ω = sqrt( k/m )
ω: angular frequency; m: mass; k: spring constant
ω = 2π/T
T: period (how long it takes for one revolution)
T = 4.59s/10rev = 0.459s/rev
ω = 2π/T = ω = 2π/0.459
ω = 13.6889 radians/s
One revolution, or 2π radians, is 8 cm. (4 cm to stretch out, the same 4 cm to retract)
13.6889 radians/s * (4cm/2πradians) = 86.01 cm/s
ω = 86.01 cm/s = 0.086 m/s
Let's take the first example, where mass is 50g and angular freq. is 4.59s.
50g = 0.05 kg (kilograms are standard in SI, not grams, and are used more directly in calculations relating to force)
ω = sqrt( k/m )
0.086 = sqrt( k/0.05 )
Square both sides
0.007396 = k/0.05
multiply both by 0.05
k = 0.0003698 N/m = 3.698 * 10^-4 N/m
Let's graph frequency in relation to mass (mass is the independent variable)
Let's calculate the slope of the period-to-mass graph
m (slope) = (T2 - T1)/(m2 - m1) (change in frequency over change in mass)
Let's use the second example for T2 and T2, and the first for ω1 and m1.
m = (6.32-4.59)/(100-50) = 1.73/50
m = 0.0346 seconds/gram, which means for every gram of mass added, the period for 10 revolutions increases by 0.0346 seconds.
Water is more dense than air so when light travels from air to water, the light slows down. This causes the light to bend which way relative to the normal?
In the given case, the light travels from the rarer medium to the denser medium.
When the light enters the denser medium, due to the refraction, it bends towards the normal such that the angle of incidence is more than the angle of refraction.
Thus, the light bends towards the normal.
What does the first law of thermodynamics state about energy?
The first law states that the internal energy change of that system is given by Q − W . Since added heat increases the internal energy of a system, Q is positive when added to the system and negative when removed from the system.
Is Nuclear Energy renewable or nonrenewable? Use in your own words.
Which is a device that stores electric charge by separating positive and negative charges?
Please help me with this question.
With 20 windings, the generator will produce a higher EMF and, consequently, a larger current. This increased current will provide more power to the light bulb, resulting in a brighter illumination compared to the dim illumination observed with only 5 windings.
When you increase the number of wire windings in the generator from 5 to 20, the effect on the light bulb will be a brighter illumination. The brightness of the light bulb is directly proportional to the number of windings in the generator.
By increasing the number of windings, you are increasing the amount of wire wrapped around the magnet. This results in a higher number of turns per unit length, leading to an increased magnetic flux passing through the wire coils.
According to Faraday's law of electromagnetic induction, a change in magnetic flux induces an electromotive force (EMF) in a conductor, which in this case is the copper wire. The induced EMF causes electric current to flow through the wire, creating a flow of electrons.
The 30-W light bulb requires a certain amount of electrical power to produce its specified brightness. With 20 windings, the generator will produce a higher EMF and, consequently, a larger current. This increased current will provide more power to the light bulb, resulting in a brighter illumination compared to the dim illumination observed with only 5 windings.
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the frequency of a pendulum has a period of 1.13 seconds is?
A) 0.88
B) 1.13
C) 1.27
D) 11.3
Answer:
A 0.88
Explanation:
frequency=1/period
=1/1.13=0.88
For the following graph indicate the title with units for the X-and Y-axis: a) Annual cray fish caught in Lambert Bay for the last 20 years.
For the graph of Annual cray fish caught in Lambert Bay for the last 20 years, the axes are as follows:
Y-axis: amount of fish caught
X-axis: year
What is a graph?A graph is a pictorial illustration of data.
There are different types of graphs such as
Bar graphsLine graphScatter plotsPie chart.Pictograph.Column chart.Bubble chart, etcA graph has the vertical axis, known as the Y-axis, and the horizontal axis known as the X-axis.
For the graph of Annual cray fish caught in Lambert Bay for the last 20 years, the axis can be labelled as follows:
Y-axis: amount of fish caught
X-axis : year
In conclusion, in a graph, the vertical axis is known as the Y-axis while the horizontal axis is known as the X-axis.
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Like-charged bodies, when brought closer together, will: repel more strongly be neutralized repel less strongly attract more strongly
Answer:
That's almost the true
Explanation:
it does not happen all the time
The answer is A: Repel More Strongly
Explanation: I took the test but two alike magnets will push away form each other
A water park has a slide that finishes with the rider flying horizontally of the bottom of the slide. The slide is designed to end 1.5 m above the water level, and the average rider is estimated to leave the bottom of the slide at 25 m/s. How far Horizontally will the rider travel from the bottom of the slide before hitting the water?
Answer:
25 m/s * √(1.5 m/g) ≈ 9.78 m
Explanation:
When effects of air resistance is neglected, the motion can be modeled as
x(t) = 25 m/s * t
y(t) = 1.5 m - g * t²
based on a coordinate system where the x axis is on the water level (modeled as a plane), y axis being parallel to the gravitational force and the point of origin sitting at the point on the water surface directly below the exit of the slide. The x value is the horizontal travel we’re interested in. Time t begins at the exit of the slide by this rider. g is the gravitational acceleration.
At the time when the rider hits water, we know y = 0.
0 = 1.5 m - g * t² ⇔ t = ±√(1.5 m/g)
Since we are only interested in the non-negative (not past) time range, it’s t = √(1.5 m/g)
The horizontal travel is thus:
x(√(1.5 m/g)) = 25 m/s * √(1.5 m/g) ≈ 25 * √(1.5/9.81) m ≈ 9.78 m
Which of the following best describes an inverse-square relationship?(A) Daylight on Mars is dimmer than daylight on Earth.(B) A camera flashbulb produces a sudden burst of light.(C) When you blow out a candle, the room darkens.(D) Installing compact fluorescent bulbs reduces your electric bill.
The inverse-square relationship states:
The intensity of the light to an observer from a source is inversely proportional to the square of the distance from the observer to the source. According to this, we can describe this mathematically as follows:
\(\frac{I1}{I2}=\frac{d1^2}{d2^2}\)In this sense:
Let:
I1 = Intensity of light in earth
I2 = Intensity of light in mars
d1 = distance from sun to the earth
d2 = distance from sun to mars
If the light on mars is dimmer:
I2besides:
d2>d1
So, we can conclude that the most accurate statement is:
(A) Daylight on Mars is dimmer than daylight on Earth.
A 4 kilogram (kg) toy car accelerates from 3.0 meters per second (m/s) to 8.0 meters per second. What is the change in the cart's momentum?
Answer:
20 kg*m/s
Explanation:
we're looking for the change in the cars momentum . the formula to identify the cars momentum is Δp=m*vf-m*vi . In this case m= mass , vf= velocity final, and vi= velocity initial . The mass is how much the car weighs , which is 4 kg . Velocity final would be 8 m/s since that's how fast it last was . Velocity initial would be 3 m/s since it had first started at that speed . Now we can jus plug it into the formula .
m= 4 kg
vf= 8 m/s
vi= 3 m/s
Δp= (4)*(8) - (4)*(3)
Δp= 32-12
Δp= 20 kg*m/s
hope this helps .
Find the change in thermal energy of a 25kg severed clown doll head that heats up from 25°C to 35°C, and has the specific heat of 1,700 J/(kg°C).
Answer:
Q = 425 kJ
Explanation:
Given that,
Mass, m = 25 kg
The clown doll head that heats up from 25°C to 35°C
The specific heat is 1700 J/kg°C
We need to find the internal energy of it. The heat required to raise the temperature is given by the formula as follows :
\(Q=mc\Delta T\\\\Q=25\times 1700\times (35-25)\\\\Q=425000\ J\\\\Q=425\ kJ\)
So, 425 kJ of thermal energy is severed.
A liquid X at 25°C is poured to a height of 40cm in a thin capillary tube of length 70cm anc diameter of 1cm. Assume that the volume of the capillary tube does not change with temperature. Find the initial volume of the liquid in cm³
The level within a capillary tube with a radius of 0.45 mm rises to a height of 3 cm above the water's surface when submerged in it.
What is the capillary pressure equation?When water saturation decreases, Pnw outside the pore throat is larger than Pw within the pore throat, resulting in a positive pressure (Pc=PnwPw), which is the definition of capillary pressure.
A micron is equal to 0.001 mm in diameter, therefore the capillaries are just big enough for red blood cells to travel through in a single line. Endothelial cells, which also make up the smooth channel surface of the bigger vessels, are the single layer of cells that make up their walls.
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Light travels 186,282 miles per second.How far does it travel in an hour? IN A DAY?
A. Light travels approximately 670,616,320 miles in an hour.
B. Light travels approximately 16,094,718,080 miles in a day.
How to find out how far it travels in an hour ?Light travels at a speed of 186,282 miles per second. To find out how far it travels in an hour, we can simply multiply this speed by the number of seconds in an hour:
Distance traveled in an hour = 186,282 miles/second x 3,600 seconds/hour = 670,616,320 miles/hour
Therefore, light travels approximately 670,616,320 miles in an hour.
How to find out how far light travels in a day?To find out how far light travels in a day, we need to multiply the distance traveled in an hour by the number of hours in a day:
Distance traveled in a day = 670,616,320 miles/hour x 24 hours/day = 16,094,718,080 miles/day
Therefore, light travels approximately 16,094,718,080 miles in a day.
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a student conducts an experiment in which a cart is pulled by a variable applied force during a 2 s time interval. in trial 1, the student exerts the force on a cart of mass m . in trial 2, the student exerts the force on a cart of mass 3m .
As long as the force and time are the same, all vehicles experience the same change in momentum, regardless of their mass.
Given the time interval force applied on cart = 2s
The mass of cart in trail 1 = m
The mass of cart in trail 2 = 3m
The mass of cart in trail 3 = 5m
From Newtons laws of motion: F = ma where F is the force applied and a is the acceleration and v = v0 + at where v0 is the initial velocity.
So, v = v0 + (F/m)t
We know that momentum is defined as mass x velocity such that:
p = mv then the change in momentum is seen as: Δp = mv - mv0
Δp = m(v0 + Ft/m) - mv0
Δp = Ft
Since the force and time are the same for all vehicles, we can see that the change in momentum is independent of the mass of the vehicles.
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complete question: A student conducts an experiment in which a cart is pulled by a variable applied force during a 2sec time interval. In trial 1, the student exerts the force on a cart of mass M. In trial 2, the student exerts the force on a cart of mass 3M. In trial 3, the student exerts the force on a cart of 5M. In which trial will the cart experience the greatest change in momentum from 0 sec to 2 sec?
A sunken treasure chest is discovered resting on the bottom of a lake. The treasure chest has a mass of 85.0 kg and a volume of 2.0 x 10-2 m3. How much force is needed to lift it?
The amount of force needed to lift the sunken treasure chest is 833 N.
What is the amount of force needed?The amount of force needed to lift the sunken treasure chest is calculated by applying Newton's second law of motion.
F = mg
where;
m is the massg is the acceleration due to gravityThe amount of force needed to lift the sunken treasure chest is calculated as;
F = 85 kg x 9.8 m/s²
F = 833 N
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How much impulse is imparted on a 0.14 kg baseball initially traveling at 32 m/s when it is struck by a baseball bat and begins to travel in the opposite direction at 49 m/s
ANSWER AND EXPLAINATION:
To calculate the impulse imparted on the baseball, we can use the impulse-momentum principle, which states that the impulse experienced by an object is equal to the change in momentum of the object. Mathematically, it can be expressed as:
Impulse = Change in momentum
The momentum of an object is given by the product of its mass and velocity:
Momentum = mass × velocity
In this case, the baseball has an initial mass of 0.14 kg and an initial velocity of 32 m/s. After being struck by the bat, it travels in the opposite direction at a velocity of 49 m/s.
Therefore, the change in momentum is given by:
Change in momentum = (mass × final velocity) - (mass × initial velocity)
Change in momentum = mass × (final velocity - initial velocity)
Change in momentum = 0.14 kg × (49 m/s - (-32 m/s))
Change in momentum = 0.14 kg × (49 m/s + 32 m/s)
Change in momentum = 0.14 kg × 81 m/s
Change in momentum = 11.34 kg·m/s
So, the impulse imparted on the baseball is 11.34 kg·m/s.
Given the functions f(x)=(1/x-3)+1 and g(x) = (1/1+4)+3
Which statement describes the transformation of the graph of function f onto the graph of function g?
O The graph shifts 2 units right and 7 units down.
O The graph shifts 7 units left and 2 units up.
O
e graph shifts 7 units right and 2 units down.
O The graph shifts 2 units left and 7 units up.
The statement that describes the transformation of the graph of function f onto the graph of function g is: The graph shifts 2 units right and 7 units down.
To determine the transformation of the graph of function f onto the graph of function g, we compare the two functions f(x) and g(x) and observe the changes in the equations.
The function f(x) = (1/x - 3) + 1 represents a reciprocal function that is shifted vertically 1 unit up and horizontally 3 units to the right. The reciprocal function is reflected about the line y = x.
The function g(x) = (1/(1 + 4)) + 3 simplifies to g(x) = 4 + 3 = 7, which is a constant function representing a horizontal line at y = 7.
By comparing the equations, we can see that the transformation from f(x) to g(x) involves the following changes:
The term 1/x in f(x) is replaced by the constant 1/(1 + 4) in g(x), resulting in a vertical shift of 7 units up.
The term -3 in f(x) is replaced by 3 in g(x), resulting in a vertical shift of 3 units up.
The +1 in f(x) is replaced by +3 in g(x), resulting in an additional vertical shift of 2 units up.
Therefore, the overall transformation is a shift of 2 units to the right and 7 units down.
Hence, the correct statement is: The graph shifts 2 units right and 7 units down.
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The product of an object's mass and velocity is it's
A) acceleration
B) inertia
C) momentum
D) weight
Answer:
C) Momentum
Explanation:
Refers to an objects mass in motion.
The thermal conductivity of copper at 300 K is 470.4 Wm ¹K¹. Calculate the electrical conductivity of copper at 300 K (L-2.45 X10 WOK -2)
The electrical conductivity of copper at 300 K is 0.566 x 10⁸ Sm⁻¹.
Thermal conductivity and electrical conductivity are two different physical quantities used to describe the ability of a material to conduct heat and electricity respectively. Copper is a metal known to be an excellent conductor of both heat and electricity.
The relationship between thermal conductivity and electrical conductivity in copper is given by the Wiedemann-Franz Law, which states that the ratio of the electrical conductivity to thermal conductivity of a metal is proportional to its temperature.
To calculate the electrical conductivity of copper at 300 K, we will make use of the Wiedemann-Franz Law. The law states that:σ / κ = L T Where σ is the electrical conductivity, κ is the thermal conductivity, L is the Lorenz number, and T is the temperature of the material.
Substituting the values given in the problem, we get:σ / 470.4 = (2.45 x 10⁻⁸) x 300σ = (2.45 x 10⁻⁸) x 300 x 470.4σ = 0.566 x 10⁸ Sm⁻¹Therefore, the electrical conductivity of copper at 300 K is 0.566 x 10⁸ Sm⁻¹.
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Find the terminal velocity of a sphere that has a mass of 600g and a radius of 30cm. Take the density of air 1.2 kg/m^3 . Report the speed in mph.
The terminal velocity of the sphere is approximately 22.68 mph.
The terminal velocity of a sphere is the constant speed at which the gravitational force pulling the sphere down is balanced by the drag force pushing the sphere up. The drag force is proportional to the velocity of the sphere, and can be calculated using the following formula:
Fd = (1/2) * rho * Cd * A * v²
where Fd is the drag force, rho is the density of the fluid (air in this case), Cd is the drag coefficient (which depends on the shape of the object), A is the cross-sectional area of the object perpendicular to the direction of motion, and v is the velocity of the object.
The gravitational force pulling the sphere down is given by:
Fg = m * g
where m is the mass of the sphere and g is the acceleration due to gravity.
At terminal velocity, the drag force is equal in magnitude to the gravitational force, so:
Fd = Fg
Substituting the expressions for Fd and Fg and solving for v, we get:
v = √((2 * m * g) / (rho * Cd * A))
where A = pi * r² is the cross-sectional area of the sphere, and r is the radius of the sphere.
Plugging in the given values, we get:
v = sqrt((2 * 0.6 * 9.81) / (1.2 * 0.47 * pi * 0.3²)) ≈ 10.13 m/s
To convert this to mph, we multiply by 2.23694:
v ≈ 22.68 mph
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if a thermometer indicates a temperature of 86F what's the equivalent temperature in Celsius scale
The equivalent temperature in Celsius scale is (86°F − 32) × 5/9 = 30°C
Take the °F temperature and subtract 32
Multiply this number by 5.
Divide this number by 9 to obtain your answer in °C.
The formula to convert °F to °C is:
T(°C) = (T(°F) - 32) × 5/9
converting 86 degrees Fahrenheit into degrees Celsius:
T(°C) = (86°F - 32) × 5/9
T(°C) = 30 °C
(86°F − 32) × 5/9 = 30°C
When doing the temperature conversion, one quick way to make certain you did the conversion right is to remember Fahrenheit temperatures are higher than the corresponding Celsius scale until you get down to -40°, which is where the Celsius and Fahrenheit scales meet. Below this temperature, degrees Fahrenheit are lower than degrees Celsius.
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Find the current flowing out of the battery.
Answer:
5A
Explanation:
** State the reason why heat transfer by radiation is faster than heat transfer by conduction
Heat transfer by radiation is faster than heat transfer by conduction because radiation can occur through a vacuum, while conduction requires the presence of a medium, such as a solid, liquid, or gas. Radiation is the transfer of energy through electromagnetic waves and does not require any medium to propagate, which means that radiation can occur even in a vacuum or through transparent materials.
On the other hand, conduction requires particles to transfer heat energy from one object to another. In a solid, this occurs through the transfer of kinetic energy from one molecule to another through direct contact, while in a liquid or gas, conduction occurs through collisions between molecules. This process of molecule-to-molecule transfer of heat energy is much slower than radiation and is limited by the physical properties of the medium, such as its thermal conductivity.
Therefore, heat transfer by radiation is faster than heat transfer by conduction because radiation can occur through a vacuum, and is not limited by the physical properties of a medium, while conduction is limited by the thermal conductivity of the medium and requires direct contact between molecules.
HI PLEASE HELP ON QUESTION ASAP USING AVERAGE (MEAN) TO ANSWER QUESTION! IF UR ANSWER AND EXPLAINATION IS CORRECT ILL RATE YOU FIVE STARS, A THANKS AND MAYBE EVEN BRAINLIEST. PLEASE MAKE SURE YOU ANSWER MY QUESTION USING AVERAGES.
1) a meal for 6 cost £12 per person. as it is one of the diners birthday , the other 5 decided to pay for his meal. how much do each of the five friends need to pay?
Each of the five friends needs to pay £12 to cover the cost of their own meals and contribute towards the birthday person's meal. Using mean allows us to distribute the cost equally among the friends, ensuring a fair division of expenses for the meal.
To determine how much each of the five friends needs to pay, we can use the concept of averages (mean) and divide the total cost by the number of people paying.
In this scenario, the total cost of the meal for 6 people is £12 per person. Since the other 5 friends have decided to pay for the birthday person's meal, they will collectively cover the cost of their own meals plus the birthday person's meal.
To calculate the total cost covered by the five friends, we can subtract the cost of one person's meal (since the birthday person's meal is being paid by the group) from the total cost. The cost of one person's meal is £12.
Total cost covered by the five friends = Total cost - Cost of one person's meal
= (£12 x 6) - £12
= £72 - £12
= £60
Now, to find out how much each of the five friends needs to pay, we divide the total cost covered by the five friends (£60) by the number of friends (5).
Amount each friend needs to pay = Total cost covered by the five friends / Number of friends
= £60 / 5
= £12
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Which law of thermodynamics does each of the following scenarios violate (if any)?
A machine that can turn 1000J of heat directly into 1000J of electricity
1.
The first law of thermodynamics
2.
The second law of thermodynamics
3.
The third law of thermodynamics
4.
It is allowed
Answer: The scenario violates the second law of thermodynamics.
Explanation: The second law states that heat cannot be converted into work without some loss of usable energy, and that the amount of usable energy in a closed system will always decrease over time. Therefore, the machine described in the scenario cannot exist because it would violate the second law by converting all of the heat into electricity without any loss of usable energy.
Metals that have shine and luster?
Answer:
luster
Explanation:
In hiking, what fitness component is required of you
Megan walks 100 m east and then travels 70 m north followed by 140 m
east. What is the total distance she travels? Show/explain how you
calculate. *
Answer:
I think it's just 100+70+140
QUESTION 3
Suppose you have a 100-kg wooden crate resting on a wood floor. Assume that the maximum force you can exert horizontally on the crate without moving it
is 588 N. If you continue to exert this force once the crate starts to move, what will be the magnitude of its acceleration (in m/s 22 Note: Use Table 5.1
in
Chapter 5 to determine the coefficient of friction for this problem.
Wood on wood static friction = 0.5
Wood on wood kinetic friction = 0.3
The force of frictions is opposed to relative motion.
The acceleration of the crate is approximately 2.937 m/s².
Reason:
The given parameters are;
The mass of the wood, m = 100 kg
The force which can move the wood, F = 588 N
Wood on wood static friction, \(\mu_s\) = 0.5
Wood on wood kinetic friction, \(\mu_k\) = 0.3
Solution;
The force of friction, \(F_f\), acting when the crate is moving is given as
follows;
\(F_f\) = m × g × \(\mu_k\)
Where;
g = The acceleration due to gravity ≈ 9.81 m/s²
Therefore, we have;
\(F_f\) = 100 × 9.81 × 0.3 = 294.3
The force of friction, \(F_f\) = 294.3 N
The force with which the crate moves, F = 588 - 294.3 = 293.7
The force with which the crate moves, F = 293.7 N
Force = Mass, m × Acceleration, a
\(a = \dfrac{F}{m}\)
Therefore;
\(a = \dfrac{293.7 \ N}{100 \ kg} = 2.937\)
The acceleration of the crate, a ≈ 2.937 m/s².
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