(a)
The average power delivered to the protons.
(a)
Explanation of Solution
Given:
Each of the proton has a kinetic energy
Formula Used:
Write the expression for the power of the protons required to reach the end of the accelerator.
Here,
Calculation:
Substitute
Conclusion:
Thus, the average power that must be delivered to the stream of protons is
(b)
The force acting on the protons.
(b)
Explanation of Solution
Given:
Each of the proton has a kinetic energy
Formula Used:
The protons will perform some work at the expense of the energy with which they are emitting from the accelerator.
Write the expression for the work done by the protons.
Here,
Write the expression for the net force on the stream protons.
Here,
Write the expression for the force on each proton.
Calculation:
Substitute
Because of the application of this constant force on the protons, they reach to the end of the accelerator by traveling a distance 1.50 m.
Substitute
Substitute
Conclusion:
Thus, the force applied to each protons is
(c)
The velocity of protons just before hitting the target.
(c)
Explanation of Solution
Given:
Each of the proton has a kinetic energy
Formula Used:
Write the expression for the acceleration of each proton.
Here,
Write the expression for the final velocity of the protons just before hitting the target.
Here,
Calculation:
Substitute
Substitute
Simplify the above expression.
Conclusion:
Thus, the speed of the protons just before hitting the target is
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