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Your friend is trying to construct a clock for a craft show and asks you for some advice. She has decided to construct the clock with a pendulum. The pendulum will be a very thin, very light wooden bar with a thin, but heavy, brass ring fastened to one end. The length of the rod is 80 cm and the diameter of the ring is 10 cm. She is planning to drill a hole in the bar to place the axis of rotation 15 cm from one end. She wants you to tell her the period of this pendulum.

Answers

Answer 1

Answer:

Answer:

The period of the pendulum is $T = 1.68 \ sec$

Explanation:

The diagram illustrating this setup is shown on the first uploaded image

From the question we are told that

The length of the rod is $L = 80 \ cm$

The diameter of the ring is $d = 10 \ cm$

The distance of the hole from the one end $D = 15cm$

From the diagram we see that point A is the center of the brass ring

So the length from the axis of rotation is mathematically evaluated as

$AP = 80 + 10 -5 -15$

$AP = 70 \ cm = (70)/(100) = 0.7 \ m$

Now the period of the pendulum is mathematically represented as

$T = 2 \pi \sqrt{(AP)/(g) }$

$T = 2 \pi \sqrt{(0.7)/(9.8 ) }$

$T = 1.68 \ sec$

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A standing wave of the third overtone is induced in a stopped pipe, 2.5 m long. The speed of sound is The frequency of the sound produced by the pipe, in SI units, is closest to:
A large aquarium has portholes of thin transparent plastic with a radius of curvature of 1.95 m and their convex sides facing into the water. A shark hovers in front of a porthole, sizing up the dinner prospects outside the tank.a) If one of the sharks teeth is exactly 46.5 cm from the plastic, how far from the plastic does it appear to be to observers outside the tank? (You can ignore refraction due to the plastic.)b) Does the shark appear to be right side up or upside down?c) If the tooth has an actual length of 5.00 cm, how long does it appear to the observers?
An air-conditioning system is to be filled from a rigid container that initially contains 5 kg of liquid R-134a at 24°C. The valve connecting this container to the air-conditioning system is now opened until the mass in the container is 0.25 kg, at which time the valve is closed. During this time, only liquid R-134a flows from the container. Presuming that the process is isothermal while the valve is open, determine the final quality of the R-134a in the container and the total heat transfer. Use data from the tables.
A piccolo and a flute can be approximated as cylindrical tubes with both ends open. The lowest fundamental frequency produced by one kind of piccolo is 522.5 Hz, and that produced by one kind of flute is 256.9 Hz. What is the ratio of the piccolo's length to the flute's length?

A horizontal force of 750 N is needed to overcome the force of static friction between a level floor and a 250-kg crate. If g-9.8 m/s, what is the coefficient of static friction? a. 3.0 b. 0.15 c. 0.28 d. 0.31

Answers

Answer:

0.31

Explanation:

horizontal force, F = 750 N

mass of crate, m = 250 kg

g = 9.8 m/s^2

The friction force becomes applied force = 750 N

According to the laws of friction,

Friction force = μ x Normal reaction of the surface

here, μ be the coefficient of friction

750 = μ x m g

750 = μ x 250 x 9.8

μ = 0.31

Thus, the coefficient of static friction is 0.31.

Based on the calculatins, the coefficient of static friction is equal to: D. 0.31.

Given the following data:

Force = 750 Newton.

Mass = 250 kg.

Acceleration due to gravity = 9.8 $m/s^2$

How to calculate the coefficient of static friction.

Mathematically, the staticfrictional force acting on an object is giving by this formula:

$F_s=\mu N=\mu mg\n\n\mu =(F_s)/(mg)$

Where:

$\mu$ is the coefficient of static friction.

N is the normal force.

m is the mass.

g is the acceleration due to gravity.

Substituting the given parameters into the formula, we have;

$\mu =(750)/(250 * 9.8)\n\n\mu =0.31$

Read more on force here: brainly.com/question/1121817

Imagine that you drop an object of 10 kg, how much will be the acceleration andhow much force causes the acceleration?

Answers

If you do this on Earth, then the acceleration of the falling object is 9.8 m/s^2 ... NO MATTER what it's mass is.

If its mass is 10 kg, then the force pulling it down is 98.1 Newtons. Most people call that the object's "weight".

A child attaches a 0.6 kg toy to a 0.9 meter length of string and spins it around in uniform circular motion. Calculate the tension in the string if the period of rotation is 4.1 seconds.

Answers

Answer:

1.26812 N

Explanation:

$m$ = Mass of toy = $0.6\ \text{kg}$

$r$ = Length of string = $0.9\ \text{m}$

$t$ = Period of rotation = $4.1\ \text{s}$

Time period is given by

$t=(2\pi r)/(v)\n\Rightarrow v=(2\pi r)/(t)\n\Rightarrow v=(2\pi 0.9)/(4.1)\n\Rightarrow v=1.3792\ \text{m/s}$

The rotational velocity is 1.3792 m/s

The tension in the rope will be the centripetal force acting on the toy

$T=(mv^2)/(r)\n\Rightarrow T=(0.6* 1.3792^2)/(0.9)\n\Rightarrow T=1.26812\ \text{N}$

The tension in the string is 1.26812 N.

A box weighing 52.4 N is sliding on a rough horizontal floor with a constant friction force of magnitude LaTeX: ff. The box's initial speed is 1.37 m/s and it stops after 2.8 s. Determine the magnitude of the friction force exerted on the box.A box weighing 52.4 N is sliding on a rough horizontal floor with a constant friction force of magnitude LaTeX: ff. The box's initial speed is 1.37 m/s and it stops after 2.8 s. Determine the magnitude of the friction force exerted on the box.

Answers

Answer:

The magnitude of the friction force exerted on the box is 2.614 newtons.

Explanation:

Since the box is sliding on a rough horizontal floor, then it is decelerated solely by friction force due to the contact of the box with floor. The free body diagram of the box is presented herein as attachment. The equation of equilbrium for the box is:

$\Sigma F = -f = m\cdot a$ (Eq. 1)

Where:

$f$ - Kinetic friction force, measured in newtons.

$m$ - Mass of the box, measured in kilograms.

$a$ - Acceleration experimented by the box, measured in meters per square second.

By applying definitions of weight ( $W = m\cdot g$ ) and uniform accelerated motion ( $v = v_(o)+a\cdot t$ ), we expand the previous expression:

$-f = \left((W)/(g) \right)\cdot \left((v-v_(o))/(t)\right)$

And the magnitude of the friction force exerted on the box is calculated by this formula:

$f = -\left((W)/(g) \right)\cdot \left((v-v_(o))/(t)\right)$ (Eq. 1b)

Where:

$W$ - Weight, measured in newtons.

$g$ - Gravitational acceleration, measured in meters per square second.

$v_(o)$ - Initial speed, measured in meters per second.

$v$ - Final speed, measured in meters per second.

$t$ - Time, measured in seconds.

If we know that $W = 52.4\,N$ , $g = 9.807\,(m)/(s^(2))$ , $v_(o) = 1.37\,(m)/(s)$ , $v = 0\,(m)/(s)$ and $t = 2.8\,s$ , the magnitud of the kinetic friction force exerted on the box is:

$f = -\left((52.4\,N)/(9.807\,(m)/(s^(2)) ) \right)\cdot \left((0\,(m)/(s)-1.37\,(m)/(s) )/(2.8\,s) \right)$

$f = 2.614\,N$

The magnitude of the friction force exerted on the box is 2.614 newtons.

Final answer:

The magnitude of the friction force acting on the box is determined by calculating the box's acceleration, establishing its mass based on its weight information, and applying these values in Newton's second law. The calculated value is 2.62 N.

Explanation:

To determine the magnitude of the friction force, we first have to compute the acceleration of the box. Acceleration (a) can be found using the formula 'final velocity - initial velocity / time'. Since the final velocity is 0 (the box stops), and the initial velocity is 1.37 m/s, and the time is 2.8 s, we get: a = (0 - 1.37) / 2.8 = -0.49 m/s^2. The negative sign indicates deceleration.

Next, we use Newton's second law, which states that the net force acting on an object is equal to its mass times its acceleration. The net force in this case is the frictional force because there is no other force acting on the box in the horizontal direction. However, we do not know the mass of the box, but we do know its weight, and weight = mass x gravitational acceleration (g). So mass = weight/g = 52.4N / 9.8m/s^2 = 5.35 kg.

Lastly, we substitute the mass and deceleration into Newton's second law to find the frictional force (f): f = mass x deceleration = 5.35kg x -0.49m/s^2 = -2.62 N. Again, the negative sign indicates that the force acts opposite to the direction of motion. Thus, the frictional force magnitude is 2.62 N.

Learn more about Friction force here:

brainly.com/question/33825279

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To see how two traveling waves of the same frequency create a standing wave. Consider a traveling wave described by the formula y1(x,t)=Asin(kx−ωt)
This function might represent the lateral displacement of a string, a local electric field, the position of the surface of a body of water, or any of a number of other physical manifestations of waves.
1. Find ye(x) and yt(t). Keep in mind that yt(t) should be a trigonometric function of unit amplitude.
2. At the position x=0, what is the displacement of the string (assuming that the standing wave ys(x,t) is present)?
3. At certain times, the string will be perfectly straight. Find the first time t1>0 when this is true.
4. Which one of the following statements about the wave described in the problem introduction is correct?
A. The wave is traveling in the +x direction.
B. The wave is traveling in the −x direction.
C. The wave is oscillating but not traveling.
D. The wave is traveling but not oscillating.
Which of the expressions given is a mathematical expression for a wave of the same amplitude that is traveling in the opposite direction? At time t=0this new wave should have the same displacement as y1(x,t), the wave described in the problem introduction.
A. Acos(kx−ωt)
B. Acos(kx+ωt)
C. Asin(kx−ωt)
D. Asin(kx+ωt)

Answers

The definition of standing wave and trigonometry allows to find the results for the questions about the waves are:

1. For the standing wave its parts are: spatial $y_e = A' \ sin \ kx$ and

temporal part $y_t = A' \ cos \ wt$

2. The string moves with an oscillating motion y = A’ cos wt.

3. Thefirst displacement is zero for $t = (\pi )/(2w)$

4. the correct result is:

A. The wave is traveling in the +x direction.

5. The correct result is:

D. Asin(kx+ωt)

Traveling waves are periodic movements of the media that transport energy, but not matter, the expression to describe it is:

y₁ = A sin (kx -wt)

Where A is the amplitude of the wave k the wave vector, w the angular velocity and x the position and t the time.

1. Ask us to find the spatial and temporal part of the standing wave.

To form the standing wave, two waves must be added, the reflected wave is:

y₂ = A sin (kx + wt)

The sum of a waves

y = y₁ + y₂

y = A (sin kx-wt + sin kx + wt)

We develop the sine function and add.

Sin (a ± b) = sin a cos b ± sin b cos a

The result is:

y = 2A sin kx cos wt

They ask that the function be unitary therefore

The amplitude of each string

A_ {chord} = A_ {standing wave} / 2

The spatial part is

$y_e$ = A 'sin kx

The temporary part is:

$y_t$ = A ’cos wt

2. At position x = 0, what is the displacement of the string?

y = A ’cos wt

The string moves in an oscillating motion.

3. At what point the string is straight.

When the string is straight its displacement is zero x = 0, the position remains.

y = A ’cos wt

For the amplitude of the chord to be zero, the cosine function must be zero.

wt = (2n + 1) $(\pi)/(2)$

the first zero occurs for n = 0

wt = $(\pi )/(2)$

t = $(\pi )/(2w)$

4) The traveling wave described in the statement is traveling in the positive direction of the x axis, therefore the correct statement is:

A. The wave is traveling in the +x direction.

5) The wave traveling in the opposite direction is

y₂ = A sin (kx + wt)

The correct answer is:

D. Asin(kx+ωt)

In conclusion using the definition of standing wave and trigonometry we can find the results for the questions about the waves are:

1. For the standing wave its parts are: spatial $y_e = A' \ sin \ kx$ and

temporal part $y_t = A' \ cos \ wt$

2. The string moves with an oscillating motion y = A’ cos wt.

3. Thefirst displacement is zero for $t = (\pi )/(2w)$

4. the correct result is:

A. The wave is traveling in the +x direction.

5. The correct result is:

D. Asin(kx+ωt)

Learn more about standing waves here: brainly.com/question/1121886

A force of 140 140 newtons is required to hold a spring that has been stretched from its natural length of 40 cm to a length of 60 cm. Find the work done in stretching the spring from 60 cm to 65 cm. First, setup an integral and find a a, b b, and f ( x ) f(x) which would compute the amount of work done.