Energy Conservation - Electric Potential Energy

In summary, the conversation discusses proton-beam therapy and how a high-energy beam of protons is used to deposit energy and break apart tumor cells. The question at hand is what is the total charge of protons needed to deposit 0.10 J of energy in the tumor, with a potential difference of 13 MV. After some calculations, the correct answer is determined to be 7.7x10^-9 C.
  • #1
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Homework Statement



In proton-beam therapy, a high-energy beam of protons is fired at a tumor. The protons come to rest in the tumor, depositing their kinetic energy and breaking apart the tumor’s DNA, thus killing its cells. For one patient, it is desired that 0.10 J of proton energy be deposited in a tumor. To create the proton beam, the protons are accelerated from rest through a 13 MV potential difference.


What is the total charge of the protons that must be fired at the tumor to deposit the required energy?
Express your answer to two significant figures and include the appropriate units.


Homework Equations



U = qv
KE = 1/2mv^2

E = 0.10 J
change in v = 13 000 000 V


The Attempt at a Solution



I took 0.10 J as the total energy, seeing as this is the amount that must be deposited in the tumor. The protons start from rest, so KE = 0 while U = qv, where q is the total charge of the protons and v is the potential difference, which is 13x10^6 V.

E = qv
0.10/13000000 = q
q = 7.0x10^-9 C

This is not the right answer though...is there something wrong with my logic?
 
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  • #2
You did the calculation wrong. Recheck.
 
  • #3
I don't quite understand what I've done wrong. I did the calculation again and I'm still getting 7.0x10^-9 C. I'm assuming the units of C are correct since the division yields Joules/Volt, and Joule = Coulomb * Volt. I also checked over my conversion of MV to V and that is correct as well.
 
  • #4
"Express your answer to two significant figures and include the appropriate units."

It should be 7.7x10^-9 C
 
  • #5
Oh I see...my calculator didn't show me those last few digits. Thanks so much for your help!
 

1. What is electric potential energy?

Electric potential energy is the energy that an object possesses due to its position in an electric field. It is the potential for an object to do work as a result of its electric charge and its position relative to other charged objects.

2. How is electric potential energy related to energy conservation?

Electric potential energy is a form of potential energy, which means that it can be converted into other forms of energy, such as kinetic energy or thermal energy. This relationship is important in the principle of energy conservation, which states that energy cannot be created or destroyed, only converted from one form to another.

3. How can electric potential energy be conserved?

Electric potential energy can be conserved by reducing the amount of energy lost through resistance in a circuit. This can be achieved by using more efficient materials in the construction of electrical components and by minimizing the length of wire used in a circuit.

4. What are some examples of electric potential energy in everyday life?

There are many examples of electric potential energy in everyday life, such as the potential energy stored in a battery, the potential energy of a charged capacitor, and the potential energy of a lightning bolt. Other examples include the potential energy of a water pump or the potential energy of a rollercoaster at the top of a hill.

5. How does electric potential energy relate to the concept of voltage?

Voltage is a measure of the potential difference between two points in an electric field. This potential difference is what allows electric potential energy to be converted into other forms of energy, such as electrical current. In other words, the higher the voltage, the greater the potential for energy to be transferred through an electrical circuit.

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