Average Power and Work-Kinetic Energy Theorem problem

In summary, to complete a master's degree in physics, a small, linear accelerator must be designed to emit protons with a kinetic energy of 8.2 keV and a rate of 1.00 x 10^9 per second to reach a target at the end of a 1.80-m-long accelerator. The average power needed to deliver the stream of protons is ? μW, the force applied to each proton is ? N, and the speed of each proton just before it strikes the target is ? m/s. To solve these questions, use the equation K=½mv² to find the velocity of the protons, and then use the protons' acceleration to determine the force.
  • #1
Keldroc
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Homework Statement


To complete your master's degree in physics, your advisor has you design a small, linear accelerator capable of emitting protons, each with a kinetic energy of 8.2 keV. (The mass of a single proton is 1.67 x 10^-27 kg.) In addition, 1.00 x 10^9 protons per second must reach the target at the end of the 1.80-m-long accelerator.
(a) What the average power must be delivered to the stream of protons?
1. ? μW

(b) What force (assumed constant) must be applied to each proton?
2. ? N

(c) What speed does each proton attain just before it strikes the target, assuming the protons start from rest?
3. ? m/s

Homework Equations


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[URL]http://upload.wikimedia.org/math/9/a/e/9aeac7ca01e03ffd4b80c513dbeb1b6a.png[/URL]Can someone help with this question? Thanks in advance
 
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  • #2
You have the mass and the kinetic energy, and K=½mv². Find v to answer part (c).

From there you can find the protons' acceleration, which will help to
find the force in part (b).
 

1. What is the formula for calculating average power?

The formula for average power is P = W/t, where P represents power, W represents work, and t represents time.

2. How is average power related to work and kinetic energy?

The average power is the rate at which work is done, and work is directly proportional to the change in kinetic energy according to the Work-Kinetic Energy Theorem. Therefore, average power is also related to kinetic energy.

3. Can the Work-Kinetic Energy Theorem be applied to all types of motion?

Yes, the Work-Kinetic Energy Theorem can be applied to all types of motion as long as there is a change in kinetic energy.

4. How can I use the Work-Kinetic Energy Theorem to solve problems?

To use the Work-Kinetic Energy Theorem to solve problems, you need to identify the initial and final kinetic energies, calculate the change in kinetic energy, and use the formula W = ΔKE to solve for work. Then, use the formula P = W/t to calculate the average power.

5. Is there a difference between average power and instantaneous power?

Yes, there is a difference between average power and instantaneous power. Average power is the total amount of work done over a period of time, while instantaneous power is the power at a specific moment in time. Average power is calculated by dividing work by time, while instantaneous power is calculated by dividing the change in energy by the change in time.

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