How fast is Barry Allen ( The Flash) in season 5 of the Flash?

A 10 g particle undergoes SHM with an amplitude of 2.0 mm and a maximum acceleration of magnitude 8.0 multiplied by 103 m/s2, an

Nat2105 [25]

Answer:

a) $T=0.0031416s$

b) $v_{max}=6.283\frac{m}{s}$

c) $E=0.1974J$

d) $F=80N$

e) $F=40N$

Explanation:

1) Important concepts

Simple harmonic motion is defined as "the motion of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke's Law (F=-Kx). The motion experimented by the particle is sinusoidal in time and demonstrates a single resonant frequency".

2) Part a

The equation that describes the simple armonic motion is given by $X=Acos(\omega t +\phi)$ (1)

And taking the first and second derivate of the equation (1) we obtain the velocity and acceleration function respectively.

For the velocity:

$\frac{dX}{dt}=v(t)=-A\omega sin(\omega t +\phi)$ (2)

For the acceleration

$\frac{d^2 X}{dt}=a(t)=-A\omega^2 cos(\omega t+\phi)$ (3)

As we can see in equation (3) the acceleration would be maximum when the cosine term would be -1 and on this case:

$A\omega^2=8x10^{3}\frac{m}{s^2}$

Since we know the amplitude A=0.002m we can solve for $\omega$ like this:

$\omega =\sqrt{\frac{8000\frac{m}{s^2}}{0.002m}}=2000\frac{rad}{s}$

And we with this value we can find the period with the following formula

$T=\frac{2\pi}{\omega}=\frac{2 \pi}{2000\frac{rad}{s}}=0.0031416s$

3) Part b

From equation (2) we see that the maximum velocity occurs when the sine function is euqal to -1 and on this case we have that:

$v_{max}=A\omega =0.002mx2000\frac{rad}{s}=4\frac{m rad}{s}=4\frac{m}{s}$

4) Part c

In order to find the total mechanical energy of the oscillator we can use this formula:

$E=\frac{1}{2}mv^2_{max}=\frac{1}{2}(0.01kg)(6.283\frac{m}{s})^2=0.1974J$

5) Part d

When we want to find the force from the 2nd Law of Newton we know that F=ma.

At the maximum displacement we know that X=A, and in order to that happens $cos(\omega t +\phi)=1$ , and we also know that the maximum acceleration is given by::

$|\frac{d^2X}{dt^2}|=A\omega^2$

So then we have that:

$F=ma=mA\omega^2$

And since we have everything we can find the force

$F=ma=0.01Kg(0.002m)(2000\frac{rad}{s})^2 =80N$

6) Part e

When the mass it's at the half of it's maximum displacement the term $cos(\omega t +\phi)=1/2$ and on this case the acceleration would be given by;

$|\frac{d^2X}{dt^2}|=A\omega^2 cos(\omega t +\phi)=A\omega^2 \frac{1}{2}$

And the force would be given by:

$F=ma=\frac{1}{2}mA\omega^2$

And replacing we have:

$F=\frac{1}{2}(0.01Kg)(0.002m)(2000\frac{rad}{s})^2 =40N$

8 0

3 years ago

Preschool girls and boys do not differ in the amount of muscle they have<br> 1) True<br> 2) False

Marina86 [1]

Explanation:

False...............

3 0

3 years ago

Consider two copper wires with circular cross-sections and equal lengths. one wire has 3 times the diameter of the other. How do

Masteriza [31]

The correct option is (C) The longer wire has 3 times the resistance of the shorter wire.

Resistance is a measure of the opposition to current flow in an electrical circuit.

Why do circuits need resistance?

Using ohms (Ω) as the unit, resistance acts as a gauge to quantify how easily current will flow through a circuit. When resistance falls, current rises, and when resistance rises, current falls. In order to make sure that current flows in circuits at the proper rate, resistors are crucial.

How can resistance be determined in a circuit?

By applying Ohm's Law, you can get the total resistance if you know the total current and voltage through the entire circuit: R = V / I. A parallel circuit, for instance, has a voltage of 9 volts and a combined current of 3 amps. Total resistance (RT) is equal to 9 volts / 3 amps, or 3.

Learn more about the Resistance in circuit with the help of the given link:

brainly.com/question/1851488

#SPJ4

I understand that the question you are looking for is "Consider two copper wires of equal cross-sectional area. One wire has 3 times the length of the other. How do the resistances of these two wires compare?

A) Both wires have the same resistance.

B) The longer wire has 1/3 the resistance of the shorter wire.

C) The longer wire has 3 times the resistance of the shorter wire.

D) The longer wire has 9 times times the resistance of the shorter wire.

E) The longer wire has 27 times times the resistance of the shorter wire."

5 0

2 years ago

PLZ HELP!!! Detailed PLZ!

Korolek [52]

Answer:

Potential Energy = 294J, Kinetic Engergy = 48.02J

Explanation:

We have these formulas:

Potential Energy = mass * gravitational force * height (m) = 1 * 9.8 * 30 = 294(J)

Kinetic Energy = 1/2 * mass * velocity^2 = 1/2 * 1 * 9.8^2 = 48.02 (J)

As the rock falling at an acceleration of 9.8m/s^2 which means for each second, the rock increases 9.8m/s. I think we are missing time to find the instantaneous velocity, the formula is (initial displacement - final displacement)/ (initial time - final time) which will directly give the final answer for you.

5 0

3 years ago

Which of the following caused tension amount the pilgrims shortly after the mayflower’s settlement at the Plymouth colony?

GrogVix [38]

Answer:

the weather cast half of them to die

8 0

3 years ago