Question

true / false
if dropped from the top of a high building a 20 kg sphere with a radius of 20 cm will reachterminal velocity before a 10 kg sphere with the same radius

Answer 1

Drag force, IIRC, is D=(1/2)CpAv^2, where C is the drag coefficient of the fluid, p is the fluid density, and A is the cross sectional area perpendicular to the direction of force. Nowhere here is mass mentioned; this is merely an upwards pointing force for all masses of the same A.

The force of gravity needs to equal D. But the force of gravity is mass-reliant, a la F=ma, or F_g=mg. With a larger m comes a larger F, and as v increases similarly for both masses, it will take longer for D to meet the larger F_g. So, yes, the one with the larger mass will take longer to reach terminal velocity.

Answer 2

Note, though, I assumed that the drag (air resistance) were negligible for the velocity's progression as time went by. If the numbers were extreme enough that they aren't, then the answer might change.

Answer 3

thank you so much thanks for taking the time to make me understand i really appreciate it