The words "... as shown ..." tell us that there's a picture that goes along
with this question, and you decided not to share it. That's sad and
disappointing, but I think the question can be answered without seeing
the picture.
The net force on the crate is zero. Evidence for this is that fact that
the crate is just sitting there. If the net force on an object is not zero,
then the object is accelerating ... it's either speeding up, slowing down,
or its the direction of its motion is changing. If none of these things is
happening, then the net force on the object must be zero.
Answer:
A sample of 5.2 mg decays to .65 mg or to 1/8 of its original amount.
1/8 = 1/2 * 1/2 * 1/2 or 3 half-lives.
3 * 30.07 = 90 yrs for 5.2 mg to decay to .65 mg
You can get these other numbers similarly:
5.2 / .0102 = 510 requires about 9 half-lives which is 30 * 9 = 270 yrs
