A small metal sphere weights 0.343 N in air and has a volume of 17.4 cm^3.?

Question

What is the accelearation of the sphere as it falls through water? Answer in units of m/s^2.

Answer 1

The acceleration is ZERO
The sphere will reach terminal velocity of .173 m/s in less than 0.5 sec.
Water resistance is EVERYTHING in this problem.

Answer 2

The assumption is that the sphere is small enough that there is no fluid resistance to the motion.

Quick check. The sphere weighs 0.343N, ie, 0.343/10 (g=10) and get 0.034 kg, or 34 gm. The volume is 17.4 cc so the density is almost 2 gm/cc, higher than water so it will sink.

There is a buoyancy force B equal to density of water * volume of object * g.

So volume = 17.4 *10^-6 m^3. Use density of water as 1000 kg/m^3, B= 1.74 *10^-1 N. or 0.174N

So mass x net accel = weight - Buoyancy force = 0.343- 0.174

You can get net accel.

Make sense. Density is 2x water so buoyance force is half the weight. So the acceleration is reduced to about 1/2 of g. in air