graph. The gradient of the graph obtained is found to be 1,06. (1) of the
The highlighted phenomenon in the graph is called the Doppler effect, which involves a modification of frequency for sound waves (or any kind of wave) due to the difference in motion between the observed and the source.
How to explain the effectAn example of this effect present in the medical field is through ultrasound imaging; doctors use it to measure the velocity and route of blood circulating throughout the patient's body by sending out high-frequency sound waves and analyzing the reflected waves.
What appears in the graphed illustration specifically is linear proportionality, meaning that there is a direct correlation between f and fs, the former being the observed frequency and the latter the source frequency.
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A cylinder with an area ratio of .5 and a diameter of 15cm extends at a velocity of 5 cm per second. What is the flow rate?
Answer:
To calculate the flow rate, we need to first find the cross-sectional area of the cylinder.
The area ratio is defined as the ratio of the cross-sectional area of the extended cylinder to the cross-sectional area of the cylinder before it was extended.
Let's call the cross-sectional area of the cylinder before it was extended A1, and the cross-sectional area of the extended cylinder A2.
We know that the diameter of the cylinder is 15cm, so the radius is 7.5cm.
The cross-sectional area of a cylinder is given by the formula A = πr^2.
So,
A1 = π(7.5)^2 = 176.71 cm^2
To find A2, we can use the area ratio:
Area ratio = A2/A1 = 0.5
A2 = 0.5 * A1 = 0.5 * 176.71 = 88.36 cm^2
Now we can calculate the flow rate using the formula:
Flow rate = velocity * cross-sectional area
Flow rate = 5 cm/s * 88.36 cm^2 = 441.8 cm^3/s
Therefore, the flow rate is 441.8 cm^3/s.
An object has mass M (uppercase) and is located at the origin of the coordinate system. A second object has mass m (lowercase) and is located at a distance r from the origin. This exercise explores the potential energy of the two-mass system. A spherical coordinate system is appropriate, but only the radial direction, r^, needs to be considered.
Enter a vector expression for the force, F⃗ , acting on mass m . The expression must be valid for all values of the radial coordinate, 0 0, and the zero of potential energy is taken as limr→∞UG=0.
Mass of the second object located at a distance r from the origin, r^ is the unit vector in the radial direction, and the negative sign indicates that the force
What is a system ?The System can refer to a set of interacting or interdependent components forming an integrated whole. The term can be applied to various fields, including physics, engineering, biology, and social sciences, among others. In physics, a system typically refers to a collection of objects or particles that are studied together, often with the goal of understanding the behavior of the system as a whole. In engineering, a system can refer to a group of components that work together to perform a specific function, such as an electrical power grid or an automobile engine. In biology, a system can refer to an organism or group of organisms that interact with their environment, such as an ecosystem or the human body.
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An electromagnetic wave traveling through water (n1 = 1.3) is incident upon a boundary with glass (n2 = 1.5). What is the angle (in degrees) of the refracted ray (θ2) is the incident angle θ1 = 25°?
The refracted angle of the electromagnetic wave in glass (θ₂) is approximately 59.64° when the incident angle (θ₁) is 25°.
The refracted angle, denoted as θ₂, can be calculated using Snell's Law, which relates the incident angle, refracted angle, and the refractive indices of the two media involved.
Snell's Law states:
n₁ × sin(θ₁) = n₂ × sin(θ₂)
where:
n₁ = refractive index of the first medium (water) = 1.3
θ₁ = incident angle of the wave in the first medium = 25°
n₂ = refractive index of the second medium (glass) = 1.5
θ₂ = refracted angle of the wave in the second medium
Plugging in the given values:
n₁ = 1.3
θ₁ = 25°
n₂ = 1.5
Can rearrange Snell's Law to solve for θ₂:
θ₂ = arcsin((n₁/n₂) × sin(θ₁))
Now we can substitute in the values and calculate θ₂:
θ₂ = arcsin((1.3/1.5) × sin(25°))
θ₂ = arcsin(0.8667)
θ₂ ≈ 59.64°
So the refracted angle of the electromagnetic wave in glass (θ₂) is approximately 59.64° when the incident angle (θ₁) is 25°.
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Problem 2.3. (5 pts) A 0.500-kg cart connected to a light spring for which the force constant is 20.0 N/m oscillates on a frictionless, horizontal air track. (a) Calculate the maximum speed of the cart if the amplitude of the motion is 3.00 cm. (b) What is the velocity of the cart when the position is 2.00 cm? (c) Compute the kinetic and potential energies of the system when the position of the cart is 2.00 cm
The maximum speed of the cart is 26.07 cm/s, the velocity of the cart when the position is 2 cm is 0.141 m/s, and the kinetic and potential energies of the system are 4.97 ×10⁻³J and 4×10⁻³J.
From the given,
Mass of the cart = 0.5 kg
Force constant = 20 N/m
The amplitude of the motion = 3 cm = 0.03 m
A) maximum speed of the cart=?
ω = √k/m
= √(20/0.5) = 8.944
v = ω×amplitude = 8.944×3 = 26.07 cm/s.
B) Velocity of the cart when the position is 2 cm
v = √k/m(A²-x²)
= √(20/0.5)((0.03)²-(0.02)²)
= 0.141 m/s
C) Kinetic energy = 1/2 (mv²)
= 1/2 (0.5×(0.141)²)
= 4.97 × 10⁻³J
K.E = 4.97 ×10⁻³J
Potential energy = 1/2 kx²
= 1/2 (20×(2×10⁻²)²)
= 4 × 10⁻³J
P.E = 4 × 10⁻³J.
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18.
As air temperature decreases, the speed of sound in air decreases.
True
False
Answer:
True
the velocity of sound in air decreases with decrease in temperature.
How many amperes of current are flowing through a circuit if the battery provides 7.0 V and the light bulb has a resistance of 39 Ω?
The amount of current flowing through the given circuit is 0.179 Amperes.
We can use Ohm's Law, which says that current (I) is equal to the voltage (V) divided by resistance (R), to figure out how much current is passing through the circuit. This can be shown mathematically as:
I = V / R
I = the amount of electricity in amperes
V = voltage in volts
R = resistance measured in ohms.
Given that the battery gives off 7.0 V and the light bulb has a resistance of 39, we can plug these numbers into the formula:
I = 7.0 V / 39 Ω
I = 0.1795 A (to four places after the decimal)
So, about 0.1795 amperes of current are moving through the circuit.
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A 15.0 kg log starts from rest then falls over a 30 m waterfall to the lake below
Answer:
17.3 m/s
Explanation:
We can use the conservation of energy principle to find the velocity of the log when it hits the water. At the top of the waterfall, the log has gravitational potential energy, and at the bottom, it has kinetic energy. We can assume that there is no energy lost to friction or air resistance.
The gravitational potential energy of the log at the top of the waterfall is given by:
U = mgh
where m is the mass of the log, g is the acceleration due to gravity, and h is the height of the waterfall. Substituting the given values, we get:
U = (15.0 kg)(9.81 m/s^2)(30 m) = 4414.5 J
At the bottom of the waterfall, all of the gravitational potential energy has been converted to kinetic energy:
U = (1/2)mv^2
where v is the velocity of the log when it hits the water. Solving for v, we get:
v = sqrt(2U/m)
Substituting the value of U and m, we get:
v = sqrt(2(4414.5 J)/(15.0 kg)) = 17.3 m/s
Therefore, the velocity of the log when it hits the water is approximately 17.3 m/s.
Hope this helps!
21. A rock is thrown straight down with an initial velocity of 14.5 m/s from a cliff. What is the rock’s displacement after 2.0 s? (Acceleration due to gravity is 9.80 m/s2 .) a. 28 m
b. 49 m
c. 55 m
d. 64 m
Explanation:
d = do + vo t + 1/2 at^2
d = 0 + 14.5 (2) + 1/2 (9.80)(2^2) = 48.6 = ~ 49 m
Explanation:
d = do + vo t + 1/2 at^2
d = 0 + 14.5 (2) + 1/2 (9.80)(2^2) = 48.6 = ~ 49 m
a vertical spring scale can measure weights up to 175N the scale extends by an amount of 13.0cm from its equilibrium position at 0N to the 175 N mark. A fish hanging from the bottom of the spring oscillates vertically at a frequency of 2.35 Hz. Ignore the mass of the spring, what is the mass Mof the fish
Answer:
Approximately 0.024 kg
Explanation:
We can use Hooke's Law, which states that the force exerted by a spring is proportional to the displacement from its equilibrium position. Mathematically, this can be written as:
F = -kx
where F is the force exerted by the spring, k is the spring constant, and x is the displacement from the equilibrium position. The negative sign indicates that the force is in the opposite direction of the displacement.
We can use the given information to find the spring constant:
k = F/x = 175 N / 0.13 m = 1346.15 N/m
The fish is oscillating vertically, which means that the force of gravity is acting on it. The weight of the fish can be calculated as:
W = mg
where W is the weight, m is the mass, and g is the acceleration due to gravity (9.81 m/s^2).
The oscillation frequency of the fish can be related to its mass and the spring constant using the formula:
f = 1/2π * sqrt(k/m)
where f is the frequency of oscillation, π is a constant (approximately 3.14), and sqrt is the square root function.
We can rearrange this equation to solve for the mass of the fish:
m = k/(4π^2 * f^2)
Substituting the given values, we get:
m = 1346.15 N/m / (4 * 3.14^2 * (2.35 Hz)^2) ≈ 0.024 kg
Therefore, the mass of the fish is approximately 0.024 kg.
How can astronomers use how long it takes an objects brightness to vary to say something about the physical size of the object?
Astronomers can use how long it takes an object's brightness to vary to estimate the physical size of the object through a method known as photometry. This method involves observing an object's brightness over time and analyzing the patterns of variation.
For example, consider a binary star system in which two stars orbit each other. As one star passes in front of the other, the combined brightness of the system will decrease. The duration of this decrease in brightness can be used to estimate the physical size of the stars, as the duration of the decrease is related to the size of the stars and the distance between them.
Similarly, if an asteroid or other small body passes in front of a star, the star's brightness will decrease for a short period of time. The duration of this decrease can be used to estimate the size of the asteroid, as the duration is related to the size of the asteroid and the distance between it and the observer.
In general, the size of an object can be estimated using photometry by comparing the observed variation in brightness to the expected variation based on the physical characteristics of the object. This can provide valuable information about the properties and behavior of celestial objects and can help astronomers to better understand the structure and evolution of the universe.