A frictionless pendulum is made with a bob of mass 12.6 kg. The bob is held at height = 0.650 meter above the bottom of its trajectory, and then pushedforward with an initial speed of 4.22 m/s. What amount of mechanical energy does the bob have when it reaches the bottom?

Answers

Answer 1

Answer: The answer to your question is 55

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Two loudspeakers, A and B, are driven by the same amplifier and emit sinusoidal waves in phase. The frequency of the waves emitted by each speaker is 641Hz . You are standing between the speakers, along the line connecting them and are at a point of constructive interference.How far must you walk toward speaker B to move to reach the first point of destructive interference?
Take the speed of sound to be 344 .

Answers

Final answer:

You must walk approximately 0.2685 m, or 26.85 cm, towards speaker B to encounter the first point of destructive interference. This calculation is arrived at by determining the half-wavelength of the sound wave.

Explanation:

Interference occurs when two sound waves from the same source meet. When they constructively interfere, their amplitudes add together creating a louder sound, while when they destructively interfere, they cancel each other out creating a point of silence. Since you are initially in a position of constructive interference, you need to move towards speaker B at a distance that would change the path length difference to be equivalent to a half wavelength.

To find this distance, we first need to find the wavelength from the frequency. The formula for this is:

Wavelength = Speed of sound / Frequency

Given the speed of sound is 344 m/s and the frequency is 641 Hz, we find the wavelength to be roughly 0.537 m. A half wavelength, which characterizes the distance needed for destructive interference from total constructive interference, would then be 0.2685 m.

You must walk approximately 0.2685 m, or 26.85 cm, towards speaker B to encounter the first point of destructive interference.

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Final answer:

To find the distance at which the first point of destructive interference occurs, divide the wavelength by 2. In this case, the distance is approximately 0.268 meters or 26.8 centimeters. Therefore, you would need to walk about 26.8 centimeters toward speaker B to reach the first point of destructive interference.

Explanation:

To determine the distance at which the first point of destructive interference occurs, we need to understand the concept of interference and the conditions for constructive and destructive interference. Constructive interference occurs when the waves from both speakers are in phase and add up to create a larger amplitude. Destructive interference occurs when the waves from both speakers are out of phase and cancel each other out, resulting in a smaller amplitude. In this case, since the speakers are emitting waves in phase, the distance at which destructive interference occurs is equal to half the wavelength of the waves.

The wavelength of a wave can be calculated using the formula:
Wavelength = Speed of sound / Frequency

In this case, the frequency is given as 641 Hz and the speed of sound is given as 344 m/s. Plugging in these values into the formula, we get:
Wavelength = 344 m/s / 641 Hz

Solving this, we find that the wavelength is approximately 0.536 meters. To find the distance to the first point of destructive interference, we divide the wavelength by 2:
Distance to first point of destructive interference = Wavelength / 2

Plugging in the calculated wavelength, we get:
Distance to first point of destructive interference = 0.536 meters / 2

Simplifying, we find that the distance is approximately 0.268 meters or 26.8 centimeters. Therefore, you would need to walk about 26.8 centimeters toward speaker B to reach the first point of destructive interference.

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Lightning can sometimes occur on hot and humid summer evenings when there are no thunderstorms.(A) True
(B) False

Answers

Answer:

(B) False

Explanation:

No, it is not possible to have thunder without lightning. Thunder is a direct result of lightning.

B False because facts

Consider different points along one spoke of a wheel rotating with constant angular velocity. Which of the following is true regarding the centripetal acceleration at a particular instant of time?a. The magnitude of the centripetal acceleration is greater for points on the spoke closer to the hub than for points closer to the rim
b. both the magnitude and the direction of the centripetal acceleration depend on the location of the point on the spoke.
c. The magnitude of the centripetal acceleration is smaller for points on the spoke closer to the hub than for points closer to the rim but the direction of the acceleration is the same at all points on this spoke.
d. The magnitude and direction of the centripetal acceleration is the same at all points on this spoke.

Answers

Answer:

Option (a).

Explanation:

Let the angular velocity is w.

The centripetal acceleration is given by

$a = r w^2$

where, r is the distance between the axle and the spoke.

So, more is the distance more is the centripetal acceleration.

(a) For the points on the spoke closer to the hub than for points closer to the rim is larger distance, so the centripetal force is more.

The statement is true.

(b) The direction of centripetal acceleration is always towards the center, so the statement is false.

(d) It is false.

Option (a) is correct.

A plastic ball in a liquid is acted upon by its weight and by a buoyant force. The weight of the ball is 4 N. The buoyant force has a magnitude of 5 N and acts vertically upward. When the ball is released from rest, what is it's acceleration and direction? [2 pts] for a Free Body Diagram correctly labeled.

Answers

Answer:

The acceleration is 2.448 meters per square second and is vertically upward.

Explanation:

The Free Body Diagram of the plastic ball in the liquid is presented in the image attached below. By Second Newton's Law, we know that forces acting on the plastic ball is:

$\Sigma F = F - m\cdot g = m\cdot a$ (1)

Where:

$F$ - Buoyant force, measured in newtons.

$m$ - Mass of the plastic ball, measured in kilograms.

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

$a$ - Net acceleration, measured in meters per square second.

If we know that $F = 5\,N$ , $m = 0.408\,kg$ and $g = 9.807\,(m)/(s^(2))$ , then the net acceleration of the plastic ball is:

$a = (F)/(m) - g$

$a= 2.448\,(m)/(s^(2))$

The acceleration is 2.448 meters per square second and is vertically upward.

Monochromatic coherent light shines through a pair of slits. If the distance between these slits is decreased, which of the following statements are true of the resulting interference pattern?A) The distance between the maxima stays the same.B) The distance between the maxima decreases.
C) The distance between the minima stays the same.
D) The distance between the minima increases.
E) The distance between the maxima increases.

Answers

Answer:

The correct statements are D and E.

Explanation:

The fringe width is given by the following formula as :

$\beta =(\lambda D)/(d)$

Here,

$\lambda$ is wavelength of light

D is distance between slit and the screen

d is slit width.

If the between these slits is decreased, the fringe width increases. As a result, the distance between the minima increases and also the distance between the maxima increases.

An electric generator contains a coil of 140 turns of wire, each forming a rectangular loop 71.2 cm by 22.6 cm. The coil is placed entirely in a uniform magnetic field with magnitude B = 4.32 T and initially perpendicular to the coil's plane. What is in volts the maximum value of the emf produced when the loop is spun at 1120 rev/min about an axis perpendicular to the magnetic field?

Answers

Answer:

11405Volt

Explanation:

To solve this problem it is necessary to use the concept related to induced voltage or electromotive force measured in volts. Through this force it is possible to maintain a potential difference between two points in an open circuit or to produce an electric current in a closed circuit.

The equation that allows the calculation of this voltage is given by,

$\epsilon = BAN \omega$