Answer: 98,000 J
Explanation: The total energy or mechanical energy is expressed in the following equation:
ME= PE + KE
PE = mgh
= 1000 kg x 9.8 m/s² x 10m
= 98000 J
ME = PE - KE
= 98000 J - 0 J
= 98000 J
We know that a charge moving in a magnetic field is subject to the force:
F = q · v · B
But we also know that:
F = m · a
Therefore, it must be:
m · a = <span>q · v · B
And solving for a:
</span>a = <span>q · v · B / m
Recall that for a proton:
q = 1.6</span>×10⁻¹⁹ C
m = 1.673×10⁻²⁷ kg
Now, you can find:
a = 1.6×10⁻¹⁹ · 7.0 · 1.7 / <span>1.673×10⁻²⁷
= 1.14</span>×10⁹ m/s²
Hence, the acceleration of the proton is 1.14<span>×10⁹ m/s²</span>.
Assuming ideal conditions, Boyle's law says that
<em>P₁ V₁ </em>= <em>P₂</em> <em>V₂</em>
where <em>P₁ </em>and <em>V₁</em> are the initial pressure and temperature, respectively, and <em>P₂</em> and <em>V₂</em> are the final pressure and temperature.
So you have
(455 mm Hg) (56.5 m³) = (632 mm Hg) <em>V₂</em>
==> <em>V₂</em> = (455 mm Hg) (56.5 m³) / (632 mm Hg) ≈ 40.7 m³
Acceleration is the rate of the change in velocity.
The answer would be the rate at which velocity changes.
