# Tutor profile: Sierra C.

## Questions

### Subject: Astronomy

If the radiation pressure of our Sun suddenly stopped, how fast would the Sun collapse on itself?

This is a free fall question. We need the free fall time equation: $$t_{ff} = \sqrt{\frac{3\pi}{32G\rho}}$$. Using cgs units, $$\rho$$ can conveniently be approximated as 1 $$\frac{g}{cm^3}$$ and the gravitational constant G is 6.67 E -8 $$cm^3 g^{-1} s^{-2}$$. Plugging this in we get: $$t_{ff} = \sqrt{\frac{3\pi}{32*6.67 E -8*1}} = 35$$ mins.

### Subject: Physics

A ball of mass m and speed v is moving towards a ball with a mass of 2m and speed \frac{-1}/{2} v. They collide and stick together. What is their final velocity v?

This is a conservation of momentum problem. First, let's visualize what's happening. We have two balls, one with positive speed and one with negative. Because velocity is considered a vector, we know the positive and negative indicates direction. So, if we choose a direction for the positive - moving to the right, the negative direction would be moving to the left. Now, we have two options. Is it an elastic collision (do they bounce off at the end) or inelastic (stick together at the end). Here, we have an inelastic collision. This shows us that we will need to use this formula: $$m_{1} v_{1} + m_{2} v_{2} = m_{total} v_{f}$$ Plugging in our results we see: $$m v + 2m * (\frac{-1}{2}v) = m v - m v = 0 $$ The correct answer is 0 m/s.

### Subject: Physical Science

If you took all the steel used to make a steel ship and melted it down into a solid ball, it would sink. Why doesn’t it sink when it’s in the shape of a ship?

The ship has a much larger volume than the condensed steel ball, and much of this volume is just air, which weighs basically nothing. So, you greatly increase the upward buoyant force by increasing volume without increasing the downward gravitational force on the ship. With enough volume, the buoyant force will grow larger than the gravitational force.

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