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bogdanovich [222]
3 years ago
14

A stretched string has a mass per unit length of 5.12 g/cm and a tension of 19.3 N. A sinusoidal wave on this string has an ampl

itude of 0.143 mm and a frequency of 76.9 Hz and is traveling in the negative direction of an x axis. If the wave equation is of the form y(x,t) = ym sin(kx + ωt), what are (a) ym, (b) k, and (c) ω, and (d) the correct choice of sign in front of ω?
Physics
1 answer:
Sati [7]3 years ago
4 0

Answer:

a. 0.143 mm b. 77.6 rad/m c. 483.18 rad/s  d. +1

Explanation:

a. ym

Since the amplitude is 0.143 mm, ym = amplitude = 0.143 mm

b. k

We know k = wave number = 2π/λ where λ = wavelength.

Also, λ = v/f where v = speed of wave in string = √(T/μ) where T = tension in string = 19.3 N and μ = mass per unit length = 5.12 g/cm = 5.12 ÷ 1000 kg/(1 ÷ 100 m) = 0.512 kg/m and f = frequency = 76.9 Hz.

So, λ = v/f = √(T/μ)/f

substituting the values of the variables into the equation, we have

λ = √(T/μ)/f

= √(19.6 N/0.512 kg/m)/76.9 Hz

= √(38.28 Nkg/m)/76.9 Hz

= 6.187 m/s ÷ 76.9 Hz

= 0.081 m

= 81 mm

So, k = 2π/λ

= 2π/0.081 m

= 77.6 rad/m

c. ω

ω = angular frequency = 2πf where f = frequency of wave = 76.9 Hz

So, ω = 2πf

= 2π × 76.9 Hz

= 483.18 rad/s

d. The correct choice of sign in front of ω?

Since the wave is travelling in the negative x - direction, the sign in front of ω is positive. That is +1.

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3 years ago
A basketball player grabbing a rebound jumps 76.0 cm vertically. How much total time (ascent and descent) does the player spend.
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Answer: Part(a)=0.041 secs, Part(b)=0.041 secs

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now we know that

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we also know that

s=76 cm= 0.76 m ( maximum s)

using kinetic equation

v^2=u^2+2as

where v is final velocity which is zero at max height and u is it initial

hence

u^2=-2(-9.81)*0.76

u=3.8615 m/s\\

now we can find time in the 15 cm ascent

s=ut+0.5at^2

0.15=3.861*t+0.5*9.81t^2\\

using quadratic formula

t=\frac{-3.861+\sqrt{3.86^2-4*0.5*9.81(-0.15)} }{2*0.5*9.81}

t=0.0409 sec

the answer for the part b will be the same

To find the answer for the part b we can find the velocity at 15 cm height similarly using

v^2=u^2+2as

where s=0.76-0.15

as the player has traveled the above distance to reach 15cm to the bottom

v^2=0^2 +2*(9.81)*(0.76-0.15)

v=3.4595

when the player reaches the bottom it has the same velocity with which it started which is 3.861

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8 0
3 years ago
A person driving her car at 48 km/h approaches an intersection just as the traffic light turns yellow. She knows that the yellow
trasher [3.6K]

Answer:

She must stop the car  before interception, distance traveled 12.66 m

Explanation:

We will take all units to the SI system

Vo = 48Km / h (1000m / 1Km) (1h / 3600s) = 13.33 m / s

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We calculate the distance traveled before stopping

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X = 13.33 2 + 1.2 (-7) 2²

X = 12.66 m

It stops car before reaching the traffic light turning to red

Let's analyze what happens if you accelerate, let's calculate the acceleration of the vehicle

     V2 = Vo + a t2

      a = (V2-Vo) / t2

      a = (19.44-13.33) /6.6

      a = 0.926 m / s2

This is the acceleration to try to pass the interception, now let's calculate the distance it travels in the time the traffic light changes from yellow to red (t = 2.0 s)

X = Vo t + ½ to t²

X = 13.33 2 + ½ 0.926 2²

X = 28.58 m

Since the vehicle was 30 m away, the interception does not happen

4 0
4 years ago
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