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3 years ago

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To what tension must you adjust the string so that, when vibrating in its second overtone, it produces sound of wavelength 0.767

m ? (Assume that the breaking stress of the wire is very large and isn’t exceeded.)

1 answer:

Anna [14]3 years ago

6 0

Answer:

Tension, T = 547.58 N

Explanation:

It can be assumed that,

Mass of the string, m = 8.75 g

Length of the string, l = 70 cm = 0.7 m

Wavelength of produced sound, $\lambda=0.767\ m$

Speed of sound, v = 344 m/s

We know that second overtone is the third harmonic. The frequency in second overtone is given by :

$f=\dfrac{v}{3\lambda}$

$f=\dfrac{344}{3\times 0.767}$

f = 149.5 Hz

The frequency in terms of length is given by :

$f=\dfrac{1}{2l}\sqrt{\dfrac{T}{m/l}}$

$T=4f^2l^2\dfrac{m}{l}$

$T=4f^2lm$

$T=4\times (149.5)^2\times 0.7\times 8.75\times 10^{-3}$

T = 547.58 N

So, the tension in the string is 547.58 N. Hence, this is the required solution.

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A cord of negligible mass runs around two massless, frictionless pulleys. A canister with mass m = 20 kg hangs from one pulley.

photoshop1234 [79]

(a) 196 N

The equation of the forces on the side of the cord where the force F is applied is:

$F-T=0$ (1)

where T is the tension in the cord.

On the other side of the cord, the equation of the forces on the canister is

$T-mg = ma$ (2)

where

m = 20 kg is the mass of the canister

$g=9.8 m/s^2$ is the acceleration of gravity

a is the acceleration

From (1),

$T=F$

Substituting into (2),

$F-mg = ma\\F=m(g+a)$

We want the canister to move at constant speed, so

a = 0

And therefore:

$F=mg=(20)(9.8)=196 N$

b) 2.0 cm

The cord is inextensible, this means that the acceleration of its parts are the same. Therefore, the acceleration of the free end must be the same as the acceleration of the canister: and this means that the two parts also cover the same distance in the same time.

Therefore, the free end of the cord must be moved exactly the same as the canister, by 2.0 cm.

c) 3.92 J, the same

The work done by the tension in the cord is

$W_T = T d$

where

T is the tension

d = 2.0 cm = 0.02 m is the displacement

As we said in part (a), the tension in the cord is equal to the force applied to the free end:

T = F

So

T = 196 N

Therefore, the work done by the tension is

$W=(196)(0.02)=3.92 J$

And since the force applied (F) is the same, then the work done by you when pulling the cord is exactly the same.

(d) -3.92 J

The weight of the canister is

$F_g = mg =(20 kg)(9.8 m/s^2)=196 N$

However, the direction of the force of gravity is opposite to the displacement. Therefore, the work done by gravity is negative:

$W_g = - F_g d$

And substituting,

$W_g=-(196)(0.02)=-3.92 J$

(e) Zero

The net work done on the canister can be simply calculated by adding the work done by the tension in the cord and the weight of the canister:

$W=W_T+W_g = 3.92 + (-3.92 ) = 0$

This is in agreement with the work-energy theorem, which states that the work done on an object is equal to its change in kinetic energy. In this situation, the canister is moving at constant speed, so its kinetic energy is not change: therefore,

$\Delta K = 0$ (change in kinetic energy = 0)

and so, the work done on it is also zero.

(f) The pulley system changes the direction of the force applied

This is a simple pulley system, which means that the system does not multiply the force applied in input. In fact, the mechanical advantage of the system is

$MA=\frac{F_{out}}{F_{in}}$

where:

$F_{out}$ is the output force, which is the weight of the canister

$F_{in}$ is the force in input, which is F

So, the mechanical advantage is 1:

$MA=\frac{196 N}{196 N}=1$

From a point of view of energy, therefore, there is no advantage in this system.

However, the advantage offered by the pulley system concerns the direction of the force: in fact, it changes the direction of the applied force (which is F, downward) into the tension of the cord (which is upward on the canister).

6 0

3 years ago

What is peer review.why is it important

madam [21]

Acc to

Publisso

Peer review is subjecting the author's scholarly work and research to the scrutiny of other experts in the same field to check its validity and evaluate its suitability for publication.

A peer review helps the publisher decide whether a work should be accepted.

6 0

3 years ago

Read 2 more answers

reviews the approach taken in problems such as this one. A bird watcher meanders through the woods, walking 0.916 km due east, 0

Verizon [17]

Answer:

Displacement: 2.230 km Average velocity: 1.274 $\frac{km}{h}$

Explanation:

Let's represent displacement by the letter S and the displacement in direction 49.7° as A. Displaement is a vector, so we need to decompose all the bird's displacement into their X-Y compoments. Let's go one by one:

0.916 km due east is an horizontal direction and cane be seen as direction towards the negative side of X-axis.

0.928 km due south is a vertical direction and can be seen as a direction towards the negative side of Y-axis.
3.52 km in a direction of 49.7° has components on X and Y axes. It is necessary to break it down using trigonometry,

First of all. We need to sum all the X components and all the Y componets.

∑ $Sx = Ax -0.916$ ⇒ ∑ $Sx = [tex]3.52cos(49.7) - 0.916$

∑ $Sx = 1.361 km$

∑ $Sy = Ay - 0.918$ ⇒ ∑ $Sy = 3.52sin(49.7) - 0.918$

∑ $Sy = 1.767$

The total displacement is calculated using Pythagoeran therorem:

$S_{total} =\sqrt{Sx^{2}+ Sy^{2} }$ ⇒

$S_{total} = 2.230 km$

With displacement calculated, we can find the average speed as follows:

$V = S/t$ ⇒ $V = \frac{2.230}{1.750}$

$V = 1.274\frac{km}{h}$

7 0

3 years ago

During the spin cycle of a washing machine, the clothes stick to the outer wall of the barrel as it spins at a rate as high as 1

Darya [45]

To answer the two questions, we need to know two important equations involving centripetal movement:

v = ωr (ω represents angular velocity <u>in radians</u>)

a = $\frac{v^{2}}{r}$

Let's apply the first equation to question a:

v = ωr

v = ((1800*2π) / 60) * 0.26

Wait. 2π? 0.26? 60? Let's break down why these numbers are written differently. In order to use the equation v = ωr, it is important that the units of ω is in radians. Since one revolution is equivalent to 2π radians, we can easily do the conversion from revolutions to radians by multiplying it by 2π. As for 0.26, note that the question asks for the units to be m/s. Since we need meters, we simply convert 26 cm, our radius, into meters. The revolutions is also given in revs/min, and we need to convert it into revs/sec so that we can get our final units correct. As a result, we divide the rate by 60 to convert minutes into seconds.

Back to the equation:

v = ((1800*2π)/60) * 0.26

v = (1800*2(3.14)/60) * 0.26

v = (11304/60) * 0.26

v = 188.4 * 0.26

v = 48.984

v = 49 (m/s)

Now that we know the linear velocity, we can find the centripetal acceleration:

a = $\frac{v^{2}}{r}$

a = $\frac{49^{2}}{0.26}$

a = 9234.6 (m/ $s^{2}$ )

Wow! That's fast!

<u>We now have our answers for a and b:</u>

a. 49 (m/s)

b. 9.2 * $10^{3}$ (m/ $s^{2}$ )

If you have any questions on how I got to these answers, just ask!

- breezyツ

5 0

3 years ago

You wish to produce an emf of 41.0 mV using an inductor whose inductance is 13.0 H. You start with a current of 1.50 mA through

Molodets [167]

Answer:

The current through the inductor at the end of 2.60s is 9.7 mA.

Explanation:

Given;

emf of the inductor, V = 41.0 mV

inductance of the inductor, L = 13 H

initial current in the inductor, I₀ = 1.5 mA

change in time, Δt = 2.6 s

The emf of the inductor is given by;

$V = L\frac{di}{dt} \\\\V = \frac{L(I_1-I_o)}{dt} \\\\L(I_1-I_o) = V*dt\\\\I_1-I_o = \frac{V*dt}{L}\\\\I_1 = \frac{V*dt}{L} + I_o\\\\I_1 = \frac{41*10^{-3}*2.6}{13} +1.5*10^{-3}\\\\I_1 = 8.2*10^{-3} + 1.5*10^{-3}\\\\I_1 = 9.7 *10^{-3} \ A\\\\ I_1 = 9.7 \ mA$

Therefore, the current through the inductor at the end of 2.60 s is 9.7 mA.

6 0

3 years ago