Complete question:
A taut rope has a mass of 0.123 kg and a length of 3.54 m. What average power must be supplied to the rope to generate sinusoidal waves that have amplitude 0.200 m and wavelength 0.600 m if the waves are to travel at 28.0 m/s ?
Answer:
The average power supplied to the rope to generate sinusoidal waves is 1676.159 watts.
Explanation:
Velocity = Frequency X wavelength
V = Fλ ⇒ F = V/λ
F = 28/0.6 = 46.67 Hz
Angular frequency (ω) = 2πF = 2π (46.67) = 93.34π rad/s
Average power supplied to the rope will be calculated as follows
where;
ω is the angular frequency
A is the amplitude
V is the velocity
μ is mass per unit length = 0.123/3.54 = 0.0348 kg/m
= 1676.159 watts
The average power supplied to the rope to generate sinusoidal waves is 1676.159 watts.
Answer:
W = 7.06 J
Explanation:
From the given information the spring constant 'k' can be calculated using the Hooke's Law.
Now, using this spring constant the additional work required by F to stretch the spring can be found.
The work energy theorem tells us that the work done on the spring is equal to the change in the energy. Therefore,
![W = U_2 - U_1\\W = \frac{1}{2}kx_2^2 - \frac{1}{2}kx_1^2 = \frac{1}{2}(275.13)[0.29^2 - 0.18^2] = 7.06~J](https://tex.z-dn.net/?f=W%20%3D%20U_2%20-%20U_1%5C%5CW%20%3D%20%5Cfrac%7B1%7D%7B2%7Dkx_2%5E2%20-%20%5Cfrac%7B1%7D%7B2%7Dkx_1%5E2%20%3D%20%5Cfrac%7B1%7D%7B2%7D%28275.13%29%5B0.29%5E2%20-%200.18%5E2%5D%20%3D%207.06~J)
The change that will always result in an increase in the gravitational force between two objects is increasing the masses of the objects and decreasing the distance between the objects.
When you're talking about gravity, it's easy to identify the equal
opposite forces.
Gravity ALWAYS produces an equal pair of opposite forces.
They both act between the centers of the two objects, one in
each direction.
Consider the equal pair of opposite gravitational forces between
you and the Earth. One force acts on you, and draws you toward
the center of the Earth. We call that force "your weight".
The other one acts on the Earth, and draws it toward the center
of you. Hardly anybody ever talks about that one, but the two
forces are equal ... your weight on Earth is equal to the Earth's
weight on you !
