The increase in surface area when the temperature rises from 20 to 75 degrees Celsius. = 11cm².
What transpires as the temperature rises?Heat waves will probably occur more frequently and persist longer as a result of the higher temperatures. Heat waves can be deadly, leading to conditions like heat cramps and heat stroke as well as actual mortality. Additionally, warmer temperatures have the potential to trigger a variety of other changes all around the world.
What is the name for rising temperatures?A fever is defined as a rise in body temperature above what is regarded as normal. It's also known as a high temperature, hyperthermia, or pyrexia, and it typically indicates that your body is attempting to protect you from an infection.
According to the given information:The increase in the surface area of the brass cube (which has six faces), which had side length L at 20 o, is
Δ A - 6(L - ΔL)² - 6L²
12LΔL = 12abL²ΔT
= 12(19 x 10⁻⁶/c)(30cm)²
=(75c - 20c)
= 11cm²
The increase in surface area when the temperature rises from 20 to 75 degrees Celsius. = 11cm².
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a ball player catches a ball 3.4 s after throwing it vertically upward. with what speed did he throw it, and what height did it reach?
The ball was thrown upward with an initial velocity of 33.32 m/s and reached a maximum height of 94.1 m.
What is speed?Speed is a scalar variable that quantifies how quickly an object's position changes in a particular direction. It is a way to gauge how far you've come in a certain amount of time.
How do you determine it?The following kinematic equations can be used to calculate the ball's initial speed and its highest point:
Vertical displacement (y) is equal to the sum of the initial vertical velocity (vo) and the acceleration (a) times time plus 0.5.
Initial velocity (vo) plus acceleration (a) times time equals final velocity (v).
where a is the acceleration caused by gravity, or -9.8 m/s2.
By setting the ball's end velocity to zero and solving for its beginning velocity and displacement, we can first determine the height to which it can travel.
vo = 9.8 * t
= 9.8 * 3.4
= 33.32 m/s
y = vo * t + 0.5 * (-9.8) * t^2
= 33.32 * 3.4 - 0.5 * 9.8 * (3.4^2)
= 94.1 m
So, the ball was thrown upward with an initial velocity of 33.32 m/s and reached a maximum height of 94.1 m.
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what must the charge (sign and magnitude) of a particle of mass 1.48 g be for it to remain stationary when placed in a downward-directed electric field of magnitude 610 n/c ? use 9.80 m/s2 for the magnitude of the free-fall acceleration.
The required charge of the given particle to remain stationary should be -2.3 × 10⁻⁵ C.
The mass of the particle is given as 1.48 g = 0.00148 kg
The magnitude of the downward directed electric field is 610 N/C.
The magnitude of the free-fall acceleration is 9.80 m/s².
Expression of electric field can be given as,
E = F/q
Making q as subject, we have,
q = F/E
The particle's force is equal to the product of its mass and the acceleration of free fall.
q = (m a) / E = (0.00148 × 9.8)/610 = 2.3 × 10⁻⁵ C
When a particle is subjected to an electric force that is directed downward, the force must be directed upward in order for the particle to remain stationary. The charge's sign should be negative for the opposing direction.
Thus, the charge of the given particle to remain stationary should be -2.3 × 10⁻⁵ C.
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a 10.0 kg experimental rocket is catapulted from kennedy space center. it leaves the launch pad with kinetic energy of 1960 j. a) what elements comprise the closed system in this problem and what is the conservative force acting on the experimental rocket? b) how high will the rocket rise?
a). The elements that comprise the system in the question above are kinetic energy and potential energy.
b). The rocket will rise to 20 m high.
Given:
Rocket mass (m) = 10.0 kgInitial kinetic energy (K1) = 1960 Jb)
To calculate the height of the rocket rise, we can use the law of conservation of mechanical energy equation:
K1 + U1 = K2 + U2
U is the potential energy that the rocket has. Its formula is
U = m * g * h
Since we have the mass and acceleration due to gravity, we can calculate the height using that formula.
So,
K1 + U1 = K2 + U2
1960 + U1 = 0 + U2 -> K2 = 0 because at max height, kinetic energy is 0.
U2 = 1960 J
1960 = m * g * h
1960 = 10 * 9.8 * h
h = 20 m
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discuss the significance of the law of energy conservation in relation to the flashlight as well as express some new energy sources that are being researched for the near future.
The law of energy conservation states that energy can be neither created nor destroyed, only converted from one form to another. This law is particularly relevant to the flashlight, as it explains why the flashlight needs a power source in order to operate. Without a power source, the flashlight cannot convert electrical energy into light energy.
In terms of new energy sources, research into renewable sources of energy such as solar, wind, and geothermal is becoming increasingly popular. Solar power is the most promising of these sources, as it can provide a clean and renewable form of energy with no emissions. Wind energy is also becoming more popular, as the technology for harnessing wind energy has improved significantly in recent years.
Geothermal energy is also being explored as a potential source of renewable energy, as it has the potential to provide a steady and reliable form of energy. Additionally, research into energy conservation technologies such as LED lighting and energy efficient appliances is being conducted in order to reduce energy consumption and increase energy efficiency.
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a 6.0-v battery that can store 500.0j of ernergy is connected to a resitor. how much charge must flow between the battery's terminals to completely drain the barrtery if it is fully charged?
Answer:
explain again please meet other people
while an object near the earth's surface is in free fall, its acceleration increases. mass increases. mass decreases. velocity increases.
The correct answer is A) Acceleration increases. When an object is in free fall near the Earth's surface, its velocity increases as it accelerates due to the force of gravity.
This acceleration is constant, and the object's mass does not affect the acceleration rate. As the object accelerates, its velocity increases, and its mass remains constant.
Acceleration is the rate at which velocity changes over time. It is a vector quantity, meaning that it has both magnitude and direction. Acceleration can be caused by a number of factors, such as a change in the speed of an object, a change in direction, or the application of a force. An object is said to be accelerating if it is changing its velocity.
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a hiker walks 6.7 miles to the east in 5.1 hours then turns around and walks 1.1 miles to the west in 1.0 hours. what was her average velocity during the trip?
To find the average velocity of the hiker during the trip, we need to find the total distance covered and the total time taken 1.28 mph
First, let's find the total distance covered:
6.7 miles to the east
1.1 miles to the west
So, the total distance covered is
6.7 + 1.1 = 7.8 miles.
Next, let's find the total time taken:
5.1 hours to the east
1.0 hours to the west
So, the total time taken is
5.1 + 1.0
= 6.1 hours.
Finally, to find the average velocity, we divide the total distance by the total time:
7.8 miles / 6.1 hours
= 1.28 mph
So, the average velocity of the hiker during the trip was 1.28 mph.
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in this experiment, you learned that the acceleration due to gravity is a constant that does not depend on the initial velocity. equation (2.3), however, has a v0 in it. are these two facts consistent? why?
These two facts are consistent because in calculating the value of acceleration due to gravity all other variables are constant.
Equation is derives using
v = u + at
[tex]a=\frac{v-u}{t}[/tex]
This is the equation for an object's final velocity or the velocity at time t when it accelerates with "a." In equation, a does not equal g; rather, it refers to the acceleration of an object that was initially travelling at a speed of u and has since acquired an acceleration.
Since a projectile only experiences the acceleration caused by gravity, we use a = g = 9.81 [tex]\frac{m}{s^{2} }[/tex] in all motion equations for a projectile.
The method used to compute the gravitational acceleration is
g = [tex]\frac{G\times M}{R^{2} }[/tex]; where R is the earth's radius and M is its mass, and G is the gravitational constant of the universe.
As a result, g will always have a constant value of a planet because all of the parameters used to calculate it are constants. similar to earth g = 9.81 [tex]\frac{m}{s^{2} }[/tex] .
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a figure skater can increase her spin rotation rate from an initial spin rotation rate from an initial rate of 1.0 rev every 1.5 seconds, to a final rate of 2.5 rev/s. if her initial moment of inertia was 4.6 kgm2, what is her final moment of inertia?
The final moment of inertia of the figure skater is approximately 1.23 kgm².
What is the Moment ?
Moment is a concept that refers to a single point in time at which an event or decision must be made. It is often used to describe a critical moment of opportunity or a crucial decision that needs to be made. It can also refer to a specific moment of clarity, when a person suddenly has a realization or an epiphany. The Moment can also refer to a feeling or emotion that can be experienced at a particular time and place. It can be a feeling of joy, love, peace, or sorrow. Whatever the feeling is, it can be a powerful experience that can leave a lasting impression.
We can use the conservation of angular momentum to relate the initial and final moment of inertia of the figure skater:
I_i ω_i = I_f ω_f
where I_i is the initial moment of inertia, ω_i is the initial angular velocity, I_f is the final moment of inertia, and ω_f is the final angular velocity.
We are given that the initial angular velocity is 1.0 rev every 1.5 seconds, which can be converted to radians per second by multiplying by 2π/1 rev:
ω_i = (1.0 rev/1.5 s) * (2π/1 rev) ≈ 4.19 rad/s
We are also given that the final angular velocity is 2.5 rev/s, which can be converted to radians per second by multiplying by 2π/1 rev:
ω_f = 2.5 rev/s * (2π/1 rev) ≈ 15.71 rad/s
Substituting these values into the conservation of angular momentum equation and solving for I_f, we get:
I_f = I_i * (ω_i / ω_f)
I_f = 4.6 kgm² * (4.19 rad/s / 15.71 rad/s)
I_f = 1.23 kgm²
Therefore, the final moment of inertia of the figure skater is approximately 1.23 kgm².
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when is it appropriate to describe a charged object as a point charge, and when is it not appropriate?
Answer: When it slows down or speeds up. Depending on which, it is appropiate.
Explanation:
if you heed the sign and slow to 35 mph , what will be your acceleration going around the curve at this constant speed? give your answer in m/s2 .
The acceleration going around the curve at a constant speed of 35 mph is 0 [tex]m/s^2[/tex].
When an object moves at a constant speed in a circular path, it experiences an acceleration known as centripetal acceleration. This acceleration is directed toward the center of the circle and is given by the formula:
acceleration = [tex]v^2[/tex] / r
where v is the velocity of the object and r is the radius of the circular path.
However, if the object is moving at a constant speed, its velocity does not change with respect to time and the acceleration is zero. This means that the car's acceleration going around the curve at a constant speed of 35 mph (15.56 m/s) would be 0 [tex]m/s^2[/tex]. The car's velocity is not changing, so there is no net force causing the car to accelerate.
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a block with a mass of 40 kg is being pushed along a very slippery surface by a 44 lb force. find the acceleration of the block rounded to three significant figures.
The acceleration of block with mass 40 kg is 4.89 m/s^2.
Force is defined as an external cause that changes or tends to change the state of the body once applied. If the body is in motion, it comes to rest, and if at rest, then it will come to motion. It can also cause a change in the direction, shape, size, etc., of the body. Pushing or pulling a door with force is an example.
Force = mass × acceleration
Force is 44 lb = 195.7218 N
Mass = 40 kg.
Now using the formula for force,
195.7218 = 40 × acceleration
Acceleration = 4.89 m/s^2
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5) How do the mathematical relationships you figured out about the effects of mass and speed of an object on its kinetic
energy help you make more-accurate predictions for whether a collision would produce damage in some cases and not
others?
The math helps us to determine the amount of kinetic energy an object has based on its mass and speed, and this information can be used to predict whether a collision would produce damage in some cases and not others. By calculating the kinetic energy of two objects, we can determine the amount of energy that would be released upon impact and whether it would be enough to cause damage. This can help us to make more informed decisions about the safety of certain activities or scenarios.
What is energy?
Energy is the ability to do work. It is the capacity to move an object or cause change. It exists in many forms, such as kinetic energy (energy of motion), potential energy (stored energy), thermal energy (heat), electrical energy, chemical energy, and nuclear energy.
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Force F1 has a magnitude of 30.0N, force F2 has a magnitude of 40 N. The angle between the forces is 60 degree. What is the magnitude and the direction of the resultant vector force, F, obtained by the vector addition of these two forces?
A. F-60.8N, 0-34.7 degrees
B. F 65.5 N. 0= 33.3degrees
C. F=70.0 N, 0= 30.0degrees
D. F 677 N.0 17.1degrees
The magnitude and direction of the resultant vector force, F, obtained by the vector addition of the two forces F1 and F2 with magnitudes of 30.0 N and 40.0 N, respectively, and an angle of 60 degrees between them, are F = 65.5 N and an angle of 33.3 degrees. Answer is Option b.
To solve this problem, we need to use vector addition. We can break down each force into its horizontal and vertical components using trigonometry, and then add the corresponding components together to get the components of the resultant vector. Finally, we can use the Pythagorean theorem and trigonometry to find the magnitude and direction of the resultant vector.
Using trigonometry, we find that the horizontal component of F1 is 15 N and the vertical component is 25.98 N. Similarly, the horizontal component of F2 is 20 N and the vertical component is 34.64 N.
Adding the horizontal components,
F_horizontal = 15 N + 20 N = 35 N
Adding the vertical components,
F_vertical = 25.98 N + 34.64 N = 60.62 N
Using the Pythagorean theorem, we can find the magnitude of F,
|F| = sqrt((35 N)^2 + (60.62 N)^2) = 65.5 N
To find the angle between F and the x-axis,
tan(theta) = F_vertical/F_horizontal
theta = atan(F_vertical/F_horizontal) = 33.3 degrees
Option b is the final answer.
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earth gains and loses mass true or false
Answer: Earth loses several hundred tons of mass to space every day, significantly more than what we're gaining from dust. So, overall, Earth is getting smaller.
Explanation:
Answer:
true
Explanation:
becuase of the gravity of earth
Please Help And Fast!!!!
A boat’s velocity changes as it reaches the dock.
Which situations would cause the boat’s velocity to change?
Select three that apply.
A. The boat is slowing down.
B. The boat is speeding up.
C. The boat is changing direction.
D. The boat is not changing direction.
If the velocity of the boat is changing, then the boat is changing direction.
option C.
What situations would cause the boat’s velocity to change?
The velocity of a boat can change due to various factors such as;
wind resistance, water currents, engine power, and the boat's interaction with the dock.Additionally, the boat's velocity can change if the boat's pilot applies the brakes or changes the direction of the boat. The boat's velocity can also be influenced by the shape and weight distribution of the boat, the speed of the water, and the presence of other boats and objects in the water.
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estimate how long it took king kong to fall straight down from the top of the building (389 m high).
For rectilinear motion with constant acceleration, equations have already been obtained. They are further simplified for free falling objects as just gravity is operating on the body.
What is the Class 9 free fall formula?Imagine that an object body is falling freely from a height of h at a terminal velocity of v for t seconds under the influence of g-force. It will move according to the equations of motion h=frac1gt2 and v2=2gh.
What is the falling object formula?
where g is the gravitational acceleration. On Earth, the value of g is 9.8 m/s/s. The velocity of the object after being dropped from rest for any given period of time can be calculated using the aforementioned equation.
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Balance is the body's ability to maintain ___________ and stability.
strength
control
speed
power
the ceiling of an arena is 19 m above the floor. what is the minimum speed that a thrown ball would need to just reach the ceiling?
The minimum speed that a ball should be thrown to reach ceiling is 19.29m/sec.
In regular use and in kinematics, the speed of an article is the extent of the difference in its situation over the long run or the greatness of the difference in its position per unit of time; it is hence a scalar amount. The typical speed of an item in a time period is the distance gone by the article partitioned by the length of the stretch; the immediate speed is the constraint of the typical speed as the span of the time stretch methodologies zero. Speed isn't equivalent to velocity.
We know that to to find the minimum speed at the base location,we need to use third equation of motion which is
v²-u²=2as
Here,v is final velocity which will be zero,u=?,a=9.8m/sec²,S=-19m
So,on putting we get
=>0² - (u²)=2×(-9.8)×19
=>u²=19.6×19
=>u²=372.4
=>u=√372.4
=>u=19.29m/sec.
Hence,minimum speed to throw a ball is 19.29m/sec
.
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A sample of hydrogen at 1. 65 atm had its pressure decreased to 0. 454 atm producing a new volume of 755 ml. What was its original volume (v^1)
The original volume of the hydrogen sample was 0.2997 L if a sample of hydrogen at 1. 65 atm had its pressure decreased to 0. 454 atm producing a new volume of 755 ml.
We can use the Ideal Gas Law to find the original volume of the hydrogen sample. The Ideal Gas Law states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature. Assuming that the temperature remains constant, we can write:
P1V1 = P2V2
where P1 is the initial pressure of 1.65 atm, V1 is the initial volume, P2 is the final pressure of 0.454 atm, and V2 is the final volume of 755 mL. Converting the volumes to liters and the pressures to atmospheres, we have:
V1 = (P2V2) / P1
V1 = (0.454 * 0.755) / 1.65
V1 = 0.2997 L
So, the original volume of the hydrogen sample was 0.2997 L.
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An object is placed 11.9 cm in front of a mirror. What type must the mirror be to form an image of the object on a wall 1.73 m away from the mirror? What is the magnification of the image? Is the image real or virtual? Is the image inverted or upright?
The mirror is a Concave mirror, the magnification is 0.55.
What is optics?The field of physics known as optics is concerned with the behaviour and characteristics of light, including how it interacts with matter and how to build instruments that can either use or detect it.
Since the image is upright and larger than the object, we need a concave mirror.
We know image height, h/object height, h = -image distance, d'/object distance, d
h'/h = -d'/d
Using the real is a positive convention,
h'= + 11.9 cm, h = + 21.3cm and d = 173 cm.
11.9 cm/ 21.3 cm = -d'/+ 173
0.55 = -d'/ 173
d' = -95.15 cm
Magnification = image height, h'/object height,h
Magnification = 11.9 / 21.3 = 0.55
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a ball with mass 0.48 kg moves at a constant speed. a centripetal force of 23 n acts on the ball, causing it to move in a circle with radius 1.7 m. what is the speed of the ball?
Answer:
The speed of the ball can be found using the formula:
v = sqrt(Fc / m) = sqrt(23 N / 0.48 kg) = sqrt(23 / 0.48) m/s
v = approximately 4.53 m/s
The speed of the ball is approximately 9.01 m/s.
The centripetal force acting on a moving object in a circular path is given by the formula:
F = (mv²) / r
where F is the force, m is the mass of the object, v is its speed, and r is the radius of the circular path.
In this case, we know the mass of the ball is 0.48 kg, the centripetal force acting on the ball is 23 N, and the radius of the circular path is 1.7 m. Solving the formula for v, we get:
v = sqrt((Fr) / m)
Plugging in the given values, we get:
v = sqrt((23 N * 1.7 m) / 0.48 kg)
v = sqrt(81.167) m/s
v ≈ 9.01 m/s
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A camper is about to drink his morning coffee. He pours 400 grams of coffee, initially at 75°C into a 250-g aluminum cup, initially at 16°C. What is the equilibrium temperature of the coffee-cup system, assuming no heat is lost to the surroundings? The specific heat of aluminum is 900 J/kg • K, and the specific heat of coffee is essentially the same as that of water, which is 4186 J/kg • K.
The equilibrium temperature of the coffee-cup system is 67.9 °C.
What is the equilibrium temperature?
The equilibrium temperature of the coffee-cup system is calculated based on the law of conservation of energy as shown below.
Heat lost by the coffee = heat gained by the aluminum
(0.4 kg x 4186 J/kg.K ) ( 75 - T ) = ( 0.25 kg x 900 J/kg.K ) ( T - 15 )
where;
T is the equilibrium temperature125580 - 1674.4T = 225T - 3375
1899.4T = 128,955
T = 128,955 / 1899.4
T = 67.9 °C
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how much energy does the battery supply in 3 h ? express your answer to three significant figures and include the appropriate units
Answer:
explain the question again
which of the following statements apply to wide-angle lens shots? check all that apply. a the space appears compressed. b they minimize movement toward or away from the camera. c they exaggerate the distance from foreground to background objects. d the sense of movement is expanded.
The statements that apply to wide-angle lens shots is that the space appears compressed and that they exaggerate the distance from foreground to background objects. The correct answer is a and c.
A wide-angle lens shot is characterized by a wider field of view than normal lenses. This results in a compressed space within the frame, as objects that are far apart appear closer together.
Additionally, a wide-angle lens has the effect of exaggerating the distance between foreground and background objects, making the background seem further away. This can be used to create a greater sense of depth in a shot.
On the other hand, wide-angle lenses minimize movement toward or away from the camera and do not necessarily expand the sense of movement. However, the wider field of view can make movements seem more pronounced, giving a greater sense of space and energy to the shot.
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8. A 5000 kg open railroad car coasts along with a constant speed of 7.0 m/s on a level
track. Snow begins to fall vertically and fills the car at a rate of 2.6 kg/min. Ignoring
friction with the tracks, what is the speed of the car after 100 min?
Answer:
The problem involves finding the effect of added mass on the speed of a moving object, which can be determined using the law of conservation of momentum.
Before the snow starts falling, the initial momentum of the car is 5000 kg * 7.0 m/s = 35000 kg m/s.
As the snow falls, it adds mass to the car, and its momentum increases. The increase in momentum can be calculated as follows:
2.6 kg/min * 100 min = 260 kg
The final momentum of the system (car + snow) is given by:
35000 kg m/s + 260 kg * 0 m/s (since the snow is falling vertically and has no initial velocity relative to the car) = 35000 kg m/s + 260 kg * 0 m/s = 35000 kg m/s
The final velocity of the system (car + snow) can be determined by dividing the final momentum by the total mass:
35000 kg m/s / (5000 kg + 260 kg) = 35000 kg m/s / 5260 kg = 6.64 m/s
So the speed of the car after 100 minutes is 6.64 m/s.
You are looking at two bars made of solid gold. The first one has a temperature of 20 °C, while the second one has a temperature of 80 °C. Gold has a melting point of 1948 °C. Which of the following statements are correct?
I The particles in the 20 °C bar are vibrating faster than the particles in the 80 °C bar.
II The particles in both bars are moving around randomly.
III The particles in the 80 °C bar have a higher average kinetic energy.
Group of answer choices
I, II, and III
I and III only
I only
III only
The particles in the 80 °C bar are vibrating faster than the particles in the 20 °C bar.
What is solid?One of the four basic states of matter is solid (the others being liquid, gas, and plasma). The least energetic molecules are those that are tightly packed together and make up solids. A solid is distinguished by its structural rigidity and resistance to external forces.
As the temperature of a solid increases, the vibration of atoms of solid bar increases. Hence, the particles in the 80 °C bar are vibrating faster than the particles in the 20 °C bar.
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imped) og 90
Does a 2-kilogram rock have twice the mass
of a 1-kilogram rock? Twice the inertia? Twice
the weight (when weighed in the same loca-b
tion)? (4.5)
urged
bib ord:
Yes, a 2kg rock will have twice the weight and inertia of a 1 kg rock.
What is the weight of an object?
The weight of an object is the measure of the effect of force of gravity on the object.
W = mg
where;
m is the mass of the objectg is acceleration due to gravityThe weight of 2 kg rock and 1 kg rock is calculated as;
W (2) = 2 kg x 9.8 m/s² = 19.6 N
W (1) = 1 kg x 9.8 m/s² = 9.8 N
The weight of 2 kg rock is twice the weight of the 1 kg rock.
Inertia is the measure of reluctance of an object to move or stop moving and it depends on mass, so 2 kg tock will have twice the inertia of 1 kg rock.
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a small mass m on a string is rotating without friction in a circle. what happens to the tangential velocity of the object
When a small mass m on a string is rotating without friction in a circle, the tangential velocity of the object increases.
How does tangential velocity affect circular motion?Tangential velocity is the linear speed of any object that moving along a circular path. A point on the outside edge of a turntable moves a larger distance in one complete rotation than a point near to the center. In uniform circular motion, the direction of the velocity changes continually, so there is always an associated acceleration, although the speed might be constant.
In this case, work is done on the object, and so its kinetic energy increased. Thus, the tangential velocity had to increase. Another way to consider the problem is that kinetic energy (KE) = L2 / 2I. Thus, the kinetic energy (and so the speed) had to increase. Translational kinetic energy = 1/2Mv cm², so if kinetic energy (KE) increases, so must V (velocity).
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The length of the vibrating air column of a simple resonance tube can be altered by adjusting a water level. Resonance is found for a fork of frequency 440 Hz when the length of the air column is 18.8 cm and again when it is 57.3 cm. Explain how each of these positions occurs; calculate the speed of sound in the air in the tube and the position of the next resonance as more water is run out. what would be the corresponding resonance distances if the tube were filled with gas in which the speed of sound is 264m/s
The two corresponding resonance distances would be:
18.8 cm * (264 m/s) / (8332 cm/s) = 0.15 m57.3 cm * (264 m/s) / (8332 cm/s) = 0.45 mWhat are resonance distances?Resonance distances refer to the lengths of the air column in a resonance tube that result in resonance. Resonance occurs when the pressure variations at the two ends of the air column are in phase, which means that the distance between the two pressure nodes must be equal to an integer multiple of one-quarter wavelength (i.e., one-quarter of the wavelength of the sound wave). The length of the air column that results in resonance is referred to as a resonance distance. When the air column is at a resonance distance, it acts as a standing wave, with both pressure and velocity antinodes at the open end of the tube and pressure nodes and velocity antinodes at the closed end. The resonance distances can be used to calculate the speed of sound in the gas filling the tube.
Calculation of Resonance distance:
For the first resonance, where the length of the air column is 18.8 cm, the distance between the pressure nodes must be equal to one-quarter of the wavelength of the sound wave at a frequency of 440 Hz:
(1/4)λ = 18.8 cm
Knowing the frequency and wavelength, the speed of sound in air can be calculated:
v = fλ
Substituting the values for frequency and wavelength:
v = (440 Hz)(18.8 cm) = 8332 cm/s
For the second resonance, where the length of the air column is 57.3 cm, the distance between the pressure nodes must be equal to three-quarters of the wavelength of the sound wave:
(3/4)λ = 57.3 cm
Solving for wavelength:
λ = (57.3 cm)(4) / 3 = 76 cm
The next resonance distance can be found by adding one-quarter of the wavelength to the previous resonance distance. In this case, the next resonance distance would be:
18.8 cm + (1/4)λ = 18.8 cm + (1/4)(76 cm) = 18.8 cm + 19 cm = 37.8 cm
If the tube were filled with a gas in which the speed of sound is 264 m/s, the wavelength of the 440 Hz sound wave would be:
λ = v / f = (264 m/s) / (440 Hz) = 0.6 m
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