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telo118 [61]
3 years ago
9

A pulse moving to the right along the x axis is represented by the function of

Physics
1 answer:
olasank [31]3 years ago
8 0

Answer:

<em>(a) Peak=2 cm, velocity= 3 cm/s (to the right)</em>

<em>(b) Peak= 2 cm, velocity= -3 cm/s (to the left)</em>

Explanation:

<u>Pulse Movement</u>

The function of a moving wave is given by

\displaystyle y(x,t)=\frac{2}{(x-3t)^2+1}

where x,y are measured in cm and t in seconds.

Please check the graph shown in the image provided below. It shows the waveform at two different times, t=0 sec and t=1 sec. The peak value is displaced by 3 cm when t varies by 1 second. It shows a velocity of 3 m/s.

(a) For a given  time, say t=0 the expression for the pulse is

\displaystyle y(x,0)=\frac{2}{x^2+1}

The maximum value or the pulse amplitude occurs when the denominator has its minimum value, that is when x=0

\displaystyle A=y(0,0)=\frac{2}{0^2+1}=2

At t=1 second, the function is

\displaystyle y(x,1)=\frac{2}{(x-3)^2+1}

Again, the maximum value of the wave occurs at the minimum value of the denominator, or when

x-3=0 \rightarrow x=3

Note the peak has moved 3 cm to the right when t increased by 1 second, this gives us a horizontal velocity of 3 cm/s.

We can corroborate for the general case knowing the peak value moves to the right at the point where

x-3t=0 \rightarrow x=3t

Taking the derivative with respect to t gives us the horizontal velocity:

x'=3\ cm/s

At t=2 seconds

\displaystyle y(x,2)=\frac{2}{(x-6)^2+1}

The amplitude and velocity are the same as determined before. The graph shown in the figure attached shows the pulse waves at t=0 and t=1

b) If the function was

\displaystyle y(x,t)=\frac{2}{(x+3t)^2+1}

Then when t increases, the peak value moves to the left on the x-axis. The velocity would be

x'=-3\ cm/s

It means the wave is traveling to the left instead of to the right

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Answer:

1.332 N

Explanation:

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1 year ago
A series circuit contains a 9-volt battery, a 3-ohm resistor and a 2-ohm resistor. What is the voltage drop across the 2-ohm res
BARSIC [14]
Since everything in the circuit is in series .. .

-- The total resistance is  (3 + 2) = 5 ohms.

-- The voltage across the 3-ohm resistor is 3/5 of the total voltage.

-- The voltage across the 2-ohm resistor is 2/5 of the total voltage.

                  (2/5) of (9 volts)  =  18/5  =  3.6 volts .

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3 years ago
Read 2 more answers
1-A train travels 100 km to reach town A in one hour and 15 min. The train stops at station A for 45 minutes. Then it travels 15
kirill [66]

Answer 1) : 62.5 km/hour is the average velocity of the train.

2) The final velocity of the car at the end of 75 m is 14.69 m/s

Explanation:

1) Displacement of the train = 100 km + 150 km = 250 km

Total time train took =1 hour 15 min+ 45 min + 2 hours = 240 min = 4 hours

Average velocity=\frac{Displacement}{time}=\frac{250 km}{4 hour}=62.5 km/h

62.5 km/hour is the average velocity of the train.

2) The acceleration of the car, a= 1.2 m/s^2

Distance covered by the car,s = 75 m

Initial velocity of the car ,v_i = 6 m/s

Final velocity of thre car ,v_f=?

Using third equation of motion:

v_{f}^2=v_{i}^2+2as=(6 m/s)^2+2\times 1.2 m/s\times 75 m=216 m^2/s^2

v_{f}=14.69 m/s

The final velocity of the car at the end of 75 m is 14.69 m/s

8 0
3 years ago
A piece of glass has a temperature of 72.0 degrees Celsius. The specific heat capacity of the glass is 840 J/kg/deg C. A liquid
Nezavi [6.7K]

Answer:

741 J/kg°C

Explanation:

Given that

Initial temperature of glass, T(g) = 72° C

Specific heat capacity of glass, c(g) = 840 J/kg°C

Temperature of liquid, T(l)= 40° C

Final temperature, T(2) = 57° C

Specific heat capacity of the liquid, c(l) = ?

Using the relation

Heat gained by the liquid = Heat lost by the glass

m(l).C(l).ΔT(l) = m(g).C(g).ΔT(g)

Since their mass are the same, then

C(l)ΔT(l) = C(g)ΔT(g)

C(l) = C(g)ΔT(g) / ΔT(l)

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C(l) = 12600 / 17

C(l) = 741 J/kg°C

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Three children are riding on the edge of a merry-go-round that is 100 kg, has a 1.60-m radius, and is spinning at 20.0 rpm. The
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Answer:

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m1 = 22 kg

m2 = 28 kg

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Initial angular momentum = final angular momentum

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(1/2 M + m1 + m2 + m3) x 2 x π x f = (1/2 M + m1 + m3) x 2 x π x f'

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2660 = 105 x f'

f' = 25.33 rpm

8 0
3 years ago
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