What is the resultant force pulling the plate down due to gravity?

Question

A plate with mass of 1.75 kg is tossed in the air, with air resistance acting like friction at k = 0.0005. What is the resultant force pulling the plate down due to gravity?

Answer 1

1. Without gravity, the force on the plate would just be F_g = mg = 1.75*g

Now to factor in air resistance, I gotta point out that this is one of the most poorly - worded physics questions I've ever seen. I'm making a few assumptions here.

1. Air resistance, like friction, acts opposite to the direction of motion. So, it matters whether this plate is moving up or down. When it's moving up, air resistance will act in the same direction as gravity, so the resultant force will be larger than just the weight of the plate. When the plate is falling down, air resistance will counter gravity, causing the resultant force to be less than the weight of the plate.
2. If you want to show off, you could solve this for both situations, but I guess I'll assume here that the plate is on its way down to the ground.
3. Air resistance has some complex formulas, but it sounds like your teacher just wants you to use the equation for frictional force to find the force of air resistance, so F_f = μ_k * F_normal
4. I think your teacher is using "k" as the same as μ_k in that formula
5. We have to assume that the plate was thrown straight up, so the normal force is the same as the weight that we found earlier
6. F_{air resistance} = k * 1.75*g
7. So, if the plate is falling downwards, F_resultant = F_g - F_{air resistance}
8. F_resultant = 1.75*g - 1.75*k*g
9. I'll leave the calculation to you.