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.
Observe that the given vector field is a gradient field:
Let 
, so that
Integrating the first equation with respect to 
, we get
Differentiating this with respect to 
gives
Now differentiating 
with respect to 
gives
Putting everything together, we find a scalar potential function whose gradient is 
,
It follows that the curl of is 0 (i.e. the zero vector).
Answer:
1,050 Joules
Explanation:
<u>Step 1:</u> work done in moving the box 30 meters
work done = force X distance
= 25N X 30 = 750 Joules
<u>Step 2: </u>calculate total internal energy
Total internal energy = work done + kinetic energy
= 750 Joules + 300 Joules
= 1,050 Joules = 1.05 KJ
Here are the answers:
1. False - Molecules is the smallest part of an element that behaves like the element.
2. False - The nucleus contains both protons and neutrons
3. True
4. True
5. A. Nucleus
6. D. Neutron
7. B. Protons and Neutrons
8. C. Electron
9. C. 6
10. C.6
