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sasho [114]
3 years ago
9

A sinusoidal, transverse wave that propagates in the positive x-direction can be described with the wave function y of xt is equ

al to A times cosine of start parenthesis k times x minus omega times t end parenthesis, where k is the wave number, x is the position of a point on the wave, omega is the angular frequency, and t is time. What is another way to express the angular frequency, omega
Physics
1 answer:
myrzilka [38]3 years ago
4 0

Answer:

\omega =\frac{2 \pi }{T} rad/s

Explanation:

The wave function is:

y(xt) = Acos(kx- \omega t)

where :

k = wave number

x = position of a point on the wave

\omega = angular frequency

t = time

What is another way to express the angular frequency (omega)

Angular frequency (omega) can be express as :

\omega =\frac{2 \pi }{T} rad/s ( i.e one repetition that it takes to repeats itself)

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A box with mass (m) it's sliding along on a friction-free surface at 9.87 m/s at a height of 1.81 meters. It travels down the hi
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A) The answer is 11.53 m/s

The final kinetic energy (KEf) is the sum of initial kinetic energy (KEi) and initial potential energy (PEi).
KEf = KEi + PEi

Kinetic energy depends on mass (m) and velocity (v)
KEf = 1/2 m * vf²
KEi = 1/2 m * vi²

Potential energy depends on mass (m), acceleration (a), and height (h):
PEi = m * a * h

So:
KEf = KEi + <span>PEi
</span>1/2 m * vf² =  1/2 m * vi² + m * a * h
..
Divide all sides by m:
1/2 vf² =  1/2 vi² + a * h

We know:
vi = 9.87 m/s
a = 9.8 m/s²
h = 1.81 m

1/2 vf² =  1/2 * 9.87² + 9.8 * 1.81
1/2 vf² = 48.71 + 17.74
1/2 vf² = 66.45
vf² = 66.45 * 2
vf² = 132.9
vf = √132.9
vf = 11.53 m/s


b) The answer is 6.78 m

The kinetic energy at the bottom (KE) is equal to the potential energy at the highest point (PE)
KE = PE

Kinetic energy depends on mass (m) and velocity (v)
KE = 1/2 m * v²

Potential energy depends on mass (m), acceleration (a), and height (h):
PE = m * a * h

KE = PE
1/2 m * v² = m * a * h

Divide both sides by m:
1/2 * v² = a * h
v = 11.53 m/s
a = 9.8 m/s² 
h = ?

1/2 * 11.53² = 9.8 * h
1/2 * 132.94 = 9.8 * h
66.47 = 9.8 * h
h = 66.47 / 9.8
h = 6.78 m
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