lab-3 (ol) periodic and simple harmonic motion – using phet rev 7-15-2020 objectives to study simple harmonic motion, and to determine the value of acceleration due to gravity by using a simple pendulum. also, to verify the equation for time period for a vertical spring-mass system.

The temperature of the gas rounded to three significant figures would be 244 Kelvin.

It is an imaginary gas for which the volume occupies by it is negligible, this gas does not exist in a practical situation and the concept of an ideal gas is only the theoretical one.

As given in the problem, the gas pressure in an oxygen tank is 3.90 atm at a temperature of 298 K. If the pressure decreases to 3.20 atm,

By using the constant volume for the ideal gas,

P₁/P₂ = T₁/T₂

3.90 /3.20 = 298 / T₂

T₂ = 244 Kelvin

Thus, the temperature of the gas rounded to three significant figures would be 244 Kelvin.

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The weight of the object in the newly heavenly body is 3000 N.

In science and engineering, the weight of an object is the pressure performed on the item due to gravity. a few widespread textbooks outline weight as a vector quantity, the gravitational pressure performed on the item. Others define weight as a scalar quantity, the significance of the gravitational pressure.

Given,

mass of earth = M

mass of new heavenly body = 12 M

the radius of the earth = r

the radius of the new heavenly body = 4r

mass of the object = m (mass always remains constant)

[tex]\frac{mM}{r^2}[/tex]

using the formula of gravity,

G₁ = g[tex]\frac{mM}{r^2}[/tex]

G₂ = g[tex]\frac{m12M}{4r^2}[/tex]

comparing G₁  and G₂

G₁ = 1000 N given

G₁ / G₂ = M × 4r² /  12 M r²

G₂ = 1000 × 12 / 4

     = 3000 N

The measure of the pressure of gravity performing on a frame. The method for weight is given by using: w = mg. As weight is a force its SI unit is also the same as that of pressure, the SI unit of weight is Newton (N).

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The first step would be to draw your circle using the compass, the second step would be to add the point to the circle, the third method would be to use the circle's radius to determine the compass's width.

You were instructed to draw a hexagon inside a circle and to list the points as you go. So, in order to pull up that image for your query, I'm going to use my snipping tool.

So, the first step would be to draw your circle using the compass, which would be step number 1. Step number 2 would then be to use the center to get the radius of your circle.

So first you would add the point on the circle, so that would be step number 2 step. Number 3 would be to use the circle's radius to set the width of the compass and then, after you have that point on the circle, you would put the compass on there and you create an arc with that compass that intersects the circle.

And then you would go ahead and mark that intersection with a point connect the consecutive points with a straight edge and then repeat the stips.

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An object that absorbs all radiation that falls on it has an emissivity with a value of 1 and is called a blackbody.

Thermal radiation is emitted by every item above absolute zero. The amount of thermal radiation emitted, however, is a function of the emissivity of the object's surface for any given wavelength and temperature.

Emissivity is defined as the ratio of energy emitted from a material's surface to that emitted from a blackbody, a perfect emitter with the same temperature, wavelength, and viewing conditions. Between 0 and 1, it is a dimensionless number.

In addition to the material, a surface's emissivity is also influenced by its composition. An oxidized and roughened metal surface, for instance, will have a greater emissivity compared to a clean and polished metal surface. Emissivity is defined as the ratio of radiation emitted from an item to that emitted from a blackbody when the temperatures and wavelengths are observed under identical conditions.

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Answer:

[tex]\boxed{m = 0.16875 \;kg}[/tex]

Explanation:

The work done by a constant force F Newtons on a mass of m kg over a distance of d m at an acceleration of a m/s² is given by the  equation:

[tex]W = F\cdot d[/tex]

This should be equal to the kinetic energy expended

[tex]KE = \dfrac{1}{2}m v^2[/tex]

By the law of conservation of energy,

W = KE

[tex]F\cdot d = \dfrac{1}{2}m v^2[/tex]

Given v = 8 m/s, F = 0.12N and d = 45m

[tex]0.12 \times 45 = \dfrac{1}{2} \times m \times 8^2[/tex]

[tex]5.4 = 32m[/tex]

[tex]m = \dfrac{5.4}{32}\\\\\boxed{m = 0.16875 \;kg}[/tex]

A hockey puck with an initial speed of 8.0 m/s coasts 45 m to a stop across the ice. If the force of friction on the puck has a magnitude of 0.12 N the puck's mass is 0.16875 Kg

Work in physics is the energy that is transferred to or from an item when a force is applied along a displacement. In its simplest form, it equals the product of the force's magnitude and the distance travelled for a constant force directed in the direction of motion.

The work done by a constant force F Newtons on a mass of m in kg over a distance of d in m at an acceleration of a m/s² is given by the  equation:

This should be equal to the kinetic energy expended

K E = 1/2 m.v²

work, W = F.d

By the law of conservation of energy,

W = K E

Given v = 8 m/s, F = 0.12 N and d = 45 m

0.12* 45 = .5*m*8²

mass, m =  0.16875 Kg

A hockey puck with an initial speed of 8.0 m/s coasts 45 m to a stop across the ice. If the force of friction on the puck has a magnitude of 0.12 N the puck's mass is 0.16875 Kg

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All living things are constantly engaged in Homeostasis.

Homeostasis is the capacity to sustain a comparatively constant internal condition that endures despite changes in the external environment. To consume energy and eventually live, all living things—from plants to puppies to people—must control their interior environments. For numerous reasons, the body sustains homeostasis. Body temperature, blood sugar levels, and varying pH levels are a few of them. Not merely at the level of the entire body as it is for temperature, homeostasis is maintained at several levels.

Homeostasis is a state that can be preserved by all living things. They have systems in place to regulate things like their internal temperature, water balance, and acidity. Normal cell functions that take place inside of them depend on homeostasis. Normal life processes are interfered with if an organism can't sustain equilibrium. Ailment or even death might follow.

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The approximate magnitude of the friction force of the stone is 2N.

Given values:

Mass(m)= 20 Kg

Velocity(v)= 3m/s

Distance(x)= 40m

Kinetic energy is given by the expression:

[tex]Ek=1/2mV^{2}\\ Ek=1/2*20Kg*(3m/s)^{2} \\Ek=90J[/tex]

If we divide the kinetic energy by the distance traveled we get the friction force:

[tex]Ff=Ek/x\\Ff=90J/40m\\Ff=2.25N[/tex]

Approximate magnitude of the friction force is: [tex]Ff=2N[/tex]

Result is 2N.

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The total distance traveled by the in-line skater is equal to 33.75m.

Equations of motion are the collection of equations that depicts the relationship between the velocity,  distance, time ad acceleration of an object.  We can use these equations of motion to calculate these parameters for a body in motion.

Given, the initial speed of the skater, u = 0

The final speed of the skater, v = 5m/s

The distance covered by the skater is d₁ in the time t₁ and with d₂ in the in time t₂.

[tex]d = d_1 + d_2[/tex]

By using the first equation of motion to calculate the acceleration:

v = u + at

5 = 0 + (4.5)×a

a= 1.11 m/s²

The distance covered in time t₁ = 4.5 sec by the skater:

v² = u²+ 2ad₁

(5)² = 0 + 2×(1.11)×d₁

d₁ = 11.25m

In the second interval t₂ = 4.5 sec, distance: d₂= vt₂

d = (5)×(4.5) = 22.5 m

The total distance covered by in-line skater, d = 22.5 + 11.25 = 33.75 m

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The combined weight of the elevator box and the passenger riding inside it acts as the pulling force on the wires in an elevator. Therefore, in a perfect world, the cable's tension would match the elevator's weight when it is at rest.

How can I determine an elevator cable's tensile force?

Total tension is equal to the weight plus the force of acceleration when lift is upward. Total tension equals the difference between weight and force caused by acceleration as lift decreases.

In medium lengths, tension exerts its force, especially in flexible materials like rope or cord. The force of tension is still a gravitational force. When the body moves.

The net force is the total of all forces acting on an object. According to Newton's Second Law, there must be a net force exerted on an item in order for it to accelerate. If an object's net force is zero, it is said to be in equilibrium and not moving forward.

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We have,

Initial velocity, u= 80 km/h

Final velocity, v= 0km/h

Distance, s= 50m

= 0.05km

Using relation, [tex]v^{2} = u^{2} + 2as\\[/tex]

We get,

[tex]0^{2} = 80^{2} + 2a(0.05)\\[/tex]

[tex]0 = 6400 + 0.1a[/tex]

[tex]-6400 = 0.1a[/tex]

∴ [tex]a = \frac{-6400}{0.1}[/tex]

[tex]a = - 64000[/tex][tex]km/h^{2}[/tex]

To convert the answer into [tex]m/s^{2}[/tex] we have to multiply the answer by [tex]\frac{1000}{3600^{2} }[/tex]

∴ [tex]a = -64000[/tex] ×    [tex]\frac{1000}{3600^{2}}[/tex]

⇒ [tex]a= -4.9382[/tex][tex]{m/s^{2}[/tex]

The deceleration required to stop the car in time to avoid hitting the vehicles ahead is [tex]4.9382[/tex][tex]m/s^{2}[/tex].

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The system in fig. 3.1 is in equilibrium with the string in the center exactly horizontal.

This is further explained below.

Generally, Tension is defined as the pulling force that is transmitted axially by the means of a string, a cable, chain or another object of a similar nature, or by each end of a rod, truss member, or another object of a similar three-dimensional nature.

Alternatively, tension can be defined as the action-reaction pair of forces that act at each end of the elements in question.

[tex]\begin{aligned}&T_1 \cos 35=40 \\&T_1=48.83 \mathrm{~N} \\&T_2=T_1 \sin 35 \\&T_2=28.01 \mathrm{~N}\end{aligned}[/tex]

[tex]\begin{aligned}&T_3 \cos \theta=50 \\\\&T_3 \sin \theta=T_2=28.01 \\\\&\tan \theta=\frac{28.01}{50} \\\\&\theta=\tan ^{-1}\left(\frac{28.01}{50}\right) \\\\&\theta=\frac{29.26}{}=\frac{50}{\cos \theta} \\\\&=\frac{50}{\cos 29.26}=57.31 \\\\&T_3=57.31 \mathrm{~N}\end{aligned}[/tex]

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The kinetic energy of an object is the energy possessed by the object due to its motion. That is when the velocity of the object is zero, i.e., when the object is at rest, the kinetic energy of the object will be zero.

The linear momentum is the product of the mass and the velocity of an object. When the momentum of the object is zero, the velocity of the object is also zer.

Thus whenever a particle has a zero momentum, its velocity and hence its kinetic energy will also be equal to zero.

Therefore, the given statement is true.

The cross-sectional area of ​​a copper conductor if its resistance is 0.2 ohm and its mass is 0.2 kg is 61.7 m²

Considering the conductor is a wire,

Density = m / V

V = A l

ρ = R A / l

m = Mass

V = Volume

l = Height / Length

R = Resistance

ρ = Resistivity

R = 0.2 Ω

m = 0.2 kg

ρ = 0.017 Ω m

Density of copper = 8.96 * 10³ kg / m³

V = 8.96 * 10³ / 0.2

V = 44.8 * 10³ m³

A l = 44.8 * 10³

l = 44.8 * 10³ / A

ρ = R A / l

0.017 = 0.2 A / l

l = 0.2 A / 0.017

Equating both the values of l,

44.8 * 10³ / A = 0.2 A / 0.017

761.6 = 0.2 A²

A² = 3808

A = 61.7 m²

Therefore, the cross-sectional area of ​​a copper conductor is 61.7 m²

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a. Your speed will be 0.0628 m/s

b. The magnitude of your acceleration is 0.000263 m/s2

c. The ratio of your weight at the top of the ride to your weight while standing on the ground is 99.997%

d. The ratio of your weight at the bottom of the ride to your weight while standing on the ground is 100.003%

Using the data given above,

Where:

Radius = 15 m

Time for each loop = 25 minutes (25*60 = 1500 seconds) to complete.

a. To find the speed, which is the length of each loop per unit of time to complete each loop, we use the equation for uniform velocity v where:

v = C/t

Where:

Circumfrence of the ferris wheel; C = ?

Time to go round; t = 1500s

Circumference of the Ferris wheel would be:

C = 2πR = 2π*15 = 94.25 m

v = 94.25 / 1500

v = 0.0628 m/s

b. Since the circular motion is constant, the only acceleration from the motion is the centripetal acceleration. To find the magnitude of acceleration, we use the equation for centripetal acceleration which is:

ac = v²/r

Where:

Velocity; v = 0.0628 m/s

Radius; r = 15

ac = 0.0628/15

ac = 0.000263m/s²

c. Let g = 9.8 ms². At top of the ride, the centripetal acceleration would be pushing you up, while gravity pushes you down, so the weight you experience (compare to standing on ground would be):

g-ac/g

Where

Gravity; g = 9.8ms² (a constant)

Centripetal acceleration; ac = 0.000263m/s²

9.8 - 0.000263/9.8

= 0.99997

= 99.997%

d. At the bottom of the ride, both centripetal acceleration and gravity would be pushing you downward, making you feel like

g+ac/g

Where

Gravity; g = 9.8ms² (a constant)

Centripetal acceleration; ac = 0.000263m/s²

9.8 + 0.000263/9.8

= 1.00003

= 100.003%

Here's the complete question:

While at the county fair, you decide to ride the ferris wheel. having eaten too many candy apples and elephant ears, you find the motion somewhat unpleasant. to take your mind off your stomach, you wonder about the motion of the ride. you estimate the radius of the big wheel to be 15 m, and you use your watch to find that each loop around takes 25 seconds.

a.What is your speed?

b.What is the magnitude of your acceleration?

c.What is the ratio of your weight at the top of the ride to yourweight while standing on the ground?

d.What is the ratio of your weight at the bottom of the ride toyour weight while standing on the ground?

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The area of the IR spectrum where there is only marginal light absorption is known as the atmospheric window. This is the measurement range 8 to 13 mm.

Wireless transmissions flow along a spectrum, which is a term for the undetectable radio frequencies. These signals let us to do everything on our mobile devices, including making calls from them, tagging people on social media, calling Uber, getting directions to a location, and more.Only a small percentage of what is known as the electromagnetic spectrum is used by wireless frequencies.

Other frequencies that we encounter on a regular basis are included in the complete electromagnetic spectrum, even if we are not aware of them. From primary school, you might recall ROYGBIV. That's an acronym for the hues that make up the visible spectrum, or the spectrum that we can see. Other portions of the spectrum carry broadcast radio and television or carry out other commonplace tasks.The fact that cellular communications can use a variety of spectrum frequencies means that various bands have marginally different properties.

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Declination. As you can see, the position has a significant impact on the compass's direction. Declination, which is measured in degrees on your map and represents the angle between magnetic north and true north.

The compass does not always point precisely toward geographic north on the surface of the Earth. An angle known as "declination" describes the compass's departure from true north (or "magnetic declination"). If you were to stand at the north geomagnetic pole, your compass would be held horizontally as usual and would not have a preference to point in any specific direction. The same would be true if you were to stand at the south geomagnetic pole. The north-pointing end of your compass would point up at the south geomagnetic pole if you were to hold it on its side, and it would point down at the north geomagnetic pole.

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a. Angle between the cable and the horizontal in order to pull the greatest possible amount of sand is θ= 19.29° b. weight of sand and box is M= 34 kgs where coefficient of static friction is 0.35.

An object experiences static friction when a force is applied to it; as a result, the object resists the applied force and stays at rest until static friction is removed. In kinetic friction, the frictional force opposes an object's motion. While surfaces at rest with respect to one another experience static friction. Static friction is defined as the difference between zero and the minimum force required to initiate motion. The minimum force needed to initiate motion or dissipate static friction is always greater than the coefficient of friction, which is the ratio between the force preventing motion between two surfaces in contact and the normal force holding them together. The Greek letter mu () is commonly used to represent it.

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The magnetic field at the center of each turn of toroid is: 2.826×10⁻⁵ T

Magnetic field is a vector field in surrounding of a magnet, electric current carrying conductor or a changing electric field, in which magnetic forces can be experienced.

Magnetic field of a toroid is calculated as (B): μ₀nI

Where, μ₀= permeability

n= Number of turns in toroid

I= Current

B= Magnetic field

In the given question,

n=15 turns/cm

I=15mA

Now turns per meter length is: 15/10⁻²=1500turns per meter

The magnetic field at the center of each turn of the toroid is(B): μ₀nI

B= (4[tex]\pi[/tex]×10⁻⁷)(1500)(15×10⁻³A)

B= 2826×10⁻⁸ T

B= 2.826×10⁻⁵ T

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The plane was flying at 39.6 m/s when the bottle was released .

[tex]h = ut + 1/2at^2[/tex]

distance fallen h= 500m

Initial velocity u=0

a=98 m/s2

[tex]h = 1/2at^2[/tex]

[tex]t^2 = 2h/a[/tex]

[tex]t^2 = 1000/9.8 = 10.1s[/tex]

[tex]d_h = 400, t = 10.1s[/tex]

[tex]v = d_h/t\\v = 400/10.1[/tex]

v = 39.6 m/s

Altitude or Height  (also known as depth) is a measurement of the distance between a reference point and a point or object, usually in a vertical or "upward" direction. The exact definition and reference value varies depending on the context (eg, aeronautics, geometry, geodesy, sports, or barometric pressure). Although the term height is often used to refer to the height of a place above sea level, in geography the term height is often preferred for this use.

The vertical measurement of distance in the "down" direction is usually called depth.

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The height of the cliff is 122.5 m and the farthest distance covered equals to 50 m.

Projectile motion is a form of motion experienced by an object or particle that is projected near Earth's surface and moves along a curved path under the action of gravity only.

Given is a ball that is thrown horizontally with an initial velocity of 10 m/s off a cliff and spends 5 seconds in the air before hitting the ground.

Horizontal initial velocity = u[x] = 10 m/s

Vertical initial velocity = u[y] = 0 m/s

Vertical acceleration = a[y] = 9.8 m/s²

Using the second equation of motion along the vertical direction -

S[y] = u[y]t + 1/2a[y]t²

S[y] = 0 + 1/2 x 9.8 x 5 x 5

S[y] = 12.5 x 9.8

S[y] = 122.5 m

Horizontal distance covered = u[x] x t = 10 x 5 = 50 m

Therefore, the height of the cliff is 122.5 m and the farthest distance covered equals to 50 m.

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60 % is the utilization factor of this cogeneration cycle neglecting the pump work of a simple rankine cycle

data sent  A straightforward Rankine cycle generates 40 MW of electricity, 50 MW of process heat, and 60 MW of heat waste that is released into the environment.

rankine cycle produces 40 MW of  power,

50 MW of process heat

60 MW of  heat to the surroundings

Total = 40 + 50 + 60  = 150 MW

Utilized = 50 + 40 = 90 MQ

Usefulness of this cogeneration cycle = 90/150 * 100= 60 %

Usefulness of this cogeneration cycle   = 60 %

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0.96 Newton is the buoyant force due to the surrounding air on a man weighing 800 n .

buoyant force = weight of equal volume of air

= Volume×density of air × g = Weight of man × density of air /density of man

Density of air at 0 degrees celsius = 1.20 kg/m^3

Buoyant force = 800 ×1.20 /1000 = 0.96 N

When a body is totally or partially submerged in a fluid, there is an upward push force on the body known as buoyant force. The buoyant force always moves in a vertical direction. This force has no horizontal component, which is zero. The center of buoyancy is the location where the buoyant force acts. Large hot gas balloons may soar into the sky and ships can float on the water's surface because to this power.

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The brightest star's name within the nighttime sky is Sirius at value. It is also known as Alpha Canis Majoris and is typically referred to as the canine megastar.

It resides in the constellation of Canis fundamental. Sirius is eight.6 mild years far away from us, close enough to be the brightest superstar in our night skies. When you examine a star, you are looking at the mild that got here from the megastar. due to the fact stars are so far away, it takes years for their mild to reach us. consequently, whilst you take a look at a star, you are surely seeing what it gave the impression of years in the past.

The brightest megastar inside the nighttime sky is the Sirius star. in keeping with NASA, it is over 20 instances brighter than our solar and two times as big, although it may not seem that manner to the bare eye. The maximum commonplace way to measure the distance to a celebrity is by way of the use of the parallax approach. this is wherein an astronomer will take note of the big name's role within the nighttime sky and then degree it again six months later.

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Taking the gradient from point B to P, 0.33 km/min is the automobile's instantaneous velocity. Option D is the right answer.

Instantaneous velocity of a moving body is the velocity of the body at an instant of time or at a specific time.

Given that an automobile travels for 90 minutes along a highway. From the graph, it is shown that the velocity is constant at point B to point Point P.

The automobile's instantaneous velocity at time = 60 seconds can be calculated by using the gradient formula along the line BP since the velocity is constant from point B to point P

Gradient = Δ distance / Δtime

Velocity V = (30 - 15) / (75 - 30)

V = 15 / 45

V = 0.33 Km/min

Therefore, the automobile's instantaneous velocity at time = 60 seconds is 0.33 km/min

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The magnitude of the induced electric field at a point near the center of the solenoid is E =0 v/m at a point 0.500 cm from the axis of the solenoid is E = 1.05 × 10^-7 v/m.

formula for magnetic field due to solenoid is ,

B=μ₀nI

E=μ₀nI/2 dI/dt

E = 4π×10^-7 × 700 ×0×48/2

E=0v/m at center of the solenoid.

at r= 0.5cm

E=4π×10^-7 × 700 ×0.5×10^-2×48/2

E=1.05×10^-4 v/m

A long, thin wire loop that is frequently wrapped around a metallic core is referred to as a solenoid in physics. When an electric current is sent through it, the solenoid creates a magnetic field. Solenoids play a crucial role since they can generate precise magnetic fields and function as electromagnets. Its magnetic field has a form that is highly reminiscent to a bar magnet's field when a direct electric current is conducted through it. In a solenoid, the field is powerful and constant. A greater overall magnetic field is created as a result of the little magnetic fields that are produced by the current in each turn of the coil.

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According to momentum conservation momentum before collision is equal to momentum after collision. velocity of trailing care after collision v1=5.047 m/s velocity of leading can after collision v2=5.947 m/s .

In physics, a collision, which is also known as an impact, is the abrupt, violent coming together in close proximity of two bodies, such as two pool cues, a golf club and a ball, a hammer and a nail, two railroad cars when linked, or a falling object and a floor. The force and the amount of time the objects are in touch, in addition to the materials the two objects are made of, have an impact on the outcome of the impact. It is generally knowledge that a hard steel ball dropped on a steel plate would rebound almost to the original position from where it was dropped, while a ball made of putty or lead will not. In a collision, an object encounters a force for a predetermined period of time, which causes a change in the mass's velocity. Each object that collides with the other experiences a force. The two forces are at odds with one another but have equal power.

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The speed of the wave will depend on the wave crest and anchor chain passing time.

What is Speed?

Speed is what it means. the speed at which an object's location changes in any direction. The distance traveled in relation to the time it took to travel that distance is how speed is defined.

Given,

Distance= 15m

Time=6.5sec

Speed=?

We know that speed = Distance/ time

v= 15/6.5

speed, v= 2.30 m/s

Hence, the speed of waves is 2.30m/s

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