The balloon needs to be charged with a minimum of 1.3 x 10-10 Coulombs for it to adhere to the wall.
To find the minimum amount of charge required on the balloon for it to stick to the wall, we can use the following equation:
Friction force = friction coefficient x normal force
The electrical attraction between the charged balloon and the molecules of the wall, which cause an equal but opposing charged polarization, produces the normal force and may be computed as follows:
Normal force = k x q1 x q2 / r^2
where k is Coulomb's constant, q1 and q2 are the charges on the balloon and the wall's molecules, respectively, and r is the average distance between the opposite charges.
The gravitational force acting on the balloon is given by:
Fg = m x g
Since the downward gravitational force is balanced by the upward static friction force, we can set the gravitational force equal to the friction force:
m x g = friction coefficient x k x q1 x q2 / r^2
Solving for q1, the charge on the balloon, we have:
q1 = (m x g x r^2) / (friction coefficient x k x q2)
Given that the mass of the balloon is 1.4 g, coefficient of static friction with the wall is 0.73, the average distance between the opposite charges is 0.75mm, and Coulomb's constant is 910^9 Nm^2/C^2.
q1 = (1.4 x 9.8 x (0.75 x 10^-3)^2) / (0.73 x 9 x 10^9)
The minimum amount of charge required on the balloon in order for it to stick to the wall is 1.3*10^-10 Coulombs
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2 attempts left enter your answer in the provided box. a metal ball-bearing with a circumference of 41.3 mm weighs 8.77 g. what is the density of the metal in g/cm3 (v of a sphere
A metal ball bearing that has a 41.3 mm circumference weights 8.77 g. the metal has a density of 7.816 g/cm3. The mass of a material per unit of volume is its density.
We must first estimate the volume of the metal ball bearing before dividing the mass by the volume to obtain the density of the metal.
First calculate the radius,
C = 2πr = 41.3mm = 4.13cm
here, we can find the radius,
r = c/2π = 4.13/2π = 0.65cm
to find the volume,
V = 4/3πr³
V = 4/3 π X 0.65³
V = 1.14cm³
now, to calculate density,
m = 8.77g
d = m/v
d = 8.77/1.14
d = 7.6 g/cm³
Finally, by dividing the mass by the volume, we get at the metal's density, which comes to around 7.6 g/cm3.
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04.06 Recording Your Cardiovascular Workout— Flexibility/Cardiovascular Log
Type Name:
Type Date:
Flexibility
Date
Stretching exercise
Muscle worked
reps/time
reps/time
reps/time
Chest/Biceps Stretch
Pectoralis, Biceps
Shoulder/Triceps Stretch
Deltoids, Triceps
Upper Back & Torso Stretch
Trapezius
Lower Back Stretch
Latisimus Dorsi
Lying Quad Stretch
Quadriceps
Modified Hurdler’s Stretch
Hamstrings
Calf Stretch
Gastrocnemius
Lying abdominal stretch
Abdominals
**Remember to use the FIT principles to help you improve your flexibility.
Target Heart Rate Zone (from lesson 04.02 Monitoring the Heart)
Lower Limit =
Upper Limit =
**Make sure you get your heart rate into this range during your workouts.
Cardiovascular
Date
Activity Selected
Starting heart rate
Heart-rate after 5 minutes
Heart rate after 10 minutes
Ending heart rate
5-minute recovery heart rate
Length of activity (minutes)
**Remember to use the FIT principles to help you improve your cardiovascular fitness.
Comments:
The FIT principles are a set of guidelines for designing effective exercise programs. They include:
Frequency: How often you perform the exercise. To improve flexibility, aim to stretch at least 2-3 times per week.
Intensity: How hard you work during the exercise. When stretching, intensity should be moderate and not painful.
Time: How long you perform the exercise. Hold each stretch for 15-30 seconds and repeat each stretch 2-4 times.
Type: The specific exercises you perform. Include a variety of stretches for different muscle groups, such as the hamstrings, quadriceps, and lower back.
How to explain the principle?By following these principles, you can create a stretching routine that is effective for improving your flexibility. It's important to keep in mind that flexibility is also depend on several factors such as age, injury history, and genetics.
So, it's always good to consult with a physical therapist or physician before starting any new exercise program.
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What is the weight of a bear on earth that has a mass of 550 kg. Round your answer to a tenth and include the correct units on your answer.
The weight of a bear on earth that has a mass of 550 kg is found to be 5390 N.
What is Mass?A mass may be characterized as a type of dimensionless quantity that significantly represents the amount of matter in a particle or object. The standard unit of mass in the International System (SI) is the kilogram (kg).
According to the question,
The mass of a bear = 550 kg.
We have to calculate its weight,
The formula for calculating weight is as follows:
Weight = mass × gravity (where gravity = 9.8m/sec).= 550 × 9.8 = 5390 N.
Therefore, the weight of a bear on earth that has a mass of 550 kg is found to be 5390 N.
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a body at temperature of 100f is placed in a room of temperature 50. the room temperature does not change appreciably. if after 10 minutes the temperature of the body has dereased to 90 f, when will the body be at a temperature of 60*f?
The body will be at a temperature of 60°F after around 72 minutes.
The problem can be solved using Newton's law of cooling, which states that the rate of change of temperature of an object is proportional to the difference in temperature between the object and its surroundings. Mathematically, this can be represented as:
T(t) = T_s + (T₀ - T_s) e^(-kt)
where T(t) is the temperature of the object after time t, T₀ is the initial temperature of the object, T_s is the temperature of the surroundings, t is time and k is a constant of proportionality called the cooling coefficient.
Use the initial condition T = 90°F at t = 10 min, T_s = 50°F, T₀ = 100°F to solve for the value of k.
T(t) = T_s + (T₀ - T_s) e^(-kt)
90°F = 50°F + (100°F - 50°F) e^(-k)(10)
40°F = 50°F e^(-k)(10)
e^-10k = 0.8
k = 0.0223
thus we can calculate the time it takes for the body to reach a temperature of 60°F:
T(t) = T_s + (T₀ - T_s) e^(-kt)
60°F = 50°F + (100°F - 50°F) e^(-0.0223)(t)
10°F = 50°F e^(-0.0223)(t)
e^(-0.0223)(t) = 0.2
t = 72.1721
t ≅ 72 minutes
Therefore, it would take around 72 minutes for the body to reach a temperature of 60*F.
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on a 500 millibar chart what type of lines are drawn to represent horizontal changes in altitude which correspond to horizontal changes in pressure? group of answer choices
Height contours are used to indicate horizontal changes in altitude on a chart with a 500 millibar scale, which are equivalent to changes in pressure on the same horizontal axis.
What causes the horizontal pressure variations that cause the Coriolis force?Vertical and horizontal pressure variations cause the Coriolis force. Surface winds would naturally blow from higher pressure to lower pressure if the earth ceased to rotate. The wind tends to cross the isobars or contours on an upper level chart at an angle that averages around 30 degrees.The contour lines on the chart for 500 hPa, which is a constant pressure chart, show how high from the sea surface 500 hPa is, in either meters or decameters.Height contours are used to indicate horizontal changes in altitude on a chart with a 500 millibar scale, which are equivalent to changes in pressure on the same horizontal axis.The complete question is,
In order to depict horizontal changes in altitude that correlate to horizontal changes in pressure on a chart with a 500 millibar scale, ___ are used.
the isobars and the jet streams
d. height contours; c. isotachs.
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a small metal sphere with a net charge of is touched to a small second metal sphere that is initially neutral. the spheres are then placed apart. what is the force between the spheres?
The force between the spheres would be an electrostatic repulsion force since the spheres have the same charge after they are touched.
What is coulombs law?Coulomb's Law is a fundamental principle in physics that describes the electric force between two charges. It states that the force between two-point charges is proportional to the product of the charges and inversely proportional to the square of the distance between the charges. Mathematically, Coulomb's Law is represented as F = kq1q2/r², where F is the force between the charges, k is the Coulomb constant, q1 and q2 are the charges, and r is the distance between the charges. The direction of the force is along the line connecting the two charges and is attractive if the charges are opposite in sign and repulsive if the charges are of the same sign.
The strength of the force would depend on the magnitude of the charge on each sphere and the distance between them according to Coulomb's Law, which states that the force between two-point charges is given by: F = kq1q2/r², where k is the Coulomb constant, q1 and q2 are the charges of the two spheres, and the distance between the spheres center is r.
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a fairgrounds ride spins its occupants inside a flying saucer-shaped container. if the horizontal circular path the riders follow has a 5.00 m radius, at how many revolutions per minute will the riders be subjected to a centripetal acceleration whose magnitude is 1.90 times that due to gravity?
The number of revolutions per minute (rpm) by dividing the speed by the circumference of the path is 14.89 rpm.
What is revolutions?A revolution is a radical, pervasive and often violent change in a society's political, economic, and social structures. It is typically associated with a dramatic shift in power, from one group of people to another, either through the overthrow of a government or through other means such as widespread protest or civil disobedience.
The centripetal acceleration of an object in a circular path is given by the equation:
a_centripetal = (v^2) / r
where v is the speed of the object, and r is the radius of the circular path.
We know the radius of the path is 5.00 m and the centripetal acceleration should be 1.90 times that due to gravity. The acceleration due to gravity is 9.8 m/s^2. Therefore, the centripetal acceleration should be:
a_centripetal = 1.90 * 9.8 = 18.82 m/s^2
Now we can solve for the speed of the riders:
v = sqrt(a_centripetal * r) = sqrt(18.82 * 5.00) = 12.76 m/s
Finally, we can calculate the number of revolutions per minute (rpm) by dividing the speed by the circumference of the path:
rpm = (v / (2 * pi * r)) * 60 = (12.76 / (2 * pi * 5.00)) * 60 = 14.89 rpm.
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an object weighing 297 n in air is immersed in water after being tied to a string connected to a balance. the scale now reads 264 n . immersed in oil, the object appears to weigh 272 n . find the density of the object. answer in units of kg/m3 .
The density of the object (weighing 297 N in air is immersed in water after being tied to a string connected to a balance, the scale now reads 264 N immersed in oil, the object appears to weigh 272 N) is:
(1) The density of the object = 9,181.81 kg/m³
(2) The density of oil = 773.03 kg/m³
The buoyant force is the upward force that a fluid exerts on an object. Archimedes' Principle states that buoyant force equals the weight of the displaced fluid.
To determine the density of an object:
First, we'd calculate the buoyant force acting on the object using the formula:
Fb = Fa - Fw
Where,
Fb = buoyant force (N)
Fa = the weight of object in air (N)
Fw = the weight of object in water (N)
= 297 - 264
= 33 N
Now, determine the volume of the object:
V = Fb/ρg
= 33 / (1000) (9.8)
= 0.0033 m³
The mass of the object in air:
Ma = Fa/g
= 297 / 9.8
= 30.30 kg
Hence,
So, the density of the object:
ρ = m/v
= 30.30 / 0.0033
= 9,181.81 kg/m³
The buoyant force in oil:
Fb = Fa = Fo
= 297 - 272
= 25 N
ρ = fb/vg
= 25 / (0.0033 ) (9.8)
= 0.03234
= 773.03 kg/m³
So, the density in oil = 773.03 kg/m³
The question is incomplete, it should be:
An object weighing 297 N in air is immersed in water after being tied to a string connected to a balance. the scale now reads 264 N, immersed in oil, the object appears to weigh 272 N, find the density of the object. answer in units of kg/m3 .
Find the density of the object.
Answer in units of kg/m³
PART TWO
Find the density of the oil.
Answer in units of kg/m³
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his state no longer recongizes alienation of affection as an issue that can be litigated. which motion should
"A motion to dismiss should be filed if alienation of affection is not recognized as an issue that can be litigated in that state.
In physics, motion is defined as a change in a body's position or orientation over time. Translation is the term for motion along a line or a curve. Rotation is another motion that modifies a body's orientation.
The four types of motion are: linear, rotary reciprocating and oscillating.
Hence , If the state does not recognize alienation of affection as a matter that can be argued, a move to dismiss should be made.
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The question is incomplete, the complete question is:
"His state no longer recognizes alienation of affection as an issue that can be litigated. Which Motion should be filed ?
a ferry boat shaped just like a brick is 7.7 m wide and 6.2 m long. when a truck pulls onto it, the boat sinks 5.57 cm in the water. what is the weight of the truck? the acceleration of gravity is 9.81 m/s 2 . answer in units of n.
The weight of the truck is approximately 254,979 N or 254.9 kN
To find the weight of the truck, we can use the principle of buoyancy, which states that the buoyant force exerted on an object submerged in a fluid is equal to the weight of the fluid that is displaced by the object.
First, we need to find the volume of the water displaced by the boat when the truck pulls onto it. We can use the dimensions of the boat and the amount it sinks in the water to calculate this. The boat is shaped like a brick, so we can assume it has the same dimensions on the top and bottom.
The boat's width is 7.7 m and its length is 6.2 m. The boat sinks 5.57 cm or 0.0557 m in the water.
The volume of the water displaced is the product of the boat's width, length, and the amount it sinks in the water.
Volume of water displaced = 7.7 m x 6.2 m x 0.0557 m = 25.9 m^3
Next, we can use the density of water, which is about 1000 kg/m^3 to find the weight of the water displaced.
Weight of water displaced = 1000 kg/m^3 x 25.9 m^3 = 25900 kg
Finally, we can use the weight of the water displaced to find the weight of the truck using the equation of buoyancy force which is equal to the weight of the fluid displaced.
Weight of truck = weight of water displaced x g
Weight of truck = 25900 kg x 9.81 m/s^2 = 254979 N
Therefore, the weight of the truck is approximately 254,979 N or approximately 254.9 kN.
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the terminals of a 15 v battery. after a long time, the capacitor is disconnected from the battery but is not discharged. what are the charge on each electrode, the electric field strength inside the capacitor, and the potential difference between the electrodes a. right after the battery is disconnected? b. after insulating handles are used to pull the electrodes away from each other until they are 1.0 cm apart? c. after the original electrodes (not the modified electrodes of part b) are expanded until they are 20 cm in diameter?
After the original electrodes 0.8nC are expanded until they are 20 cm in diameter.
What is meant by diameter?
A line that is straight and cuts through the middle of a body or figure. Particularly: the length of a diameter; a line segment passing through the centre of a circle with its ends on the circumference.It is twice as long as a circle's radius, or Diameter = 2 Radius.The diameter of a circle cuts through the centre whereas the radius extends from the centre to the edges of the circle. The diameter of a circle effectively divides the shape in two.The diameter or length of a circle is its circumference. A straight line connecting a point on one end of the circle to a point on the other end, passing through the centre, is the diameter.To learn more about diameter refer to
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A rock is thrown horizontally from a height of 6.00 m. what
is the time required for the rock to reach the ground
The time required for the rock to reach the ground is 1.11 second.
What is acceleration?
Acceleration is rate of change of velocity with time. Due to having both direction and magnitude, it is a vector quantity. Si unit of acceleration is meter/second² (m/s²).
Initial height of the rock: h = 6.00 m.
Acceleration due to gravity: g = 9.8 m/s²
Let, the time required for the rock to reach the ground is = t.
Then:
h = 1/2 × gt²
t = √(2h/g)
= √ {(2 × 6.00)/9.8} second.
= 1.11 second.
Hence, the time required for the rock to reach the ground is 1.11 second.
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at a specific moment, a falling object with mass 4 kg is moving 7 m/s and is 3 meters above the ground. how many joules of mechanical energy does the object have?
A falling item with a mass of 4 kg is 3 metres above the earth and is travelling at a speed of 7 m/s at that precise time. The item has a mechanical energy of 216.4 Joules.
A falling object's kinetic energy (KE) and potential energy may be used to compute its mechanical energy (PE).
KE = 1/2 mv ²
= 1/2 X 4 X 14 = 98
where m is the item's mass and v is its velocity,
The equation PE = m * g * h gives the potential energy of an item.
PE = 4 X 9.8X 3 = 117.6
E = KE + PE gives the object's total mechanical energy.
E = 98 + 117.6
= 215.6 J
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what is the approximate line-to-ground arcing fault value on a 480/277-volt system where the line-line-line fault current has been calculated to be 30,000 amperes?
On a 480/277-volt system where the line-line-line fault current has been estimated to be 30,000 amperes, the approximate line-to-ground arcing fault value is 17,321 amperes.
The approximate line-to-ground arcing fault value for a 480/277-volt system is determined by calculating the line-line-line fault current and then dividing it by the square root of three (√3). The value of the line-line-line fault current must first be determined, which is 30,000 amperes in this case.
Next, the line-to-ground arcing fault current value is calculated by dividing the line-line-line fault current by the square root of three (√3), which is equal to 17,321 amperes. To arrive at this number, we use the following formula:
Line-to-ground arcing fault current = line-line-line fault current / √3
Therefore, the approximate line-to-ground arcing fault current value for a 480/277-volt system where the line-line-line fault current has been calculated to be 30,000 amperes is 17,321 amperes.
To summarize, the approximate line-to-ground arcing fault value for a 480/277-volt system is determined by calculating the line-line-line fault current, which is 30,000 amperes in this case, and then dividing it by the square root of three which is equal to 17,321 amperes. This is the approximate line-to-ground arcing fault current value that would be expected in such a system.
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how fast, in rpm , would a 6.0 kg , 27- cm -diameter bowling ball have to spin to have an angular momentum of 0.22 kgm2/s ?
The ball should spin with the speed of 28.8 rpm in order to have an angular momentum of 0.22 kgm2/s .
Given,
mass = 6 kg and diameter = 27 cm
radius = 27/2 = 13.5
angular momentum = L = 0.22kgm^2/sec
we know that,
angular momentum is L= I*w,
where, I = moment of inertia and
w = angular frequency.
The moment of inertia of a spherical shell is 2/3*M*R^2.
Where , R = radius and M= mass
therefore, I = (2/3)(6kg)*(0.135^2).
= 0.0729 kg.m^2
solve for speed w,
L = I x w
0.22 = 0.0729 x w
therefore, speed = 3.014 m/sec.
3.014 m/s = 3.014 x 60 / 2π
= 28.8 rpm
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a person walks first at a constant speed of 5.10 m/s along a straight line from point circled a to point circled b and then back along the line from circled b to circled a at a constant speed of 3.30 m/s. (a) what is her average speed over the entire trip?
The average speed of that person with two constant speed for a certain distance is 4 m/s.
How to calculate average speed over the entire trip?Assume the distance from point a and b is c, As per data given velocity from a to b = 5.10 m/sec. So,
time a to b = c : 5.10.
Since the constant speed is 3.3. then
time b to a = c : 3.30
The we can determine the average speed as follow:
Total distance = c + c = 2c
Total time = time a to b + time b to a
Total time = c : 5.10 + c : 3.30
Total time = 0.196c + 0.303c
Total time = 0.499c
Average speed = total distance : total time
Average speed = 2c : 0.499c
Average speed = 4.00801603206
Let round the result, so the average speed = 4 m/s
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when two cars collide in real life they come to a stop. does this prove that conservation of momentum is not true in real life? explain
Some of the velocity from a collision between two vehicles crumples their bodies. A purposeful loss of kinetic energy occurs.
According to the rule of conservation of momentum, when two bodies contact in a closed or isolated system, their combined momentum before and after the collision must be identical if no outside force is acting on them. In other words, the system momentum is unchanged.
Momentum is defined as p = mv (in kg/s).
Where V is a body's speed, m = the body's mass, In order to maintain momentum
mv = unchanging
This is,
m1v1 = m2v2
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PART 1
A merry-go-round rotates at the rate of
0.37 rev/s with an 73 kg man standing at
a point 1.2 m from the axis of rotation.
What is the new angular speed when the
man walks to a point 0 m from the center?
Consider the merry-go-round is a solid 29 kg
cylinder of radius of 1.2 m.
Answer in units of rad/s.
PART 2
What is the change in kinetic energy due to
this movement?
Answer in units of J.
The angular velocity is infinity.
it's not possible to calculate the kinetic energy change when the angular velocity becomes infinity, it's an abstract concept.
What is angular speed?PART 1
The angular velocity of an object is given by the formula:
ω = v/r
where
v is the linear velocity and
r is the distance from the axis of rotation.
The man's initial angular velocity is:
ω = (0.37 rev/s) * (2π rad/rev)
= 2.34 rad/s
As the man moves closer to the center, his distance from the axis of rotation decreases, so his angular velocity will increase.
To find the new angular velocity, we can use the same formula:
ω = v/r
since the radius decreases to 0, the angular velocity becomes infinity.
PART 2
The change in kinetic energy is given by the formula:
ΔK = 1/2 * I * (ω_f^2 - ω_i^2)
where
I is the moment of inertia and ω_i and ω_f are the initial and final angular velocities respectively.For a solid cylinder, the moment of inertia is:
I = (1/2) * m * r^2
where
m is the mass and r is the radius.The moment of inertia for the merry-go-round is:
I = (1/2) * (29 kg) * (1.2 m)^2
= 15.12 kg * m^2
The change in kinetic energy can be calculated as:
ΔK = 1/2 * (15.12 kg * m^2) * (∞^2 - (2.34 rad/s)^2)
= infinity J
Note that it's not possible to calculate the kinetic energy change when the angular velocity becomes infinity, it's an abstract concept.
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Position (m)
0
12
10
5. Using the graph, describe what is happening between 4 and 6 seconds.
Position vs Time
6
Time (s)
8
10
12
In the position time graph, between 4 and 6 seconds, the object is at rest because the change in position with time is zero.
What is position - time graph?
A position - time graph is a type of graph in which the position of an object is plotted against time of motion of the object.
In a position time graph, the slope of the graph is the velocity of the object since velocity is defined as the change in displacement with change in time.
From the given position - time graph, between 4 to 6 seconds, the change in position of the object is constant, hence the velocity of the object will be zero, so we can conclude that the object is at rest between 4 to 6 seconds.
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the pipe of length l that is open at both ends is resonating at its fundamental frequency. which statement about sound is correct?
The correct statement would be that the wavelength is 2L and there is a displacement node at the pipe's mid point, if L is the length of the open pipe.
The fundamental frequency is the smallest resonant frequency of a vibrating object. Most of the vibrating objects possess more than one resonant frequency and which are used in musical instruments. On the other hand, a harmonic is defined as an integer multiple of the fundamental frequency.
Vibrating strings, open pipe, and conical air columns vibrate at all harmonics of the fundamental. Cylinders with only one end opened vibrate with only odd harmonics of the fundamental.
Hence the correct option is A.
--The given question is incomplete, the complete question is:
"The pipe of length L that is open at both ends is resonating at its fundamental frequency. which statement about sound is correct? A) The wavelength is 2L and there is a displacement node at the pipe's mid point. B) the wavelength is L and there is a displacement antinode at the pipe's mid point C) the wavelength is 2L and there is a displacement antinode at the pipe's mid point D) the wavelength is L and there is a displacement node at the pipe's mid point
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A science teacher ran a marathon. She showed her students the silver blanket she was given after the race to keep her warm.
A group of students investigated how the colour of the blanket affected how much infrared radiation was absorbed.
Give one reason why the infrared lamp was placed the same distance from both cans
The matte with is silver should be metallic, so it reflects light at all wavelengths, so that the infrared light returns to the body and decreases the radiation radiation emitted, thus keeping it warmer.
What is meant by radiation?
Energy that emanates from a source and moves through space at the speed of light is referred to as radiation. This energy has wave-like qualities and is accompanied by an electric field and a magnetic field. Radiation may also be referred to as electromagnetic waves.Let's now examine the various radiation types. There are four main categories of radiation: gamma rays, alpha rays, beta rays, and neutrons.One of the main sources of natural radiation is the makeup of the earth's crust. Natural uranium, potassium, and thorium deposits that naturally decay and generate modest amounts of ionising radiation are the principal contributors.To learn more about radiation refer to
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The internal energy of a gas decreases by 344 J. If the process is adibiatic, how much energy is
transferred as heat? How much work is done on or by the gas?
The energy that is transferred as heat if the process is adiabatic is 0J and the work is done on or by the gas is 344J.
Given the internal energy of a gas decreases by (ΔU) = 344J
In an adiabatic process, an ideal gas' internal energy reduces by an amount equal to the work the system performs.
ΔU = work done + heat exchange
There is no heat exchange in an adiabatic process according to first law of thermodynamics.
The gas is doing work since the process is adiabatic and the amount of energy transferred as heat will be Q= 0J. If there is no heat exchange during the operation, a change in internal energy equals work done.
Then the work done by the gas is (W) = 344J
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The direction of a vector cannot be different in different coordinate systems. A vector can have a component equal to zero even when its magnitude is non-zero. The component of a vector can be different in the different coordinate systems it is possible to multiply a vector by a scalar. true or false
It is true that a vector's component can vary depending on the chosen coordinate system, that a vector can be multiplied by a scalar, and that a vector can have a component equal to 0 even if its magnitude is not 0.
The idea that a vector cannot have a different direction in different coordinate systems is untrue. A physical quantity that exists without us is represented by a vector. As a result, the vector itself is independent of the coordinate system we use. However, the vector's coordinates are affected by the coordinate system. Only when two vectors have the same magnitude and direction are they regarded as being equal. The coordinate system has no influence on a vector.
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A roller coaster begins at rest 120 m above the ground, as
shown. Assume no friction from the wheels and air, and that no
energy is lost to heat, sound, and so on. The radius of the loop
is 40 m. Find the speed of the roller coaster at points E and F.
Note:-Use g = 10 mlsz
The speed of the roller coaster at point E is 40 m/s.
The speed of the roller coaster at point F is 49 m/s.
What is the speed of the roller coaster at point E?
The speed of the roller coaster at point E is calculated by applying the following formula as shown below.
v = √ ( 2gΔh )
where;
g is acceleration due to gravityΔh is the change in height of the roller coasterAt point E, the change in height of the coaster, Δh = 120 m - 40 m = 80 m
v = √ ( 2gΔh )
v = √ ( 2 x 10 x 80 )
v = 40 m/s
At point F, the change in height of the coaster, Δh = 120 m - 0 m = 120 m
v = √ ( 2gΔh )
v = √ ( 2 x 10 x 120 )
V = 49 m/s
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The spring-held follower AB has a mass of 0. 45 kg and moves back and forth as its end rolls on the contoured surface of the cam, where r = 0. 15 m and z=(0. 02cos2θ)m. The cam is rotating at a constant rate of 30 rad/s. The spring is uncompressed when θ = 90∘
The body and through a specific angle experience angular accelerations of 0.87266 rad/sec2 and 12566.8 rad, respectively.
Calculate angular acceleration ?A rotating rigid body's angular velocity rises from 500 to 1500 rev/min under the given conditions.
Time= 120s
Finding - Angle and angular acceleration
The basic idea is that we must change rev/min to rad/sec.
ωf= ωi + αt
ωf- ωi = αt
Formula for angular acceleration: = [f- i]/t
Angle deviation formula: =it + t2/2
Calculations-
Rev/Min to rad/Sec conversion
I equals 500 rev/min
500 x 2 rad/rev x 1 minute and 60 seconds equals 52.3598 rad/sec.
f = 1500 rev/min
=1500 x 2 rad/rev x 1 minute and 60 seconds = 157.079 rad/sec
52.3598 rad/sec for I
ωf=157.079rad/sec
Now, to calculate angular acceleration, use the formula: [f- i]/t.
52.3598 rad/sec − 157.079 rad/sec = 120
1.872666 rad/sec
To calculate the angle deviated, enter -=i t + t2/2.
=52.3598 x 120 + [0.87266 x 120 x120]/2
ΔФ= 12566.8rad
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_____ is the magnitude of gravitational force acting on an object.
Question 5 options:
Weight
Net Force
Gravity
Kinetic Energy
Answer:
Weight
Explanation:
The magnitude of the gravitational force acting on an object is weight of the object.
Answer: Option B
Explanation:
Any kind of force is a vector quantity having magnitude and direction. And it is also known that all kinds of forces obey Newton’s second law of motion. This means that the magnitude of any kind of force will be equal to the product of mass and acceleration exhibited by the object.
As the term acceleration is also a vector quantity in the second law of motion, so the direction of acceleration will define the direction of force. Thus for the gravitational force, the acceleration will be acting downward and the acceleration of the object pulled due to gravitational force will have acceleration due to gravity.
So the Newton’s second law of motion representation of gravitational force will be
Now this product is also equal to the weight of the object as weight of any object is defined as the mass of the object influenced by gravitational pull.
A 40 kg child is in a swing that is attatched to ropes that are 2 meters long. FInd the gravitational potential energy associated with the child relative to the child's lowest position: when the ropes are horizantal, when the ropes make a 30 degree angle with vertical, when at the bottom of the circular arc?
The gravitational potential energy (GPE) of an object is given by the equation:
GPE = mgh
where m is the mass of the object, g is the acceleration due to gravity ([tex]9.8 m/s^2[/tex] on the surface of the Earth), and h is the height of the object relative to some reference point.
To calculate the GPE of the child relative to the child's lowest position, we need to know the height of the child at different positions of the swing.
When the ropes are horizontal: The height of the child is the same as the lowest position, which is considered to be zero. So, the GPE is 0 J (Joules).
When the ropes make a 30-degree angle with vertical: The height of the child is [tex]h = 2 * sin(30) = 1 m[/tex] (using the sine function, where the angle is measured in radians)
At the bottom of the circular arc: The height of the child is[tex]h = 2 * (1-cos(30)) = 0.866 m[/tex] (using the cosine function, where the angle is measured in radians)
So the GPE of the child relative to the child's lowest position:
At the horizontal position: GPE [tex]= 40 * 9.8 * 0 = 0 J[/tex]
At the 30-degree angle with the vertical: GPE[tex]= 40 * 9.8 * 1 = 392 J[/tex]
At the bottom of the circular arc: GPE [tex]= 40 * 9.8 * 0.866 = 337.44 J[/tex]
What is GPE?Gravitational potential energy (GPE) is the energy possessed by an object as a result of its position in a gravitational field. It is the energy an object has due to its height above a reference point and is directly related to the force of gravity acting on the object. The greater the height of an object, the more potential energy it possesses.
The formula for gravitational potential energy is:
GPE = mgh
where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object relative to the reference point.
For example, when an object is lifted from the ground to a height h, it gains GPE equal to mgh. Similarly, when an object is allowed to fall from a height of h, it loses GPE as it converts that energy into other forms like kinetic energy.
GPE is a scalar quantity and its unit is Joule(J). It is important to note that the reference point chosen will affect the value of GPE, but it doesn't affect the relative changes in GPE.
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A piano tuner tretche a teel piano wire with a tenion of 879 N. The wire i 0.400 mm long and ha a ma of 3.30 g.
What i the frequency of it fundamental mode of vibration? What i the number of the highet harmonic that could be heard by a peron who i capable of hearing frequencie up to 10000 Hz?
The highest frequency audible is the 24th harmonic. The fact that a standing wave on a wire generates an identical sound wave in the air is used in component (b).
The basic frequency formula is what?V = v/2l corresponds to the fundamental frequency (n = 1). Overtones or harmonics are higher frequencies that are multiples of the fundamental frequency. The first harmonic, also known as the first overtone, is typically referred to as the fundamental; the second harmonic, or n = 2 yields the first harmonic.The highest frequency audible is the 24th harmonic. Evaluate, The fact that a standing wave on a wire generates an identical sound wave in the air is used in component (b).For each instrument, the overtone intensities (f2 = 524 Hz, f3 = 786 Hz, f4 = 1048 Hz, etc.) change despite the fact that the fundamental tone's frequency (f1 = 262 Hz) is the same for all of them.To learn more about frequency refer to:
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1) define the term zenith. what constellation is at zenith right at sunset on january 20, 2023, and how did you use stellarium to figure it out?
The point of the celestial sphere that is directly opposite the nadir and vertically above the observer is known as Zenith.
Perseus, auriga, taurus, gemini are zenith at sunset tonight. Stellarium is a open software that shows real time 3d sky images. From which you can know the position of stars, planets, constellations and other sky objects. If you are using stellarium mobile app, just point it towards the sky and it will show the celestial objects with names. The rising constellations rotate based on our Earth and where it is as it travels through space. It can be predicted through stellarium. The time period zenith every so often approach the best factor, way, or stage reached with the aid of using a celestial frame on its every day obvious direction round a given factor of observation.
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The point in the sky or the celestial sphere that is immediately above the observer is called the zenith.
The point on the celestial sphere that is immediately above a viewer on Earth is called the zenith. The nadir is the point directly beneath you that is 180 degrees opposite the zenith. To see your sky, drag the "Markings" pane to the side. You can now figure out the limits of the constellations.
On the meridian, roughly in the middle of the "sky," is where the zenith is located the area of the sky directly overhead, altitude = 90 degrees. In more specific terms, it is situated where declination and observer latitude are equal. The celestial equator and the ecliptic are additional reference points on the planisphere.
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1. A quarterback passes a football at a velocity of 15.2 m/s at an angle of 40° to the horizontal
toward an intended receiver 27.4 m downfield. The pass is released 1.3 m above the ground. Assume
that the receiver is stationary. Does he catch the ball to complete the pass if he were to catch the ball
at the same height it is released?
The intended receiver did not receive the ball since the ball travelled a shorter distance.
What is the time of motion of the ball?
The time of motion of the ball is calculated by applying the following formula as shown below.
h = vt + ¹/₂gt²
where;
v is the velocity of the ballg is the acceleration due to gravityt is the time of motion1.3 = ( 15.2 x sin40 )t + ¹/₂ ( 9.8 )(t²)
1.3 = 9.8t + 4.9t²
4.9t² + 9.8t - 1.3 = 0
solve the quadratic equation suing formula method;
t = 0.13 second
The horizontal distance of the ball is calculated as;
d = Vₓt
d = ( 15.2 x cos 40) x 0.13
d = 1.51 m
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