A mass weighting 48 lbs stretches a spring 6 inches. The mass is in a medium that exerts a viscous resistance of 27 lbs when the mass has a velocity of 6 ft/sec. Suppose the object is displaced an additional 6 inches and released.

Required:
a. Find an equation for the object's displacement, u(t), in feet after t seconds.
b. What is the mass of the object?
c. What is the damping coefficient?
d. What is the spring constant?

Answers

Answer 1

Answer:

a)

\(u(t)=0.499ft.e^{-\frac{144.76lb/s}{2(48lb)}t}cos(\omega t)\\\\u(t)=0.499ft.e^{-1.5t}cos(\omega t)\)

b)

m = 48lb

c)

b = 144.76lb

Explanation:

The general equation of a damping oscillate motion is given by:

\(u(t)=u_oe^{-\frac{b}{2m}t}cos(\omega t-\alpha)\)    (1)

uo: initial position

m: mass of the block

b: damping coefficient

w: angular frequency

α: initial phase

a. With the information given in the statement you replace the values of the parameters in (1). But first, you calculate the constant b by using the information about the viscous resistance force:

\(|F_{vis}|=bv\\\\b=\frac{|F_{vis}|}{v}\\\\|F_{vis}|=27lbs=27*32.17ft.lb/s^2=868.59ft.lb/s^2\\\\b=\frac{868.59}{6}lb/s=144.76lb/s\)

Then, you obtain by replacing in (1):

6in = 0.499 ft

\(u(t)=0.499ft.e^{-\frac{144.76lb/s}{2(48lb)}t}cos(\omega t)\\\\u(t)=0.499ft.e^{-1.5t}cos(\omega t)\)

b.

mass, m = 48lb

c.

b = 144.76 lb/s


Related Questions

The first P-wave of an earthquake travels 5600 kilometers from the epicenter and arrives at a seismic station at 10:05 a.m. At what time did this earthquake occur?

Ahhhhhh I have a Regent's test in 2 hours and I don't know how to solve this type of question! Any help would be appreciated.

Anyone know what the steps to do this are? I dont even need an answer, just how to get to it. Thank you!

Answers

The earthquake would occur 13 minutes before 10:05 a.m. which will be at 9.52 am.

The p-waves travel with a constant velocity of 7 km/s

The time can be calculated by using the formula

t = d / v

where

T1 =  10:05 a.m

d is the distance they take to travel from the epicenter

v is the speed of the p-waves

On average, the speed of p-waves is

v = 7 km/s

d = 5600 km (given)

Substituting the values in the formula;

t = d / v

t = 5600 ÷ 7

t = 800 seconds

Converting into minutes,

t = 800 ÷ 60

t = 13.3

≈ 13 mins

T1 -  13 mins = T2

10:05 - 13 mins = 9.52 am

It means the earthquake occurred prior 13 minutes, that is at 9.52 am.

Therefore, the earthquake occurred at 9.52 am.

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what is an Electrical transformer?​

Answers

Answer:

A transformer is a passive electrical device that transfers electrical energy from one electrical circuit to another, or multiple circuits.

Explanation:

Hope it helps

Answer:

A transformer with eletric abilities.

Explanation:

A car traveling at a speed of 35.0 m/s encounters an emergency and comes to a complete stop.
How much time will it take for the car to stop if it decelerates at -4.0 m/s²?

Answers

Answer:

time will it take for the car to stop = 8.75 s

Explanation:

The formula linking final velocity(v), initial velocity(u), acceleration(a) and time(t) is

v = u + at

The final velocity is 0 m/s since the car comes to a stop

Initial velocity u = 35 m/s

a = -4 m/s²

We have to find t

Plug in values

0 = 35 + (-4)t

-4t + 35 = 0

-4t = -35

t = -35/-4 = 8.75 s

Which of the following statements is TRUE?
A. When muscles contract they become longer.
B. Involuntary muscle can be identified by its unique striped appearance.
C. The biceps and quadriceps are an antagonistic pair.
D. The origin of a muscle is attached to the bone that does NOT move.

Answers

D the origin of a muscle is attached to the bone that does not move

How has information technology impacted the economy? Choose three answers.

Answers

Information technology has greatly impacted the economy, leading to increased productivity, efficiency, and innovation across industries.

The widespread adoption of information technology in the business world has led to a significant transformation in the way companies operate. Through the use of computers, software, and other digital tools, businesses are now able to streamline their operations, automate processes, and access vast amounts of data that can inform decision-making.

This has resulted in increased productivity, efficiency, and cost savings for companies. Additionally, information technology has facilitated the rise of new industries, such as e-commerce and digital marketing, while also enabling existing industries to adapt and innovate in response to changing market conditions.

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--The complete question is, How has information technology impacted the economy?--

describe one similarity and one difference between the velocity on the reference circle and the velocity on the pendulum

Answers

SHM can be acquired by perpendicular projection of uniform circular motion of a particle on its diameter such a particle is called reference particle and its circular path is called reference circle.

A pendulum reaches its maximum velocity when the block is at its lowest point (the pendulum is vertical and pointing straight down). We can then use the term for conservation of energy to determine the maximum height of the block.

What is the velocity at the bottom of a pendulum?

As the pendulum swings downward, gravity converts this potential energy into kinetic energy, so that at the bottom of the swing, the pendulum bob has zero potential energy, and its kinetic power, (1/2)mv2, equals the initial potential energy (mgh). (So the velocity, v, equals √(2gh).)

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Find the magnitude of the free-fall acceleration at the orbit of the Moon (a distance of 60RE from the center of the Earth with the radius of RE). Use the gravitational acceleration on the surface of the Earth is 9.8m/s2.

Answers

Answer:

The magnitude of the free-fall acceleration at the orbit of the Moon is \(2.728\times 10^{-3}\,\frac{m}{s^{2}}\) (\(\frac{2.784}{10000}\cdot g\), where \(g = 9.8\,\frac{m}{s^{2}}\)).

Explanation:

According to the Newton's Law of Gravitation, free fall acceleration (\(g\)), in meters per square second, is directly proportional to the mass of the Earth (\(M\)), in kilograms, and inversely proportional to the distance from the center of the Earth (\(r\)), in meters:

\(g = \frac{G\cdot M}{r^{2}}\) (1)

Where:

\(G\) - Gravitational constant, in cubic meters per kilogram-square second.

\(M\) - Mass of the Earth, in kilograms.

\(r\) - Distance from the center of the Earth, in meters.

If we know that \(G = 6.674\times 10^{-11}\,\frac{m^{3}}{kg\cdot s^{2}}\), \(M = 5.972\times 10^{24}\,kg\) and \(r = 382.26\times 10^{6}\,m\), then the free-fall acceleration at the orbit of the Moon is:

\(g = \frac{\left(6.674\times 10^{-11}\,\frac{m^{3}}{kg\cdot s^{2}} \right)\cdot (5.972\times 10^{24}\,kg)}{(382.26\times 10^{6}\,m)^{2}}\)

\(g = 2.728\times 10^{-3}\,\frac{m}{s^{2}}\)

What is the best description of realistic fiction o texts that are written in first person about a period in an author's life?

Answers

An autobiography, like a memoir, is the writer's recounting of his or her life and is written in the first person, making the writer the protagonist of the narrative.

What phrase best sums up a realistic piece of fiction?

Contemporary/Realistic: In order to accurately portray our environment and society, realistic fiction develops fictional people and circumstances. Growing up and dealing with social and personal issues are the main themes. Characters in this genre are depicted as they learn about both themselves and others.

Which of these two realistic fiction subgenres predominates?

Historical and contemporary fiction make up realistic fiction's two subgenres. Unlike current fiction, which takes place in the present or recently past, historical fiction takes place at a period that is far enough back in history to be deemed history.

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Answer: the answer is b

Explanation:

edge

PLEASE ANSWER FASG I WILL MARK BRAINELIST PLEASEEEEE
The number of protons in the nucleus of an atom determines the species of the atom, i.e., the element to which the atom belongs. An atom has the same number of protons and neutrons. But the electron number cannot be used instead because (5 points)
a. electrons are not within the nucleus
b. electrons are negatively charged
c. electrons can be removed from or added to an atom
d. electrons are lighter than protons

Answers

The electron number cannot be used instead because electrons can be removed from or added to an atom (option C)

Why the electron number cannot be used instead?

The element of an atom is determined by its proton count, while the electron count can exhibit variability. Take, for instance, a sodium atom, which encompasses 11 protons and 11 electrons. However, it has the capacity to relinquish one electron, transforming into a sodium ion housing only 10 electrons.

This occurs due to the relatively loose binding of electrons to the nucleus, enabling their removal through the influence of an electric field or alternative mechanisms.

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5. You are driving at a constant speed of 35.0 m/s
when you pass a traffic officer on a motorcycle
hidden behind a billboard. One second after your
car passes the billboard, the traffic officer sets out
from the billboard to catch you, accelerating at a
constant rate of 3.0 m/s². How long does it take the
traffic officer to overtake your car?

Answers

The traffic cop needs 23.3 seconds to pass the automobile.

What is the acceleration of a car moving in a straight line at a constant speed?

When your velocity (not speed) changes, you are accelerating. A automobile moving at a steady 100 km/h in a straight line has no acceleration. Average acceleration is equal to (change in velocity) / (duration). The car's acceleration is zero because its change in velocity is also zero.

\(d1 = v1*t1 = 35.0 m/s * 1 s = 35.0 m\)

\(d = d1 = 35.0 m\)

\(d2 = v2*t + (1/2)at^2\)

\(d2 = (1/2)at^2\)

\(v2*t + (1/2)at^2 = (1/2)at^2\)

\(v2*t = (1/2)at^2\)

Solving for t, we get:

\(t = (2v2/a) = (235.0 m/s)/3.0 m/s^2 = 23.3 s\) (rounded to 2 decimal places)

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Mrs Turner has a scale drawing of her apartment.IN the scale drawing the lenght of her apartment is 6.25 inches and the width is 2.75 onches. If Mrs. Turner used the scale factor 1 inc/18ft, what would the area of the apartment be?

Answers

The area of Mrs. Turner's apartment is approximately 0.05304 square feet.

To find the area of Mrs. Turner's apartment, we need to convert the measurements from the scale drawing to the actual measurements in feet, using the given scale factor of 1 inch/18 feet.

Length of apartment in feet = 6.25 inches × (1 foot/18 inches) = 0.34722 feet

Width of apartment in feet = 2.75 inches × (1 foot/18 inches) = 0.15278 feet

Now, we can calculate the area of the apartment in square feet by multiplying the length and width:

Area of apartment in square feet = Length × Width = 0.34722 feet × 0.15278 feet = 0.05304 square feet

Therefore, the area of Mrs. Turner's apartment is approximately 0.05304 square feet.

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Which of the following categories of motion is mutually exclusive with each of the others? A. Translational motion B. Rectilinear motion C. Rotational motion D. Curvilinear motion

Answers

Answer:

C.  Rotational motion

Explanation:

The kinematics of rotational motion describes the relationships between the angle of rotation, angular velocity, angular acceleration, and time. It only describes motion—it does not include any forces or masses that may affect rotation (these are part of dynamics). Recall the kinematics equation for linear motion: v = v+at (constant a).

Rotational motion is mutually exclusive with each of the others. Hence, option (C) is correct.

What is  Rotational motion?

"The motion of an object around a circular route, in a fixed orbit, is referred to as rotational motion."

Rotational motion dynamics are identical to linear or translational dynamics in every way. The motion equations for linear motion share many similarities with the equations for the mechanics of rotating objects. Rotational motion only takes stiff bodies into account. A massed object that maintains a rigid shape is referred to as a rigid body.

What is  Curvilinear motion?

Curvilinear motion is the movement of an object along a curved route. Example: A stone hurled at an angle into the air.

The motion of a moving particle that follows a predetermined or known curve is referred to as curvilinear motion. Two coordinate systems—one for planar motion and the other for cylindrical motion—are used to examine this type of motion.

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is it better to walk or run in the rain?

Answers

Answer:

Not gonna lie. I actually had to think about this a lot XD

Running in the rain can cause you to slip and get hurt. Which I think isn't what you would want.

Walking in the rain (although it is sad), is actually a better idea than running.

Hope this helps!

Answer:

Walk

Explanation:

Running might stop you from being outside for as long, but running on wet ground will most likely result in a not-so-graceful faceplant.

The United States uses only 10% of the world's energy.
True
False

Answers

Answer:

False

Explanation:

17%

the answer to your question is false

sci 207 snhu Thermal shielding tiles on the wing were damaged at takeoff, but presented no problems through the mission until low-level reentry. Why is this so?

Answers

Answer:

This is because there is no problem of heating up of the atmosphere around the shuttle at takeoff, but on low-level reentry, the atmosphere around the shuttle is heated up.

Explanation:

When a rocket takes off, it is relatively travelling at a lower speed at low-level atmosphere where the atmosphere is densest. This slow speed means that the air drag on the shuttle is not too much that the air is compressed and heated up. The result is that not much atmospheric heating is encountered, as the rocket's speed accelerates slowly and is only very fast at high-level atmosphere where the air is thinnest.

For low-level reentry, the shuttle is accelerated from outer space, under the influence of gravity, and has reached a sufficiently high speed at low-level atmosphere where the air is densest. At this level, the atmosphere immediately in front of the shuttle is greatly compressed. The effect is that the compressed atmosphere becomes exceedingly hot, and ignites into a burning flame in front of the shuttle. At this stage, the thermal shielding tiles on the wings of the shuttle is very important, and a damaged tile that was no problem on takeoff becomes a problem at this stage.

Which is a characteristic of an electromagnetic wave?
The fields are at right angles to each other and to the direction of the wave.


The waves are produced when an electric charge is at rest.


The fields are aligned with each other and to the direction of travel.


The fields are independent of each other.

Answers

Answer:

The fields are at right angles to each other and to the direction of the wave.

Explanation:

Compare and contrast climate and weather

Answers

It’s 49% of its original gig hope this helps!
Compare: climate: is more directed to the weather conditions for a long period of time. Weather: is more directed to the short time of what the weather conditions are. Contrast: both and used to look at the conditions outside. For example: It is rainy outside. This is an example of how the weather condition is which is what weather and climate both do.

What physical quantity does the slope of the v2/2 v/s h graph represent: #Hint: The algebraic statement of the conservation of Mechanical Energy is FEequals 1 half m v squared plus m g h where E,m, and g are constants. Solve for v2/2and determine what the slope would be if 'h' was on the horizontal axis. slope--g slope=-Elm slope-E slope-h

Answers

The physical quantity that does the slope of the v2/2 v/s h graph represent is the slope-g. The slope is representing the change in v over the change in time.

By definition, that is the acceleration. Also extra than only a gimmick, it is geometry's manner of displaying us how variables now no longer most effective relate to 1 another, however how they are able to constitute the fee of alteration among the variables.

The slope of the displacement time graph offers us the bodily amount called pace. The slope of a pace graph represents an object's acceleration. As a result, the cost of the slope at a given time represents the object's acceleration at that time. The fee of changing of an object's pace with admire to time is described as acceleration.

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When a car of mass 1079 kg accelerates from 3.00 m/s to some finals speed, 2.00x10^5 J of work are done. Find the final speed

Answers

Answer:

Explanation:

The work-energy theorem says that the change in kinetic energy of a system is equal to the work done.

\(\frac{1}{2}mv^2_f-\frac{1}{2}mv^2_i=\Delta W^{}\)\(\frac{1}{2}m(v^2_f-v^2_i)=\Delta W^{}\)

Now in our case

\(\begin{gathered} m=1079\operatorname{kg} \\ vf=\text{unknown} \\ v_i=3.00m/s \\ \Delta W=2.00\times10^5J \end{gathered}\)

Therefore, the above equation gives

\(\frac{1}{2}(1079)(v^2_f-(3.00)^2^{}_{})=2.00\times10^5J\)

Now we need to solve for v_f .

Mutlipying both sides by 2 gives

\((1079)(v^2_f-(3.00)^2_{})=2.00\times10^5\times2\)

dividing both sides by 1079 gives

\((v^2_f-(3.00)^2_{})=\frac{2.00\times10^5J}{1079}\times2\)

Finally, adding 3.00^2 to both sides gives

\(v^2_f=\frac{2.00\times10^5J}{1079}\times2+3.00^2\)

Finally, simplifying the right-hand side gives

\(v^2_f=379.71\)

taking the square root of both sides gives

\(\boxed{v_f=19.49m/s}\)

Hence, the final speed of the car is 19.49 m/s.

What is the magnitude of the change in potential energy of the block-spring system when it travels from its lowest vertical position to its highest vertical position?

Answers

Answer:

 ΔU = 2 mg h

Explanation:

In a spring mass system the potential energy is U = m g h

where h is measured from the equilibrium point of the spring

the potential energy at the highest point is

         U₁ = m g h

the potential energy at the lowest point is

         U₂ = m g (-h)

instead in this energy it is

          ΔU = 2 mg h

In this two points the kinetic energy is zero, but there is elastic potential energy that has the same value in the two points, so its change is zero

Potential energy is defined as the energy stored in a body which may convert into kinetic energy when moved.

The Formule of the potential energy is \(mgh\) The correct answer is 0

Hence, \(U = 2 mg h\)

 The H stated as the measured from the equilibrium point of the spring

Therefore, the potential energy at the maximum point is  \(U_1 = m g h\)  and the potential energy at the minimum point is    \(U_2 = m g (-h)\)

Hence, after solving it we got

         \(U_1 -U_2 = 2 mg h\)

Therefore, the energy change in the process is 0.

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Explain why the sound waves always reach the observer after the light waves

Answers

Answer:

I think it's because the light waves travel faster than the sound waves.

The speed of light is far greater than the speed of sound hence, sound waves always reach the observer after the light waves.

What is the speed of light?

Light occurs in the electromagnetic spectrum. Recall that light can be transmitted through vaccuum unlike sound.

The speed of light is far greater than the speed of sound hence, sound waves always reach the observer after the light waves.

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The rabbit flea Spilopsyllus has a mass of 0.45 mg. It can jump vertically to aheight of about 3.5 cm. Biologists have hypothesized that the energy for the jump is most likely derived from the elastic potential energy stored in the resilin pads ofthe two rear legs of the flea. Each pad is estimated to have a volume of about and its strain typically reaches a value of 100%. The elastic modulus of resilience is about . Is the hypothesis plausible

Answers

Answer:

Therefore The hypothesis is not plausible Because

\(P.E \geq P.E_e\)

\(P.E=12.435*10^{-5}J \geq 1.4*10^{-7}J\)

Explanation:

From the question we are told that:

Mass \(M=0.45mg\)

Jump height \(h=3.5cm \approx 0.03m\)

Percentage strain \(\mu =100\%\)

Generally the equation for potential energy is mathematically given by

\(P.E=mgh\)

\(P.E=0.45*10^{-3}*9.8*0.03\)

\(P.E=12.435*10^{-5}J\)

Generally the equation for Elastic potential energy is mathematically given by

\(P.E_e=0.5*stress*strain *volume\)

\(P.E_e=0.5*1*2*10^6*1*1.4*10^{-4*(10^-3)^3}\)

\(P.E_e=1.4*10^{-7}J\)

The hypothesis is only plausible at conditions where

\(P.E\leq P.E_e\)

Therefore The hypothesis is not plausible Because

\(P.E \geq P.E_e\)

\(P.E=12.435*10^{-5}J \geq 1.4*10^{-7}J\)

How does a wind turbine transform mechanical energy into electrical energy?

Answers

Answer:

"A turbine takes the kinetic energy of a moving fluid, air in this case, and converts it to a rotary motion. As wind moves past the blades of a wind turbine, it moves or rotates the blades. These blades turn a generator."

When studying energy, the main units to consider are the calories. However, many times the needed numbers are not readily available. Often, conversions need to be done in order to calculate the correct values. Knowledge of the metric system is essential to do this successfully.

If a female lion runs a distance of 469.2 meters while chasing an antelope, how many millimeters did she run?
A.
0.0004692 mm
B.
0.4692 mm
C.
46,920 mm
D.
469,200 mm

Answers

Answer:

B. O.4692 mm

Explanation:

I hope its help keep safe

Answer:

Its  D trust me it is

Explanation:

derivative equation of F = kx

Answers

Given that,

The equation is "F=kx"

To find,

The derivative equation.

Solution,

We are given with the given equation which is as follows :

F = kx ...(1)

Where, F is force, k is spring constant and x is distance covered by the spring

Differentiate equation (1) wrt x.

\(\dfrac{dF}{dx}=\dfrac{d}{dx}(kx)\\\\\dfrac{dF}{dx}=k\)

As k is constant.

Hence, this is the required solution.

Why are doorknobs placed at the edge of a door rather than in the center

Why are doorknobs placed at the edge of a door rather than in the center

Answers

Answer: so it can reach the frame

Explanation:

Answer:

To increase force on the door

Suppose that the two speakers in the figure below are separated by 2.50 m and are vibrating exactly out of phase at a frequency of 429
Hz. The speed of sound is 343 m/s. Does the observer at C observe constructive or destructive interfernce when his distance from
speaker B is (a) 1.15 m and (b) 2.00 m?

Suppose that the two speakers in the figure below are separated by 2.50 m and are vibrating exactly out

Answers

(a) The observed interference is destructive, as the phase difference between the waves exceeds π.

(b) The phase difference between the waves is less than π, so the observed interference is constructive.

What does observer observe at the positions?

When the observer is 1.15 m from speaker B, the path difference between the waves from the two speakers is:

Δx = x₂ - x₁ = 2.50 m - 1.15 m = 1.35 m

The corresponding phase difference is:

Δφ = 2π (Δx / λ) = 2π (1.35 m / (343 m/s / 429 Hz)) ≈ 4.16 rad

Since the two speakers are vibrating exactly out of phase, the phase difference between their waves is π, which is approximately 3.14 rad. Therefore, the observed interference is destructive, as the phase difference between the waves exceeds π.

When the observer is 2.00 m from speaker B, the path difference between the waves from the two speakers is:

Δx = x₂ - x₁ = 2.50 m - 2.00 m = 0.50 m

The corresponding phase difference is:

Δφ = 2π (Δx / λ) = 2π (0.50 m / (343 m/s / 429 Hz)) ≈ 1.55 rad

Since the phase difference between the waves is less than π, the observed interference is constructive.

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A student pours a spoonful of dirt into a cup of water. The water and dirt are stirred together. The water turns a light brown color. Some dark pieces float to the top of the cup and another dark layer forms on the bottom of the cup. Which statement BEST describes the contents of the cup?

Answers

The statement that is correct is that the contents of the cup form a mixture.

What is the nature of the cup?

Though the question is incomplete but I would try to give you a good explanation as much as I can. We must recall that when we talk about a mixture, we have to note that the term mixture would refer to the combination of two or more substances that do not chemically react together.

In this case, we have been told that we have a water that was pure and then we add dirt to it. It is clear that the water and the dirt do not react in any way hence what we have formed is a mixture.

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In which of these sports can one not observe the Magnus effect?

Answers

The Magnus effect can not be observed in skiing.

What is the Magnus effect?

Magnus' effect: When there is relative motion between the spinning body and the fluid, a sideways force is generated on a rotating cylindrical or spherical solid immersed in the fluid (liquid or gas). The effect, bears the name H.G. Magnus Phenomenon, after the German scientist and chemist who first experimentally explored the effect in 1853.

The ball is pushed higher into the air by the Magnus Effect, which has an equal-and-opposite effect to the friction between the air and the ball.

A deflection in the direction perpendicular to the spinning axis and the velocity vector results from the spinning. Tennis players frequently use top or backspin when striking the ball.

When a fastball has a backspin, the upward Magnus Effect works against gravity to keep the ball in the air longer. When a curveball has topspin, however, the downward Magnus Effect works in favor of gravity to shorten the baseball's flight.

In skiing, there is no Magnus effect

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In which of these sports can one not observe the Magnus effect?

a) Baseball

b) Tennis

c) Basketball

d) Skiing

А
B
W
Figure 21-36 shows four
identical conducting spheres that are
actually well separated from one an-
other. Sphere W (with an initial
charge of zero) is touched to sphere Fig. 21-36 Problem 38.
A and then they are separated. Next, sphere W is touched to sphere
B (with an initial charge of -32e) and then they are separated.
Finally, sphere W is touched to sphere C (with an initial charge of
+48c). and then they are separated. The final charge on sphere W is
+ 18c. What was the initial charge on sphere .1?

Answers

Answer:

Photosynthesis is a process used by plants and other organisms to convert light energy into chemical energy that, through cellular respiration, can later be released to fuel the organism's activities.

Explanation:

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