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Ratling [72]
3 years ago
6

A 16 pound weight attached to a spring exhibits simple harmonic motion. Determine the equation of motion if the spring constant

is 8 lb/ft and if the weight is released 6 inches below the equilibrium position with a downward velocity of 1 ft/s.
Physics
1 answer:
yarga [219]3 years ago
8 0

Answer:

T = 2.82π s

x = Acos(0.71t)

Explanation:

This problem can be solved by using the expressions

T = 2\pi \sqrt{\frac{m}{k} }    ( 1 )

x=Acos(\omega t) = Acos(\frac{2\pi }{T}t )   ( 2 )

where T is the period of oscillation of the system, m is the mass of the object attached to the spring, k is the spring constant and x is the position of the object.

By replacing in the expression (1):

T=2\pi \sqrt{\frac{16 lb}{8lb/ft}} = 2.82\pi s

Taking 6 inches as the amplitude of the motion, we have

x=6cos(\frac{2\pi }{2.82\pi }t ) = 6cos(0.71t)

I hope this is useful for you

Regards

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Two uniform solid cylinders, each rotating about its central (longitudinal) axis, have the same mass of 3.56 kg and rotate with
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Answer:

(a) 3107.98 J

(b) 14530.6 J

Explanation:

mass, m = 3.56 kg

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Moment of inertia of solid cylinder, I = 1/2 mr^2

where, m is the mass and r be the radius of the cylinder.

(a) radius, r = 0.330 m

I = 0.5 x 3.56 x 0.330 x 0.330 = 0.194 kgm^2

The formula for the rotational kinetic energy is given by

K = \frac{1}{2}I\omega ^{2}

K = 0.5 x 0.194 x 179 x 179 = 3107.98 J

(b) radius, r = 0.714 m

I = 0.5 x 3.56 x 0.714 x 0.714 = 0.907 kgm^2

The formula for the rotational kinetic energy is given by

K = \frac{1}{2}I\omega ^{2}

K = 0.5 x 0.907 x 179 x 179 = 14530.6 J

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3 years ago
Real world System of equations
valina [46]
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3 years ago
How does the sun transmit energy from millions of miles away into the Earth system? 'Energy' and 'power' are often confused, but
Leona [35]

Answer:

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  • Energy is the capacity to do the work whereas power is the rate of doing work or the rate of energy transfer.
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Positive feedback are not good when it disturbs the stability too much over a wide range.

No, negative feedback are not always bad because they enhance the stability of our system, resist the change in a system making it consistent and have a narrower range of variation.

Explanation:

The energy from the sun travels a huge distance in vacuum and atmosphere.

  • The solar energy travels to the earth in the form of electromagnetic radiations which do not require any medium of transmission and are capable of travelling in vacuum by the mode called radiation. In this mode the packets of energy get directly transmitted from the source to its surroundings. This packet of energy is called quanta.
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  • We can burn a gallon of fuel only once because it undergoes a chemical change and the chemical changes are mostly permanent in nature. There is a certain direction to which the energy can  flow spontaneously. When we burn the fuel then the stored chemical energy of the fuel gets converted into heat and light and the heat energy released during the combustion of the fuel is sufficient to further provide the heat of combustion of fuel.
  • Energy always transforms from high grade to the lower grade and the converse is not possible spontaneously.

Positive feedback are not good when it disturbs the stability too much over a wide range.

No, negative feedback are not always bad because they enhance the stability of our system, resist the change in a system making it consistent and have a narrower range of variation.

6 0
3 years ago
What is the relation between the weight of a body and acceleraton due to gravity?​
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A tennis ball is hit into the air with a racket. When is the ball’s kinetic energy the greatest? Ignore air resistance. when it
natita [175]
<h3><u>Answer;</u></h3>

just before it reaches the ground

<h3><u>Explanation;</u></h3>
  • Kinetic energy is the energy possessed by a body or an object in motion.
  • <em><u>Kinetic energy is given by 1/2mv², where m is the mass of the object and V is the velocity of the body. Thus, kinetic energy depends on the velocity of the body if mass is kept constant.</u></em>
  • <em><u>As soon as the ball leaves the racket it has more kinetic energy and zero potential energy. As it moves up its velocity decreases, and thus the kinetic energy is being converted to kinetic energy up to maximum height reached where kinetic energy will be zero since the velocity is zero.</u></em>
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