FHSST Physics/Newtonian Gravitation/Comparative Problems

= Comparative problems =

Here always work with multiplicative factors to find something new in terms of something old.

Worked Example 57 Comparative Problem 1
Question: On Earth a man weighs 700 N. Now if the same man was instantaneously beamed to the planet Zirgon, which has the same size as the Earth but twice the mass, what would he weigh?

Answer:

Step 1 :

We start with the situation on earth:

Step 2 :

Now we consider the provje

but we know that $$m_Z = 2m_E$$ and we know that rZ = r so we could write the equation again and substitute these relationships in:

Step 3 :

Step 4 :

Step 5 :

so on Zirgon he weighs 1400 N.

Principles

 * Write out first case
 * Write out all relationships between variable from first and second case
 * Write out second case
 * Substitute all first case variables into second case
 * Write second case in terms of first case



Worked Example 58 Comparative Problem 2
Question: On Earth a man weighs 70 kg. On the planet Beeble how much will he weigh if Beeble has mass half of that of the Earth and a radius one quarter that of the earth.

Answer:

Step 1 :

We start with the situation on earth:

Step 2 :

Now we consider the provje

but we know that $$m_Z = \frac{1}{2}m_E$$ and we know that $$r_Z = \frac{1}{4}r$$ so we could write the equation again and substitute these relationships in:

Step 3 :

Step 4 :

Step 5 :

$$\begin{matrix}W_Z= 8(W)\end{matrix}$$

But although the man exerts 8 times as much force due to gravity, he still weighs 70 kg on Beeble!

