Answer:
Absolute Pressure at depth h =
Explanation:
<u>Given:</u>
- Radius of the bubble at depth h,
- Radius of the bubble at the surface of the water,
- Acceleration due to gravity,
<u>Assumptions:</u>
- Atmospheric pressure,
- Density of water,
- Pressure at depth h =
- Pressure at the surface of water =
According to Ideal Gas Law,
where,
- P = pressure.
- V = volume.
- n = number of molecules.
- k = Boltzmann constant.
- T = absolute temperature.
For the given case, the temperature of the air bubble is constant. The number of molecules of the bubble also does not change, therefore,
PV = constant.
The pressure at the surface is equal to the atmospheric pressure,
The pressure at depth h is equal to sum of atmospheric pressure and the pressure of the water upto depth h,
Using these values,
The absolute temperature at that depth is given by
Answer:
well at the rate he goes he would be at 2.5km
Answer:
Tension force does no work
78 m/s
55701 J
Explanation:
The work done by the tension force of the rope is the dot product of the tension force vector and the distance travel vector as he swings. However, as these 2 vectors are always perpendicular to each other, their dot product would be 0 (cos(90) = 0). So the work done by tension force is 0.
If we neglect air resistance, then only gravity does work on the swimmer. We can apply the following energy conservation equation to calculate the kinetic energy once we let go of the rope.
where m is the mass of the swimmer, g = 9.81 m/s2 is the gravitational constant, Δh = 415 - 105 = 310 m is the height difference as he swings from horizontal point to the let go point. v is the let go speed. We can divide both sides by m
If the swimmer actually end up with only 67.8 m/s, then the loss in kinetic energy is due to air resistance during the swinging process. We can also find this by calculating the difference between the kinetics energies