184_notes:fab_physics [Projects & Practices in Physics]

Before we go to Mars we need to test safety features such as the ability to stop harmful radiation. You are part of a team that is designing a “force” field that will deflect alpha particles. You need to create a design that will stop alpha particles that are shooting directly at a group of astronauts who are creating a habitat on the moon as a test run. The alpha particles are traveling with a speed of 1.28 * $10^{+07}$ m/s from very far away.

Your shield comes in the form of a charged sphere (think of a space balloon) with the balloons having a mass of 1*10 kg and a charge of -150C. Your supervisor and lead engineer Gert Frobe would like to know what would be the closest distance (in meters) that an alpha particle could get before bouncing back from the shield?

Space Shield Fab Physics Week 1 Learning Goals

Apply energy principles to a situation with charges (energy conservation, transfer of energy, system definitions, etc.)
Think about what might change when there are multiple sources of charge in the problem

Learning Issues/ Common Pitfalls

Connecting ideas from Physics 1 - we're asking students to remember ideas like force, speed, energy (kinetic), from Physics 1. For some students it may have been a few semesters.
Thinking about multiple charges → what changes and what doesn't change. Students seeing / thinking about the interaction between two charges for the first time here.
“Really far away” vs “very big” vs “very small” - how do you make these decisions? You may need to have a conversation about these terms and emphasize that it is big/small/far compared to what?

For this problem, it is easy to get trapped in the numbers without thinking about what is actually going on in this problem. Push student to talk through qualitatively what it is they are trying to solve for in this situation first.

Starting Questions

Question: Just conceptually/qualitatively, what is happening to the charges in this situation?
Answer: There is one large charge that is stationary on the moon and a smaller incoming charge. Need to think about the direction the small charge is moving in relation to the big charge.

Question: Based on the signs of the charges, what is going to happen as the small charge moves toward the large charge?
Answer: The two charges are the same charge, so the smaller charge will be repelled by the larger charge. This means that the small charge will slow down and eventually be repelled by the large charge.

Finding Shortest Separation Distance

For this part, we will make the following assumptions:

Approximate the large charge as a point charge with a negative charge

We choose the system to be the two charges and everything else is the surroundings. With the assumption that no energy is transferred at any point, energy is conserved for the system. We will also make the assumption that the large charge is being held in place so that as the small charge gets closer, electrostatic repulsion does not drive them apart. This can be done without losing any energy to the moon.

With the assumptions made, the only energies in play are kinetic and electric potential energy of the charges themselves. Since the large charge is fixed, it has no kinetic energy, but the small charge does. With conservation of energy, the initial energy and the final energy must be the same. $$U_i+K_i=U_f+K_f$$ Because we assume that the small charge starts far away, $U_i=0$. We are asked to find the smallest separation distance which is when all the $K_i$ is transferred to $U_f$. At this point the small charge is the closest it will be to the large cloud, and is not moving $K_f =0$. $$K_i=U_f$$

Tutor Question

Question: What is it that causes the small charge to lose its kinetic energy?
Answer: The repulsive force between the like charges

$$.5(m)(v)^2 = k \frac{q_{1}*q_{2}}{r_{sep}}$$

$$.5(6.645*10^{-27})(1.28*10^{7})^2 = 8.99*10^9 \frac{-150*2*(-1.6*10^{-19})}{r_{sep}}$$

$$r_{sep}=-7.9331e+5 \quad {meters}$$

Discussion Prompts

Question: What is your system when you were looking for the shortest separation distance between the clouds?
Answer: We needed to consider the interaction between the two clouds so both were in the system.

Question: In this problem, you used electric potential energy, what is meant by this?
Answer: Electric potential energy tells you about the interaction between the two charges.

Question: What would you expect to happen if the balloon was not stabilized on the moon? Which would move faster? Which charge exerts a larger force (the large or small charge)?
Answer: The smaller charge would also exert a force on the bigger charge and push it away. The small charge would still move faster than the big charge because it has a smaller mass - they experience the same force.

Question: How did you simplify this problem?
Answer: See the “Assumptions should include” list above

Extension Questions

Question: How much force would the moon have to exert on the big charge to keep it in place?
Answer: Here would you have to use net force where the magnitude of the contact (or normal) force from the moon should be equal to the magnitude of the electric force $F=\frac{k*q*Q}{r^2}$. This can tie into the next question about force diagrams

Question: What does the free body (force) diagram look like for the large and small charge?

Space Shield Fab Physics Week 1