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3 years ago

The wave y1 = 0.12 sin π/3(5x+200t-1) propagates on a string of linear density 0.02 kg/m.

1 answer:

5 0

The average power transmitted by string wave is given by the expression $P=\frac{1}{2} \mu\omega^2A^2v$ , Where μ is a linear density of a string, ω is angular frequency of the wave, A is an amplitude of the wave, v is a speed of wave.

Since $y(x,t)= A sin (kx+\omega t-\psi )$ comparing with $y_1 = 0.12 sin \frac{\pi}{3}(5x+200t-1)$

A = 0.12 m, ω = $\frac{200\pi }{3} s^{-1}$ , k = $\frac{5\pi }{3} m^{-1}$

Speed of wave, $v = \frac{\omega }{k} = \frac{\frac{200\pi }{3}}{\frac{5\pi }{3} } =40m/s$

So power $P = \frac{1}{2} *0.02*(\frac{200\pi }{3} )^2*0.12^2*40=253 W$

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The patellar tendon attaches to the tibia at a 20 deg angle 3 cm from the axis of rotation at the knee. If the force generated i

gregori [183]

Answer:

the resulting angular acceleration is 15.65 rad/s²

Explanation:

Given the data in the question;

force generated in the patellar tendon F = 400 N

patellar tendon attaches to the tibia at a 20° angle 3 cm( 0.03 m ) from the axis of rotation at the knee.

so Torque produced by the knee will be;

T = F × d⊥

T = 400 N × 0.03 m × sin( 20° )

T = 400 N × 0.03 m × 0.342

T = 4.104 N.m

Now, we determine the moment of inertia of the knee

I = mk²

given that; the lower leg and foot have a combined mass of 4.2kg and a given radius of gyration of 25 cm ( 0.25 m )

we substitute

I = 4.2 kg × ( 0.25 m )²

I = 4.2 kg × 0.0626 m²

I = 0.2625 kg.m²

So from the relation of Moment of inertia, Torque and angular acceleration;

T = I∝

we make angular acceleration ∝, subject of the formula

∝ = T / I

we substitute

∝ = 4.104 / 0.2625

∝ = 15.65 rad/s²

Therefore, the resulting angular acceleration is 15.65 rad/s²

8 0

3 years ago

Two objects, Object A and Object B, need to be identified. Object A's index of refraction is determined to be 1.77, and Object B

Slav-nsk [51]

The correct answer is

C. Light can pass through Object B faster than it can pass through Object A.

In fact, the index of refraction of a material is defined as:

$n=\frac{c}{v}$

where c is the speed of light in vacuum and v is the speed of light in the material. Rearranging the equation, we can write the speed of light in the material as:

$v=\frac{c}{n}$

So we that, the smaller the refractive index n, the greater the speed of light in the material, v. In this problem, object B has lower refractive index than object A, so light travels faster in object B.

4 0

3 years ago

Read 2 more answers

Estimate the mass of the Great Pyramid of Giza, in tons. You make may use of the following information: the Great Pyramid is in

postnew [5]

Answer:

6005803.83105 short tons

Explanation:

The definition of density is $\rho = \frac{m}{V}$ , and the volume of a pyramid is (confusingly written on the proposal) $V=\frac{1}{3} Ah$ , so we can write:

$m=\rho V=\rho V \frac{1}{3} Ah=\rho V \frac{1}{3} s^2h$

Where s is the side of the base, being $s^2$ the area of that square.

We will write everything in S.I., and the best way to convert units is using conversion factors, for example, since 1m=100cm, we know that $\frac{1m}{100cm}=1$ , and we can use this factor to convert anything written in cm to anything written in m. Example:

$500cm=500cm\frac{1m}{100cm}=5m$

Here we just multiplied 500cm by something that is equal to 1 (as every conversion factor must), so <em>it's not doing anything but changing the units</em>.

We can use this tool like this:

$2.1\frac{g}{cm^3}=2.1\frac{g}{cm^3}(\frac{1Kg}{1000g})(\frac{100cm}{1m})^3=2100Kg/m^3$

Where we have used the fact that $1^3=1$ (<u>we can elevate any conversion factor to any number and they still will be 1</u>) and where we have placed strategically what is the numerator and what in the denominator so the units we don't want cancel out and the units we want appear.

Substituting then our values:

$m=\rho V \frac{1}{3} s^2h=(2100Kg/m^3)\frac{1}{3} (230.34m)^2(146.7m)=5448373586.96Kg$

And now we will convert to short tons using two conversion factors at the same time:

$m=5448373586.96\ Kg(\frac{1\ lb}{0.45359237\ Kg})(\frac{1\ short\ ton}{2000\ lb} )=6005803.83105\ short \ tons$

Remember, their value is 1, and we place the units to cancel the ones we don't want and keep the ones we want, here Kg cancel out, and lb cancel out, leaving the short tones.

8 0

3 years ago

Red, green, and blue light rays each enter a drop of water from the same direction.Which light ray's path through the drop will

geniusboy [140]

Blue light will bend more than the others because it has a slightly greater refractive index. This is because blue light has a shorter wavelength and more energy, meaning it has to slow down more than the others when it hits the water.

5 0

3 years ago

When a magnet moves above a conducting ladder, the currents induced in the ladder produces a magnetic field. This field interact

pav-90 [236]

Answer:

) pulls the ladder in the direction opposite

Explanation:

This is in line with lenz law that states that the magnetic field induced in a conductor act to oppose the magnetic field that produced it

4 0

3 years ago