6: The atoms are the same age. On average, the atoms were made in stars billions of years ago.
16: Cobalt has atomic number 27. This means that all isotopes of cobalt have 27 protons. Thus Cobalt 59 has 27 protons and 59 - 27 = 32 neutrons. Cobalt 60 has 27 protons and 33 neutrons. Both isotopes, if neutral, have 27 electrons.
26: Germanium is element number 32. If you add a proton to a Germanium nucleus, then it becomes element 33, which is Arsenic. Arsenic is poisonous.
Chapter 13:
Project: Eggs sink in water. You need to dissolve a LOT
of salt in water to make an egg float. This means that an egg is
denser than fresh water but less dense than salt water (if there is enough
salt in the water). This is a fun project to do with children.
Exercises:
2: An ordinary bed contacts your body in a few locations,
typically your head, shoulders, backside, and legs. A waterbed is
much more yielding and contacts your body at all points. Thus
although the upward force of the bed on your body is the same in both
cases, because the contact area of a waterbed is much greater, the
pressure exerted when you lie on a waterbed is much less.
3: The sharper the knife, the smaller the surface area of the edge
of the blade. Since you apply the same force to the knife, a smaller
surface area means a larger pressure.
6: He is demonstrating the same physics principle that I
demonstrated with the 'seat of nails'. If you step on one piece of
glass (or sit on one nail), the contact area is very small and the
pressure is VERY large. Ouch! If you step on many pieces of glass,
the contact area is not as small and the pressure is not as large. By
making sure that all the broken pieces are small and that there are
lots of pieces, he ensures that contact area is larger and thus the
pressure smaller.
Problems:
2: Density = mass/volume = 6 kg/ 1 l = 6 kg / 0.001 m^3 = 6000 kg/m^3.
6 kg/l is also an acceptable answer (but you would lose 1 point on
a test because I want the answers in standard units) .
4: The boy has to apply a force that is equal to the force exerted by the water. This force is the water pressure times the area of the hole. The pressure is p = d g h = 1000 kg/m^3 * 10 m/s^2 * 2 m = 20,000 Pa. The area of the hole is 1 cm^2. Since 100 cm = 1 m, we can fit 100*100 square centimeters into 1 square meter. Thus A = (1/10,000) m^2. Force = pressure * area = 20,000 Pa * (1/10,000) m^2 = 2 N. 2 N is the weight of 0.2 kg or about 1/2 pound. The child can easily stop the leak.
Extra Credit:
If you are 3 m below the water surface then the pressure is P =
dgh = 1000 kg/m^3 * 10 m/s^2 * 3 m = 30,000 Pa = 3*10^4 Pa. The front
of my body can be approximated as being 2 m tall by 1/2 m wide = 1
m^2. Thus, the force on my body is
F = PA = 3*10^4 Pa * (1 m^2) = 3*10^4 N (Newtons)
remembering that 1 Pascal = 1 N/m^2. This is the weight of
3*10^4 N / 10 m/s^2 = 3000 kg or 3 tons. Rather a lot!
If your answer has too many significant figures (for example, if
you had 2967 kg), then it is partially wrong. Remember that the more
digits we include, the more precise we think our answer is. If you
use too many digits, you are falsely claiming that your answer is very
precise.