Answer:
dart's speed is 11.77 m/s
Explanation:
given data
mass of the gun m = 355 gram = 0.355 kg
height = 18.3 centimeters = 0.183 m
dart = 57.0 gram = 0.057 kg
to find out
dart's speed
solution
we apply here law of conservation of energy that is express as
mgh = 0.5 × m × v² ...........1
so speed of gun will be here as
V = 
..................2
V = 
V = 1.89 m/s
and
now we find speed of dart by use law of conservation of momentum that is
M×V = m×v ...............3
so speed of the dart is
v = 
v = 
v = 11.77 m/s
so dart's speed is 11.77 m/s
The overall efficiency of the conversion is 6.93%.
<h3>What is the overall efficiency?</h3>
We know that generation of electricity from radioactive fuels is one of the major ways by which we can generate electricity in many countries. Now the efficiency of each of the steps have been shown in the question;
- Conversion efficiency = 35%
- Transmission efficiency = 90%
- Light efficiency = 22%
Overall efficiency = (0.35 * 0.90 * 0.22) * 100 = 6.93%
The energy is obtained from;
6.7X10^13 J * 6.93/100
= 4.6 * 10^12 J
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Missing parts;
The atomic number of uranium-235 is 92, its half-life is 704 million years and the radioactive decay of l kg of 235U releases 6.7X10^13 J. Generally, radioactive material is considered safe after 10 half-lives.
Assume that a nuclear powerplant can convert energy from 235U into electricity with an efficiency of 35%, the electrical transmission lines operate at 90% efficiency, and flourescent lights operate at 22% efficiency.
1.) What is the overall efficiency of converting the energy of 235U into flourescent light?
2.) How much energy from 1 kg of 235U is converted into flourescent light?
I think d would be the answer.
The terminal velocity as it falls through still air is 4.65154 in/s.
The diameter of small water droplet is 1.25 mil= 1.25×0.0254×10^-3 m
= 3.175 × 10^-5 m
Now the viscosity of still air is η = 1.83× 10⁻⁵ Pa
So the formula for drag force is:
Fd = 6πηrv
where, v is the velocity.
Now to attain terminal velocity acceleration must be zero.
→ W = Fd
ρVg = 6πrηv
ρ × 4/3 πr³×g = 6πrηv
v = 2/9 × ρgr³/ η
v = 2/9 × 10³×9.81×(3.175×10^-3) / 18.6×10^-6
v = 0.1181 m/s
v = 4.65154 in/s
Learn more about terminal velocity here:
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