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Oksanka [162]
3 years ago
13

A swinging pendulum has a total energy of

bsmiddle" class="latex-formula">. The amplitude of the pendulum's oscillations is then increased by a factor of 4. By what factor does the total energy stored in the moving pendulum change? Ignore damping.
Physics
1 answer:
Zolol [24]3 years ago
3 0

Answer:

\frac{E_{2}}{E_{1}} \approx 1 -\frac{3\theta}{1-\theta} (for small oscillations)

Explanation:

The total energy of the pendulum is equal to:

E_{1} = m\cdot g \cdot (1-\cos \theta)\cdot L

For small oscillations, the equation can be re-arranged into the following form:

E_{1} \approx m\cdot g \cdot (1-\theta) \cdot L

Where:

\theta = \frac{A}{L^{2}}, measured in radians.

If the amplitude of pendulum oscillations is increase by a factor of 4, the angle of oscillation is 4\theta and the total energy of the pendulum is:

E_{2} \approx m\cdot g \cdot (1-4\theta)\cdot L

The factor of change is:

\frac{E_{2}}{E_{1}} \approx \frac{1 - 4\theta}{1-\theta}

\frac{E_{2}}{E_{1}} \approx 1 -\frac{3\theta}{1-\theta}

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A horizontal wire is hung from the ceiling of a room by two massless strings. The wire has a length of 0.11 m and a mass of 0.01
AnnZ [28]

Answer:

Explanation:

The magnetic force acting horizontally will deflect the wire by angle φ from the vertical

Let T be the tension

T cosφ = mg

Tsinφ = Magnetic force

Tsinφ = BiL  , where B is magnetic field , i is current and L is length of wire

Dividing

Tanφ = BiL / mg

= .055 x 29 x .11 / .010 x 9.8

= 1.79

φ = 61° .

Tension T = mg / cosφ

= .01 x 9.8 / cos61

= .2 N .

5 0
3 years ago
Can you explain that gravity pulls us to the Earth & can you calculate weight from masses on both on Earth and other planets
schepotkina [342]
I don't actually understand what your question is, but I'll dance around the subject
for a while, and hope that you get something out of it.

-- The effect of gravity is:  There's a <em>pair</em> of forces, <em>in both directions</em>, between
every two masses.

-- The strength of the force depends on the <em>product</em> of the masses, so it doesn't matter whether there's a big one and a small one, or whether they're nearly equal. 
It's the product that counts.  Bigger product ==> stronger force, in direct proportion.

-- The strength of the forces also depends on the distance between the objects' centers.  More distance => weaker force.  Actually, (more distance)² ==> weaker force.

-- The forces are <em>equal in both directions</em>.  Your weight on Earth is exactly equal to
the Earth's weight on you.  You can prove that.  Turn your bathroom scale face down
and stand on it.  Now it's measuring the force that attracts the Earth toward you. 
If you put a little mirror down under the numbers, you'll see that it's the same as
the force that attracts you toward the Earth when the scale is right-side-up.

-- When you (or a ball) are up on the roof and step off, the force of gravity that pulls
you (or the ball) toward the Earth causes you (or the ball) to accelerate (fall) toward the Earth. 
Also, the force that attracts the Earth toward you (or the ball) causes the Earth to accelerate (fall) toward you (or the ball).
The forces are equal.  But since the Earth has more mass than you have, you accelerate toward the Earth faster than the Earth accelerates toward you.

--  This works exactly the same for every pair of masses in the universe.  Gravity
is everywhere.  You can't turn it off, and you can't shield anything from it.

-- Sometimes you'll hear about some mysterious way to "defy gravity".  It's not possible to 'defy' gravity, but since we know that it's there, we can work with it.
If we want to move something in the opposite direction from where gravity is pulling it, all we need to do is provide a force in that direction that's stronger than the force of gravity.
I know that sounds complicated, so here are a few examples of how we do it:
-- use arm-muscle force to pick a book UP off the table
-- use leg-muscle force to move your whole body UP the stairs
-- use buoyant force to LIFT a helium balloon or a hot-air balloon 
-- use the force of air resistance to LIFT an airplane.

-- The weight of 1 kilogram of mass on or near the Earth is 9.8 newtons.  (That's
about 2.205 pounds).  The same kilogram of mass has different weights on other planets. Wherever it is, we only know one of the masses ... the kilogram.  In order
to figure out what it weighs there, we need to know the mass of the planet, and
the distance between the kilogram and the center of the planet.

I hope I told you something that you were actually looking for.
7 0
3 years ago
PLS HELPPP! Why are ions harmful and why are they not harmful?
Fittoniya [83]

Answer:

This is because we are surrounded by positive ions from electromagnetic fields generated by computers, cell phones, and other electronic devices which can impair brain function and suppress the immune system causing symptoms such as: anxiety, breathing difficulty, fatigue, headaches, irritability, lack of energy, poor concentration, nausea, and vertigo,

Explanation:

5 0
3 years ago
Read 2 more answers
A Ferris wheel has diameter of 10 m. It rotates at a uniform rate and makes one revolution in 8.0 seconds. A person weighing 670
Nikolay [14]

Answer:  459.14 N

Explanation:

from the question, we have

diameter = 10 m

radius (r)  = 5 m

weight (Fw) = 670 N

time (t) = 8 seconds

Circular motion has centripetal force and acceleration pointing perpendicular and inwards of the path, therefore we apply the equation below

∑ F = F c =  F w − Fn ..............equation 1

Fn = Fw − Fc = mg − (mv^2 / r) ...................equation 2

substituting the value of v as (2πr / T) we now have

Fn = mg − (m(2πr / T )^2) / r

Fn= mg − (4(π^2)mr / T^2)   ..........equation 3

Fw (mass of the person) = mg

therefore m = Fw / g

                m = 670 / 9.8 = 68.367 kg

now substituting  our values into equation 3

Fn = 670 - ( (4 x (π^2) x 68.367 x 5 ) / 8^2)

Fn = 670 - 210.86

Fn = 459.14 N

4 0
3 years ago
The potential energy for a certain mass moving in one dimension is given by U(x)=(2.0J/m3)x3−(15J/m2)x2+(36J/m)x−23JU(x)=(2.0J/m
Angelina_Jolie [31]

Answer:x=2 and x=3

Explanation:

Given

Potential Energy for a certain mass is

U(x)=2x^3-15x^2+36x-23

and we know force is given by

F=-\frac{\mathrm{d} U}{\mathrm{d} x}

F=-(2\times 3x^2-15\times 2x+36)

For Force to be zero F=0

\Rightarrow 6x^2-30x+36=0

\Rightarrow x^2-5x+6=0

\Rightarrow x^2-2x-3x+6=0

\Rightarrow (x-2)(x-3)=0

Therefore at x=2 and x=3 Force on particle is zero.

8 0
3 years ago
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