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Margarita [4]
2 years ago
14

A stretched string has a mass per unit length of 5.00 g/cm and a tension of 10.0 N. A sinusoidal wave on this string has an ampl

itude of 0.12 mm and a frequency of 100 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, (c) ω, and (d) the correct choice of sign in front of ω?
Physics
1 answer:
8_murik_8 [283]2 years ago
4 0

Answer:

0.12 mm ; 140.50 rad/m ; 628.32 rad/sec ; +

Explanation:

Given the wave equation of the form :

y(x, t) = ym sin(kx ± ωt)

Mas per unit length (u) = 5 g/cm = (5÷1000)kg / 0.01m) = 0.005kg/0.01m = 0.5kg/m

Tension, T = 10 N

Amplitude, A = 0.12 mm

Frequency, F = 100 Hz

Comparing with the general wave equation :

y = Asin(kx ± ωt)

A = amplitude = ym = 0.12 mm

2.) k = 2π / λ

Recall :

v = fλ

v = sqrt(T/u) = sqrt(10/0.5) = sqrt(20) = 4.472

λ = v/ f = 4.472 / 100 = 0.04472

Hence,

k = (2 * π) / 0.04472

k = 140.50 rad/m

3.) Angular frequency, ω

ω = 2πf = 2 * 3.14 * 100 = 628.32 rad/sec

4.) sign is +ve

Direction of wave propagation as given is in the negative x axis

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Explanation:

(4566 m / 4 min) × (1 km / 1000 m) × (60 min / h) = 68.49 km/h

3 0
3 years ago
You apply a horizontal force of 25N to push a shopping cart across the parking lot at a constant velocity. a) what is the net fo
AlekseyPX

(a) The net force on the shopping cart is zero.

(b) The the force of friction on the shopping cart is 25 N.

(c) When same force is applied to the shopping cart on a wet surface, it will move faster.

<h3>Net force on the shopping cart</h3>

The net force on the shopping cart is calculated as follows;

F(net) = F - Ff

where;

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  • Ff is the frictional force

ma = F - Ff

where;

  • a is acceleration of the cart
  • m is mass of the cart

at a constant velocity, a = 0

0 = F - Ff

F(net)  = 0

F = Ff = 25 N

Net force is zero, and frictional force is equal to applied force.

<h3>On wet surface</h3>

Coefficient of kinetic friction of solid surface is greater than that of wet surface.

Since frictional force limit motion, when the frictional force is smaller, the object tends to move faster.

Thus, the cart will move faster on a wet surface due to decrease in friction.

Learn more about frictional force here: brainly.com/question/24386803

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4 0
2 years ago
A two slit pattern is viewed on a screen 1.00m from the slits if the two third-order minima are 22.0 cm apart what is the width
Bingel [31]

Answer:

4.4 cm

Explanation:

Given:

Distance of the screen from the slit, D = 1 m

Distance between two third order interference minimas, x = 22 cm

Let's say, minima occurs at:

x_n = (n + \frac{1}{2}) \frac{wL}{d}

We have:

2x_2 = 2(2 + \frac{1}{2}) * \frac{w*22}{d}

Calculating further for the width of the central bright fringe, we have:

\frac{w}{d} = \frac{22}{5}

= 4.4 cm

Note: w in representswavelength

8 0
3 years ago
Which of the following is represented by the letter A in the diagram below?
Kruka [31]

We have that the letter A in the diagram below given as

Amplitude

Option A

<h3>Amplitude</h3>

Question Parameters:

Amplitude

Crest

Trough

Wavelength

Generally, the amplitude of a wave is the maximum  displacement of the wave in the medium from its initial position.

Amplitude is denoted with the letter A

Therefore,Amplitude

Option A

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6 0
2 years ago
1. Two forces act on a box as follows: F1 = 100 N at 01 = 170° and F2 = 75 N
lilavasa [31]

Answer:

a)  F = 64.30 N,  b) θ = 121.4º

Explanation:

Forces are vector quantities so one of the best methods to add them is to decompose each force and add the components

let's use trigonometry

Force F1

          sin 170 = F_{1y} / F₁

          cos 170 = F₁ₓ / F₁

          F_{1y} = F₁ sin 170

          F₁ₓ = F₁ cos 170

          F_{1y} = 100 sin 170 = 17.36 N

          F₁ₓ = 100 cos 170 = -98.48 N

Force F2

          sin 30 = F_{2y} / F₂

          cos 30 = F₂ₓ / F₂

          F_{2y} = F₂ sin 30

          F₂ₓ = F₂ cos 30

          F_{2y} = 75 sin 30 = 37.5 N

          F₂ₓ = 75 cos 30 = 64.95 N

the resultant force is

X axis

          Fₓ = F₁ₓ + F₂ₓ

          Fₓ = -98.48 +64.95

          Fₓ = -33.53 N

Y axis

         F_y = F_{1y} + F_{2y}

         F_y = 17.36 + 37.5

         F_y = 54.86 N

a) the magnitude of the resultant vector

let's use Pythagoras' theorem

         F = Ra Fx ^ 2 + Fy²

         F = Ra 33.53² + 54.86²

         F = 64.30 N

b) the direction of the resultant

let's use trigonometry

        tan θ’= F_y / Fₓ

        θ'= tan^{-1}  \frac{F_y}{F_x}

        θ'= tan⁻¹ (54.86 / (33.53)

        θ’= 58.6º

this angle is in the second quadrant

The angle measured from the positive side of the x-axis is

        θ = 180 -θ'

        θ = 180- 58.6

        θ = 121.4º

5 0
2 years ago
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