Comparing KE of Electron & Alpha Particle w/ Same R of Curvature

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To compare the kinetic energy of an electron and an alpha particle with the same radius of curvature in a magnetic field, the relevant equations are qvB = mv^2/r and KE = 1/2 mv^2. The discussion focuses on whether to set the equations equal for both particles to solve the problem. Participants suggest that the approach should involve analyzing both particles' equations separately. The problem is deemed manageable, and assistance is encouraged for those who have attempted a complete solution. Understanding the relationship between charge, mass, and velocity is crucial for this comparison.
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Homework Statement



Suppose that I want to compare the Kinetic Energy of an electron to the Kinetic Energy of an alpha particle if they both have the same radius of curvature in a magnetic field.

Homework Equations



qvB = mv^2/r
KE = 1/2 mv^2

The Attempt at a Solution



I am studying for my PE and I have run across this problem. I just want to know if the equations that I show are the correct ones for this problem. I am wondering if I have to set two (2) versions of these equations equal to each other (one for electron -- one for a-particle) ??

If anyone has a solution then please share it with me.
 
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Have you tried working the problem all the way through? It shouldn't be hard...
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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