What is the speed, in m/s, of a proton after being accelerated from rest through a potential difference?
We have to find the speed, in m/s, of a proton after being accelerated from rest through a potential difference.
Energy of the proton in the potential difference is
The mass of the proton is . So if the velocity of the proton is then we have
So the velocity of the proton will be .
A rocket is fired from the earth to the moon at a speed of . Let two events be “rocket leaves earth” and “rocket hits moon.” a. In the earth’s reference frame, calculate ∆x, ∆t, and the space time interval s for these events.
b. In the rocket’s reference frame, calculate ∆x′, ∆t′, and the space time interval s′ for these events.
c. Repeat your calculations of part a if the rocket is replaced with a laser beam.
Two rockets are each long in their rest frame. Rocket Orion, traveling at relative to the earth, is overtaking rocket Sirius, which is poking along at a mere According to the crew on Sirius, how long does Orion take to completely pass? That is, how long is it from the instant the nose of Orion is at the tail of Sirius until the tail of Orion is at the nose of Sirius?
A typical nuclear power plant generates electricity at the rate of . The efficiency of transforming thermal energy into electrical energy is and the plant runs at full capacity for of the year. (Nuclear power plants are down about of the time for maintenance and refueling.)
a. How much thermal energy does the plant generate in one year?
b. What mass of uranium is transformed into energy in one year?
The nuclear reaction that powers the sun is the fusion of four protons into a helium nucleus. The process involves several steps, but the net reaction is simply . The mass of a proton, to four significant figures, is , and the mass of a helium nucleus is known to be .
a. How much energy is released in each fusion?
b. What fraction of the initial rest mass energy is this energy?
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