The spring scale read just before the mass touches the lower spring is 80.36N, the spring constant for the lower spring is 2765N/m and at 2.9cm length the scale will read zero.
Given the mass of spring = 8.2kg
The force exerted for compressing of spring = 14N
The compression in spring = 2.4cm = 0.024m
(A.) Initially the spring scale reads only the weight of the mass = mg
W = 8.2 * 9.8 = 80.36N
(B) Let the value of spring constant = k
The net force exerted so that the scale reads(F') = 80.36N - 14 = 66.36N
We know that according to Hooke's law the force exerted on spring F = kx such that:
F' = kx then:
66.36 = k * 0.024
k = 66.36/0.024 = 2765N/m
(C) the compression where scale reads zero = x'
The scale reads zero when the restoring force equals to the weight of the mass then the scale reads zero such that:
x' = 80.36/2765 = 0.029m = 2.9cm
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How did Newton discovered gravity?
Answer:
Isaac Newton, the English physicist, mathematician, and astronomer, discovered the concept of gravity in the late 17th century. The story of his discovery of gravity is one of the most famous in scientific history.
The most well-known anecdote is that Newton was sitting under an apple tree when an apple fell from the tree and hit him on the head. This event, however, is likely to be a myth created to make the story more memorable. Nonetheless, it is true that Newton began to wonder why objects fall to the ground instead of flying off into space.
Newton's curiosity led him to conduct experiments to understand the behavior of falling objects. He reasoned that the same force that caused an apple to fall to the ground was responsible for holding the moon in orbit around the Earth.
Newton's breakthrough came when he realized that the force that causes objects to fall to the ground is the same force that governs the motion of the planets in the solar system. He described this force as "gravity" and formulated his famous law of universal gravitation, which states that every object in the universe attracts every other object with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them.
Newton's discovery of gravity was a major scientific achievement that revolutionized our understanding of the physical world. It laid the foundation for the development of classical mechanics, and the law of gravitation has since been used to explain a wide range of phenomena in physics, from the motion of planets to the behavior of subatomic particles.
In summary, Newton discovered gravity through a process of curiosity, experimentation, and mathematical reasoning. Although the apple falling on his head is unlikely to be true, his discovery has had a profound impact on our understanding of the universe.
Answer:
Isaac Newton did not "discover" gravity, as it was already known that objects were attracted to each other. However, he did discover the law of universal gravitation, which states that every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of their separation distance.
if an 80 kg person is 5 m away from a 100 kg person, what is the force of gravity between them?
The force of gravity between the 80 kg person and the 100 kg person, who are 5 meters apart, is approximately 1.07269 × 10^-6 Newtons.
To find the force of gravity between them?The force of gravity between two objects is given by the formula:
F = G(m1*m2)/r^2
Where
F is the force of gravity G is the gravitational constant (6.67430 × 10^-11 N·(m/kg)^2) m1 and m2 are the masses of the two objectsr is the distance between themPlugging in the given values, we get:
F = 6.67430 × 10^-11 N·(m/kg)^2 * (80 kg) * (100 kg) / (5 m)^2
Simplifying this expression, we get:
F = 1.07269 × 10^-6 N
Therefore, the force of gravity between the 80 kg person and the 100 kg person, who are 5 meters apart, is approximately 1.07269 × 10^-6 Newtons.
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What is Albert Einstein theory?
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics.
Where is the contradiction between quantum physics and Einstein’s gravity?Rμν−12gμνR=8πGT^μν.
This is Einstein’s field equation. Essentially, this equation is general relativity. The left-hand side represents the geometry of spacetime. The right-hand side, the energy, momentum, and stresses of matter.
What this equation describes, in the words of Wheeler, is this: Spacetime tells matter how to move; matter tells spacetime how to curve.
But look closely. That T
on the right-hand side. It has a hat.
It has a hat because it is a quantum-mechanical operator. Because we know that matter consists of quantum fields. So it is described by operator-valued quantities (Dirac called them q-numbers). They are unlike ordinary numbers. For instance, when you multiply them, the order in which they appear matters. That is, when you have two operators p^
and q^
, p^q^≠q^p^
most of the time. So they are definitely not like numbers.
When Einstein wrote down his field equation over 100 years ago, the T
did not have a hat. But that’s because they didn’t know about operator-valued quantities at the time. Now we do. So I have to put the hat there.
But there are no hats on the left-hand side. And because of that, my equation might as well say something like, some apples = some oranges. It makes no sense. The stuff on the left-hand side (which consists of numbers) can never equal the stuff on the right-hand side (which definitely does not consist of numbers.)
I can make it work, though. I can replace that operator with its so-called expectation value:
Rμν−12gμνR=8πG⟨Tμν⟩.
This is called semiclassical gravity. And it works well, very well indeed. A little too well, as a matter of fact. Gravity is so weak, quantum effects are so irrelevant, this equation accurately describes Nature everywhere we can look. But we still don’t like it, because using that expectation value trick is a cheat, a cop-out.
Now you might wonder, why don’t I put hats on top of the things on the left-hand side? I would… if I knew how to quantize spacetime. That is, how to turn the numbers that describe gravity into quantum-mechanical operators.
But I do not. And nobody does. The standard methods all fail, leading to equations that make no sense at all.
So we are kind of stuck… we don’t know how to quantize gravity, and our observations don’t help us, don’t offer any hints as to how to get beyond semiclassical gravity. Theorists keep trying to come up with new ideas (or recycle old ones) but basically, we’ve been pretty much just spinning our wheels for decades.
You leave Fort worth ,Texas,at 2:41 p.m. and arrive in Dallas at 3:23 p.m. , covering a distance of 58km. what is your average speed in metres per second ?
Answer:
Explanation:
The time taken to travel from Fort Worth to Dallas is:
t = 3:23 pm - 2:41 pm = 42 minutes = 0.7 hours
The distance covered is:
d = 58 km
The average speed is:
v = d/t = 58 km / 0.7 hours = 82.86 km/h
To convert km/h to m/s, we can use the conversion factor:
1 km/h = 0.2778 m/s
Therefore, the average speed in m/s is:
v = 82.86 km/h × 0.2778 m/s/km = 23.06 m/s (rounded to two decimal places)
So the average speed is 23.06 m/s.
A stone is dropped in a mine shaft 15 m deep. The speed of sound is 343 m/s. How long does it take to hear the echo?
It takes 0.1311 seconds to hear the echo of the stone.
How to calculate the time it takes to hear the echo of the stone.First we need to determine the time it takes for the sound wave to travel from the stone to the bottom of the mine shaft and back up to our ears.
Let's start by finding the time it takes for the sound wave to reach the bottom of the mine shaft. We can use the formula:
time = distance / speed
The distance is the depth of the mine shaft, which is 15 meters. The speed of sound is 343 m/s, as given in the problem. Therefore, the time it takes for the sound wave to reach the bottom of the mine shaft is:
time = 15 m / 343 m/s
time = 0.0437 s
Now, we need to find the time it takes for the sound wave to travel back up to our ears. Since the sound wave travels at the same speed, 343 m/s, the distance it needs to cover is twice the depth of the mine shaft, or 30 meters. Therefore, the time it takes for the sound wave to travel back up to our ears is:
time = 30 m / 343 m/s
time = 0.0874 s
Finally, to find the total time it takes to hear the echo, we add the time it takes for the sound wave to reach the bottom of the mine shaft to the time it takes to travel back up to our ears:
total time = 0.0437 s + 0.0874 s
total time = 0.1311 s
Therefore, it takes 0.1311 seconds to hear the echo of the stone.
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Two spheres of masses 200kg and 100kg respectively have the centres seperated by a distance of 0.5m. Calculade the magnitude of force of attraction between them. G = 6·7x 10" N m² kg - ²
A 1.20 kg copper rod resting on two horizontal rails 0.90 m apart carries a
current I = 55.0 A from one rail to the other. The coefficient of static friction
between the rod and rails is μs= 0.60.
(a) What is the smallest vertical magnetic field B that would cause the rod to
slide?
(b) Suppose a B field is directed at some angle to the vertical φ, with the current
along the rod directed into the page, as shown. Find an expression for B as a
function of φ for the case when the rod is just on the verge of beginning to slide.
(c) Find the value of φ which yields the smallest value of B that would cause
the rod to slide, together with the corresponding value of B.
(a) The smallest vertical magnetic field B that would cause the rod to
slide is 0.145 Tesla for given The coefficient of static friction
between the rod and rails is μs= 0.60
What is magnetic field ?A magnetic field is a vector field that describes the magnetic influence on moving charges, currents, and magnetic materials. A moving charge in a magnetic field is subjected to a force that is perpendicular to both its own velocity and the magnetic field.
(a) using formula
μs × m × g = I × L × B
μs= 0.60
M= 1.2 kg
I = current = 55.0 A
L = Length = 0.9 m
magnetic field (B) = 0.145 Tesla
(b) expression
force (f) = I × L × B × sinФ
(c) given B = 0.145 Tesla
μs × m × g= I × L × B × sinФ
Ф = 90°
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Who discovered energy quanta and earned a Nobel Prize in Physics?
Answer: Max Planck
He won the Nobel Prize for Physics in 1918.
A porter can climb 10 staircase of 30cm each in 10 sec by carrying a 50kg bag. Calculate the power of the porter
Therefore, the power of the porter is 441,450 J/s, or approximately 441.5 watts.
What is work done?The work done by the porter in lifting the 50 kg bag up the stairs can be calculated as the product of the force applied and the distance moved.
The force applied is the weight of the bag, which is given by:
F = m * g
where m is the mass of the bag and g is the acceleration due to gravity, which is approximately 9.81 m/s². Substituting the given values, we get:
F = 50 kg * 9.81 m/s²
F = 490.5 N
The distance moved by the porter in lifting the bag up one staircase is 30 cm, and the porter climbs 10 staircases in 10 seconds, which gives a speed of:
v = (10 * 30 cm) / 10 s
v = 30 cm/s
The power of the porter is the rate at which work is done, which can be calculated as:
P = W / t
where W is the work done and t is the time taken. Substituting the values, we get:
P = F * d * v / t
P = 490.5 N * 10 * 30 cm * 30 cm/s / 10 s
P = 441,450 J/s
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Mary walked north from her home to Sheila's home, which is 4.0 kilometers away. Then she turned right and walked another 3.0 kilometers to the supermarket, which is 5.0 kilometers from her own home. She walked the total distance in 1.5 hours. What were her average speed and average velocity?
A.
Her average speed was about 4.6 km/hr, and her average velocity was about 3.3 km/hr.
B.
Her average speed was about 3.3 km/hr, and her average velocity was about 4.6 km/hr.
C.
Her average speed was about 3.3 km/hr, and her average velocity was 0 km/hr.
D.
Her average speed was 0 km/hr, and her average velocity was about 4.6 km/hr.
Her average speed was about 4.6 km/hr, and her average velocity was about 3.3 km/hr.
The entire distance travelled divided by the total time taken is the definition of average speed. In this case, the total distance travelled was 7.0 km, and the total time taken was 1.5 hours. Hence, the average speed can be determined as follows:
Average Speed = [tex]\frac{7.0 km }{ 1.5 \ hours }= 4.6 km/hr[/tex]
The displacement divided by the whole time travelled is the average velocity. In this case, the displacement was 3.0 km (from Mary's home to Sheila's home), and the total time taken was 1.5 hours.The average velocity can therefore be determined as follows:
Average Velocity = [tex]\frac{3.0 km }{1.5 \ hours} = 3.3 km/hr[/tex]
Therefore,Her average velocity was roughly 3.3 km/hr, and her average speed was roughly 4.6 km/hr.
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How much heat is necessary to change 10 g of ice at -20°C into water at 10°C?
Answer:
Explanation:
The process can be broken down into two steps:
Heat required to raise the temperature of ice from -20°C to 0°C.
Heat required to melt ice at 0°C and raise the temperature of water from 0°C to 10°C.
Step 1:
The heat required to raise the temperature of ice can be calculated using the specific heat capacity of ice, which is 2.09 J/g°C.
Heat required = mass × specific heat capacity × change in temperature
Heat required = 10 g × 2.09 J/g°C × (0°C - (-20°C))
Heat required = 418 J
Step 2:
The heat required to melt ice and raise the temperature of water can be calculated using the heat of fusion of ice and the specific heat capacity of water.
Heat required to melt ice = mass × heat of fusion of ice
Heat required to melt ice = 10 g × 334 J/g
Heat required to melt ice = 3340 J
Heat required to raise the temperature of water can be calculated using the specific heat capacity of water, which is 4.18 J/g°C.
Heat required = mass × specific heat capacity × change in temperature
Heat required = 10 g × 4.18 J/g°C × (10°C - 0°C)
Heat required = 418 J
Total heat required = Heat required in Step 1 + Heat required to melt ice + Heat required in Step 2
Total heat required = 418 J + 3340 J + 418 J
Total heat required = 4176 J
Therefore, 4176 J of heat is required to change 10 g of ice at -20°C into water at 10°C.
Faculty of Medicine
Tutorial No 3
1. When an 81.0-kg adult uses a spiral staircase to climb to the second floor of his house, his
gravitational potential energy increases by 2.00 × 103
J. By how much does the potential
energy of an 18.0-kg child increase when the child climbs a normal staircase to the second
floor?
Work Energy Theorem QUESTION: A 1200kg automobile is moving at 25m/s along level ground. What is the initial KE of the automobile? What is the final KE of the automobile? What is the change in KE of the automobile?What is the work done?
(a) The initial kinetic energy (KE) of the automobile is 375,000 J
(b) The final KE will also be 375,000 J.
(c) The work done on the automobile is zero
What is the initial kinetic energy?The initial kinetic energy (KE) of the automobile can be found using the formula:
KE = 1/2mv²
where;
m is the mass of the automobile and v is its velocity.KE = 1/2 x 1200 kg x (25 m/s)²
KE = 375,000 J
The final KE of the automobile will be the same as the initial KE if the velocity remains constant. However, if there is a change in velocity, the final KE can be found using the same formula as above.
The change in KE can be found by subtracting the initial KE from the final KE, or by using the work-energy theorem:
ΔKE = W
where;
ΔKE is the change in kinetic energy and W is the work done.Assuming there is no external work done on the automobile, the change in KE will be zero.
Therefore, the final KE will also be 375,000 J.
The work done on the automobile can be found using the work-energy theorem:
W = ΔKE = 0 J (since there is no change in KE)
Therefore, the work done on the automobile is zero.
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a Toyota Celica, travelling initially at 26.9 m/s [S], comes to a stop in 2.61 s. The mass of the car with the driver is 1.18 × 103 kg. Calculate the car’s acceleration.
The initial velocity of the car is 26.9 m/s [S], and the final velocity is 0 m/s [S]. The time taken for the car to come to a stop is 2.61 s. Using the formula:
acceleration = (final velocity - initial velocity) / time
we can find the car's acceleration:
acceleration = (0 m/s - 26.9 m/s) / 2.61 s
acceleration = -10.305 m/s^2
The negative sign indicates that the car is decelerating, or slowing down.
To calculate the force acting on the car during the deceleration, we can use Newton's second law:
force = mass x acceleration
force = (1.18 × 10^3 kg) x (-10.305 m/s^2)
force = -12,166.1 N
The force acting on the car during deceleration is -12,166.1 N, or approximately 12.2 kN.
There are two objects (A and B) each with its own mass and charge. The electrostatic force between them has a value of 23.2N and is attractive. The two objects are separated by a distance of 2.3cm with object A being to the left of B. Assume one charge has 4 times the charge of the other.
a. Do the two charges have the same signs or opposite signs?
b. IF the two charges have opposite signs, is charge A or B negative?
c. Which charge (A or B) has the higher value?
d. Find the value of each charge.
Answer:
Explanation:
a. Since the electrostatic force is attractive, the charges must have opposite signs.
b. Let's assume that charge A is positive and charge B is negative. Then, the electrostatic force would be given by:
F = (k * |qA| * |qB|) / r^2
where k is Coulomb's constant, r is the distance between the charges, and |qA| and |qB| are the magnitudes of the charges. Since the force is attractive, |qA| > |qB|.
c. From the given information, we know that:
F = 23.2 N
r = 2.3 cm = 0.023 m
Let |qB| = q, then |qA| = 4q. Substituting these values into the equation for the electrostatic force, we get:
23.2 = (k * 4q * q) / (0.023)^2
Solving for q, we get:
q = 3.38 x 10^-7 C
Then, |qA| = 4q = 1.35 x 10^-6 C.
d. Charge A has a value of 1.35 x 10^-6 C and charge B has a value of -3.38 x 10^-7 C.
The rate of flow of heat through different materials of the same thickness is different. Plan and design an experiment to test this statement based on the rate of flow of heat
Based on the results of the experiment, it can be concluded that the rate of flow of heat through different materials of the same thickness is different.
What is the experiment plan?Here is an experimental plan to test the rate of flow of heat through different materials of the same thickness:
Materials:
Three blocks of different materials (e.g., metal, plastic, and wood)
Thermometer
Heat source (e.g., hot plate)
Stopwatch
Insulating material (e.g., foam)
Procedure:
Cut three blocks of the same thickness from each of the three materials.
Measure the initial temperature of each block using a thermometer.
Place the three blocks on a heat source (e.g., hot plate) with the same amount of heat and start the stopwatch.
Measure the temperature of each block every 30 seconds using the thermometer.
Record the temperature of each block at each time interval.
After 5 minutes, turn off the heat source and measure the final temperature of each block.
Calculate the temperature difference between the initial and final temperatures for each block.
Calculate the rate of heat flow for each block by dividing the temperature difference by the time interval.
Repeat the experiment at least three times for each block and take an average of the results.
Place each block on an insulating material (e.g., foam) and repeat the experiment to compare the effect of insulation on the rate of heat flow.
Data analysis:
Plot a graph of the rate of heat flow (y-axis) versus time (x-axis) for each block.
Compare the slopes of the graphs to determine the rate of heat flow for each block.
Compare the rates of heat flow for the three blocks to test the statement that the rate of flow of heat through different materials of the same thickness is different.
Compare the rates of heat flow for each block with and without insulation to determine the effect of insulation on the rate of heat flow.
Conclusion:
The rate of heat flow depends on the thermal conductivity of the material, which is a measure of how well a material conducts heat. Materials with higher thermal conductivity will have a higher rate of heat flow, while materials with lower thermal conductivity will have a lower rate of heat flow.
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In deep space, there is very little friction. Once they launch a probe into deep space, where there are no external forces acting on it, scientists shut the probe’s engines off because the scientists want the probe to
stop immediately.
speed up.
slow down.
move at constant velocity.
could any of you please help i really need it
Answer: B is insulating and A is conducting
Explanation:
I really hope that's right. If not, I am so sorry.
A missile weighing 400N on the earth surface is shot into the atmosphere to an altitude of 6.4 x 106 m. Taking the earth as a sphere of radius 6.4 x 10-6 m and assuming the inverse-square law of universal gravitation, what would be the weight of the missile at that altitude?
Answer:
Explanation:
We can use the inverse-square law of universal gravitation to determine the weight of the missile at an altitude of 6.4 x 10^6 m. The law states that the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
Let M be the mass of the Earth and m be the mass of the missile. At the Earth's surface, the weight of the missile is:
F1 = mg
where g is the acceleration due to gravity on the Earth's surface, which we assume to be 9.81 m/s^2.
At an altitude of 6.4 x 10^6 m, the distance between the center of the Earth and the missile is:
r = R + h
where R is the radius of the Earth (6.4 x 10^6 m) and h is the altitude of the missile (6.4 x 10^6 m).
The weight of the missile at this altitude can be calculated using the inverse-square law of universal gravitation:
F2 = G * M * m / r^2
where G is the gravitational constant (6.6743 x 10^-11 N * m^2 / kg^2).
Substituting the given values, we get:
F2 = (6.6743 x 10^-11 N * m^2 / kg^2) * (5.97 x 10^24 kg) * (400 N) / (6.4 x 10^6 m + 6.4 x 10^6 m)^2
F2 = 39.61 N
Therefore, the weight of the missile at an altitude of 6.4 x 10^6 m is approximately 39.61 N.
The epicenter of an Earthquake was located 1800 kilometers away. If the S-wave arrived at the seismic station at 10:06:40 am, at what time did the P-wave arrive?
Answer:
The P-wave travels faster than the S-wave and arrives at the seismic station before the S-wave. The time difference between the arrivals of the P-wave and S-wave can be used to determine the distance between the seismic station and the earthquake epicenter.
Explanation:
Which correctly describes a different evolutionary stage of a star like the sun
A) it’s forms from a cold, dusty molecular cloud
B) During a yellow giant stage, it burns carbon in its core and helium in the shell surrounding the core.
C) After leaving the main sequence, its core is stable due to electron degeneracy
D) It becomes a white dwarf after exploding as a supernova
E)During a red giant stage, its core contracts and cools
The statement that correctly defines an evolutionary stage of a star like the sun is that after leaving the main sequence, its core is stable due to electron degeneracy. That is option C.
What are the stage of life cycle of a star?The stages of the life cycle of a star include the following:
Giant Gas CloudProtostarT-Tauri PhaseMain SequenceRed GiantThe Fusion of Heavier ElementsSupernovae and Planetary NebulaeThe evolutionary stage is also called the main sequence stage of the life cycle of the star.
In this stage, the core temperature reaches the point for the fusion to occur whereby the protons of hydrogen are converted into atoms of helium. This leads to the stability of the core of the newly formed start due to electron degeneracy.
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Two stars, Bucky and Badger, form in the same giant molecular cloud. Bucky has 5 solar mass and Badger has 1 solar mass. Which of the followings is correct?
A) The main-sequence life of Bucky is 5 times longer
B) Bucky has a longer time to become a protostar
C) We can detect Badger first when it becomes a pre-main- sequence star
D) They have the same heavy elements
Answer:
Most likely the answer is D;
Explanation:
Because they formed from the same molecular cloud.
Bucky definitely will live shorter. And we can detect Bucky faster due it's enormous rate of burring fuel.
Both of the stars will have the same heavy elements.
The two stars, Bucky and Badger are formed in the same giant molecular cloud. Among them Bucky has five solar mass, which is five times the solar mass of Badger.
As a result of the higher solar mass of Bucky, its fuel will burn up very faster than Badger. So, Bucky will have shorter life. Also it will spin faster and become a protostar in short time.
Since, both the stars, Bucky and Badger are formed in the same giant molecular cloud, both of them will have the same heavy elements.
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A 65 kg-mass person stands at the end of a diving board, 1.5 m from the board's pivot point. Determine the torque the person is exerting on the board with respect to the pivot point. Show your work.
Answer:
Explanation:
The torque is given by the formula:
τ = F × r × sin(θ)
where τ is the torque, F is the force applied, r is the distance between the force and the pivot point, and θ is the angle between the force and the lever arm.
In this case, the person's weight is the force being applied, and it can be calculated as:
F = m × g
where m is the mass of the person and g is the acceleration due to gravity (9.81 m/s^2).
F = 65 kg × 9.81 m/s^2 = 637.65 N
The distance between the person and the pivot point is 1.5 m, so r = 1.5 m.
The angle between the person's weight and the lever arm is 90 degrees, so sin(θ) = 1.
Therefore, the torque the person is exerting on the board is:
τ = F × r × sin(θ) = 637.65 N × 1.5 m × 1 = 956.475 N·m
So the person is exerting a torque of 956.475 N·m on the diving board with respect to the pivot point.
Sound travels through air at a speed of 342m/s
342
m
/
s
at room temperature. What is the frequency of a sound wave with a wavelength of 1.8m
1.8
m
Answer:
Explanation:
The formula relating the speed of sound, frequency, and wavelength is:
speed = frequency x wavelength
Rearranging this formula to solve for frequency:
frequency = speed / wavelength
Substituting the given values:
frequency = 342 m/s / 1.8 m
frequency = 190 Hz
Therefore, the frequency of the sound wave is 190 Hz.
A Car accelerate Cuniformly from) 13 ms -1 to 31ms-1 while entering the motor way Covering the distance 220m
Answer:
3.84 m/s^2.
Explanation:
To solve this problem, we can use the following kinematic equation:
v^2 = u^2 + 2as
where:
v is the final velocity (31 m/s)
u is the initial velocity (13 m/s)
a is the acceleration (which is assumed to be constant)
s is the distance traveled (220 m)
We want to solve for the acceleration, so we can rearrange the equation as follows:
a = (v^2 - u^2) / 2s
Substituting the given values:
a = (31^2 - 13^2) / (2 x 220)
a = 3.84 m/s^2
Therefore, the acceleration of the car is 3.84 m/s^2.
please rate
Suppose the angles shown in Fig. 5.31 are 52° and 25°. If the left-hand mass is 2.5 kg, what should the right-hand mass be so that it accelerates (a) downslope at 0.64 m/s2 and (b) upslope at 0.76 m/s2?
Downslope at 0.64 m/s², m = 12.4 kg
Upslope at 0.76 m/s², m = 6.35 kg
Define Mass?In Physics, mass is the most basic property of matter, and it is one of the fundamental quantities. Mass is defined as the amount of matter present in a body. The SI unit of mass is the kilogram (kg). The formula of mass can be written as:
Mass = Density × VolumePart A)
The sum of forces on the left-hand mass
T - mgsin(angle) = ma
T - (2.6) (9.8) (sin 70) = 2.6(.64)
T = 25.6 N
m = left mass.........M = right mass
T - mg×sin70 = ma
Mg×sin16 - T = Ma
Mg×sin16 - mg×sin70 = a×(M+m)
M×g×sin16 - mg×sin70 = Ma + ma
M× (g×sin16 -a) = m× (a + gsin70)
M = m× (a + gsin70) / (g×sin16 -a)
a) a = 0.64
M = 10.98 Kg
b) M = 11.82 kg
For the right-hand mass, the sum of forces...
mgsin(angle) - T = ma
m (9.8) (sin 16) - 25.6 = m (.64)
2.7m - 25.6 = .64m
m = 12.4 kg
Part B)
For the left-hand mass
mgsin(70) - T = ma
(2.6) (9.8) (sin 70) - T = (2.6) (.76)
T = 21.97 N
Then for the right-hand mass
T - mgsin(16) = ma
21.97 - m (9.8) (sin 16) = m (.76)
21.97 - 2.7m = .76m
m = 6.35 kg
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The right-hand mass should be 3.3 kg to accelerate up the slope at 0.76 m/s². To solve this problem, we need to use the principles of Newton's laws of motion and trigonometry.
We know that the force of gravity acting on the mass is equal to its weight, which can be calculated using the formula Fg = mg, where Fg is the force of gravity, m is the mass, and g is the acceleration due to gravity (which is approximately 9.8 m/s²).
To find the force acting down the slope, we need to calculate the component of the weight that acts down the slope, which is given by Fg sin θ, where θ is the angle of the slope. Using the given angle of 52°, we can calculate the force acting down the slope for the left-hand mass as:
Fdown = Fg sin θ
Fdown = (2.5 kg)(9.8 m/s²) sin 52°
Fdown = 18.9 N
To find the required mass for the right-hand mass to accelerate at 0.64 m/s^2 down the slope, we can use Newton's second law of motion, which states that the force acting on an object is equal to its mass times its acceleration (F = ma). Therefore, we can calculate the required force for the right-hand mass as:
F = ma
F = (m)(0.64 m/s²)
Since the force acting down the slope is 18.9 N, we can set these two equations equal to each other and solve for the mass:
F = Fdown
(m)(0.64 m/s²) = 18.9 N
m = 29.5 kg
Therefore, the right-hand mass should be 29.5 kg to accelerate down the slope at 0.64 m/s².
To find the required mass for the right-hand mass to accelerate at 0.76 m/s² up the slope, we can use the same approach, but this time we need to use the component of the weight that acts up the slope, which is given by Fg cos θ, where θ is the angle of the slope. Using the given angle of 25°, we can calculate the force acting up the slope for the right-hand mass as:
Fup = Fg cos θ
Fup = (m)(9.8 m/s²) cos 25°
Setting this equal to the force required for the right-hand mass to accelerate up the slope, we get:
Fup = ma
(m)(0.76 m/s²) = (m)(9.8 m/s²) cos 25°
m = 3.3 kg
Therefore, the right-hand mass should be 3.3 kg to accelerate up the slope at 0.76 m/s².
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A current of O.S.A flows in a circuit with resistance 60 calculate the potential difference of the circuit
Therefore, the potential difference of the circuit is 30 volts.
What in electricity is a potential difference?The external effort required to move a charge from one position to another in an electric field is known as an electric potential difference, or voltage. A test charge that has an electric potential differential of +1 will experience a shift in potential energy.
To calculate the potential difference (V) of the circuit, we can use Ohm's Law, which states that V = IR, where I is the current flowing through the circuit and R is the resistance of the circuit.
In this case, the current (I) is given as 0.5 A and the resistance (R) is given as 60 Ω. Therefore, we can substitute these values into Ohm's Law to find the potential difference:
V = IR
V = 0.5 A × 60 Ω
V = 30 volts
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Two identical cars (m-1350 kg) are traveling at the same speed of 35.7 m/s. They are moving in the directions shown in the drawing
What is the magnitude of the total momentum of the two cars?
Car 1 - 60°
Car 2 - 30°
The magnitude of the total momentum of the two cars is 68,245.5 kg m/s.
What is the magnitude of the car's total momentum?To calculate the total momentum of the two cars, we need to first calculate the momentum of each car and then add them together.
The momentum of an object is given by the product of its mass and velocity. So, the momentum of each car can be calculated as:
p = m x v
where;
p is momentum, m is mass, and v is velocity.Since both cars have the same mass, their momenta will be equal if they have the same velocity. In this case, both cars are traveling at the same speed of 35.7 m/s.
The momentum of car 1 can be calculated by resolving its velocity into horizontal and vertical components:
vx1 = v1 cos(60°) = 0.5 x 35.7 = 17.85 m/s
vy1 = v1 sin(60°) = 0.866 x 35.7 = 30.97 m/s
The momentum of car 1 is then:
p₁ = m x v₁ = 1350 x √(vx₁² + vy₁²)
p₁ = 1350 x √(17.85² + 30.97²)
p₁ = 48,256.85 kg m/s
Similarly, the momentum of car 2 can be calculated by resolving its velocity into horizontal and vertical components:
vx2 = v2 cos(30°) = 0.866 x 35.7 = 30.97 m/s
vy2 = v2 sin(30°) = 0.5 x 35.7 = 17.85 m/s
The momentum of car 2 is then:
p₂ = m x v₂ = 1350 x √(vx₂² + vy₂²)
p₂ = 1350 x √(30.97² + 17.85²)
p₂ = 48,256.85 kg m/s
The total momentum of the two cars is the vector sum of their momenta, which can be calculated using the Pythagorean theorem:
ptotal = √(p₁² + p₂²)
= √((48,256.85 )² + (48,256.85²) = 68,245.5 kg m/s
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The bigger the spring constant, the more__________the spring is.
The bigger the spring constant, the more stiff or rigid the spring is.
What does it signify when a spring's spring constant is higher?The exact amount of force needed to bend a spring depends on the spring constant. Although pounds/inch is a common measurement in North America, the standard international (SI) unit for spring constants is Newtons/meter. A stiffer spring has a greater spring constant, and vice versa.
What does it signify when the spring constant is higher?The exact amount of force needed to bend a spring depends on the spring constant. Although pounds/inch is a common measurement in North America, the standard international (SI) unit for spring constants is Newtons/meter. A stiffer spring has a greater spring constant, and vice versa.
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5. A pool ball leaves a table with an initial horizontal velocity of 2.4 m/s and lands
0.84 m away from the table. Predict the time required for the pool ball to fall to the
ground and height of the table.
Answer:
Explanation:
Since the initial velocity is purely horizontal, we know that it won't affect the time taken for the ball to fall. So, we can use the equations of motion for a freely falling object to determine the time taken to fall and the height of the table.
Let's use the following equations:
h = vit + 1/2gt^2 ---(1)
vf = vi + gt ---(2)
where h is the height of the table, vi is the initial vertical velocity (which is zero), vf is the final velocity (which is the velocity with which the ball hits the ground), t is the time taken to fall, g is the acceleration due to gravity.
First, let's find the time taken for the ball to fall:
From equation (2), we have:
vf = vi + gt
vf = gt
t = vf/g
Now, we need to find vf. We know that the ball lands 0.84 m away from the table, which means that it has traveled a horizontal distance of 0.84 m. We can use this information along with the initial horizontal velocity to find the time taken for the ball to travel this distance:
d = vit
t = d/vi
t = 0.84 m / 2.4 m/s
t = 0.35 s
So, the time taken for the ball to fall is:
t = vf/g = 0.35 s
Now, we can use equation (1) to find the height of the table:
h = vit + 1/2gt^2
h = 0 + 1/2 * 9.81 m/s^2 * (0.35 s)^2
h = 0.6 m
Therefore, the height of the table is 0.6 m.