1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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}

You might be interested in
If you were lost in space how would you get back to the space station explain scientifically
iris [78.8K]

You would use a object called The big dipper to find the closest space station.

5 0
3 years ago
The whale shark is the largest of all fish and can have the mass of three adult
ch4aika [34]

Answer:

m = 20,000 kg

Explanation:

Force, F=2.5\times 10^4\ N

Acceleration of the shark, a=1.25\ m/s^2

It is required to find the mass of the shark. Let m is the mass. Using second law of motion to find it as follows :

F = ma

Putting the value of F and a to find m

m=\dfrac{F}{a}\\\\m=\dfrac{2.5\times 10^4}{1.25}\\\\m=20,000\ kg

So, the shark's mass is 20,000 kg.

3 0
3 years ago
In the voltage multiplier experiment, why not use a zener diode?​
Svet_ta [14]

Answer:

<em>A voltage multiplier is an electrical circuit that converts AC electrical power from a lower voltage to a higher DC voltage, typically using a network of capacitors and diodes.</em>

6 0
2 years ago
Two charges that are separated by one meter exert 1-n forces on each other. if the magnitude of each charge is doubled, the forc
Goshia [24]
The electrostatic force between the two charges is
F=k_E  \frac{q_1 q_2}{r^2}
where q1 and q2 are the magnitudes of the two charges, and r the distance between them.

We can see from the formula that F is proportional to the product between the two charges:
F \sim q_1 q_2
so, if the magnitude of each charge is doubled, the new force will get a factor 4:
F' \sim (2 q_1 )(2 q_2 )=4 q_1 q_2 =4 F
So, the new force will be 4 times the original force:
F' = 4 \cdot 1N= 4N
5 0
3 years ago
A 10-cm long solenoid has 100 turns and a radius of 5 cm. If it carries a current of 2 A, What is the magnetic field B inside th
OLga [1]

Hi there!

We can use Ampère's Law:

\oint B \cdot dl = \mu_0 i_{encl}

B = Magnetic field strength (B)
dl = differential length element (m)
μ₀ = Permeability of free space (T/Am)

Since this is a closed-loop integral, we must integrate over a closed loop. We can integrate over a rectangular-enclosed area of the rim of the solenoid - ABCD - where AD and BC are perpendicular to the solenoid.

Thus, the magnetic field is equivalent to:
\oint B \cdot dl = \int\limits^A_B {B} \, dl  + \int\limits^B_C {B} \, dl   + \int\limits^C_D {B} \, dl   + \int\limits^D_A {B} \, dl

Since AD and BC are perpendicular, and since:
\oint B \cdot dl = B \cdot L = BLcos\phi

BLcos(90) = 0

If perpendicular to the field, the equation equals 0.

Additionally, since AB is outside of the solenoid, there is no magnetic field present, so B = 0. The only integral we integrate now is:
\oint B \cdot dl = \int\limits^C_D {B} \, dl

Which is horizontal and inside the solenoid. Let the distance between C and D be 'L', and the enclosed current is equivalent to the number of loops multiplied by the current:

B L = \mu_0 Ni

N = # of loops per length multiplied by the length, so:
BL = \mu_0 nL i \\\\B = \mu_0ni

Plug in the given values and solve. Remember to convert # of loops to # of loops per unit length.

B = \mu_0 (100/0.1)(2) = (4\pi *10^{-7})(1000)(2) = \boxed{0.00251 T}

6 0
2 years ago
Other questions:
  • What evenally happens to all materials and finishes that use the traditional sustainality
    15·2 answers
  • During a free fall Swati was accelerating at -9.8m/s2. After 120 seconds how far did she travel? Use the formula =1/2 * t2 to so
    15·2 answers
  • (a) At a distance of 0.200 cm from the center of a charged conducting sphere with radius 0.100 cm, the electric field is 480 N&g
    9·1 answer
  • the mass of one water drop is 0.0008kg and the gravitational field strength is 10N/kg what is its weight
    7·1 answer
  • 5750 milliliters converted to Liters
    9·2 answers
  • With the same block-spring system from above, imagine doubling the displacement of the block to start the motion. By what factor
    7·1 answer
  • Which statement describes a climate condition?
    13·1 answer
  • A child is stationary on a swing.(a)The child is given a push by his brother to start him swinging.His brother applies a steady
    12·1 answer
  • How is energy transferred and transformed? and examples with full explanation.
    7·1 answer
  • A car travels 460km in 7 hours. How would you calculate the speed?
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!