Which one or more of the following is true about both the drag force and the force of kinetic friction.?

Question

A. They are always equal in magnitude to forces acting in the opposite direction.

B.Their magnitudes increase with increasing speed.

C.They always act in the same direction as the object's acceleration.

D.They act in a direction opposite to the object's motion.

E. They always act in a direction opposite to the object's acceleration.

Answer 1

D.

Drag (D) is the force that pulls back on a jet when its engines are pushing (P) the jet forward. Friction is the force (F) that pulls back on a block of wood when it is pushed (P) forward.

If we have a block of mass m, we have f = (P - F) = ma; where P is the push forward and F is the friction force backward. Thus the block accelerates in the same direction as P and oppostie to F at a = (P - F)/m; so we see as F increases for the same push P, the acceleration gets smaller.

If P = F or D, the block or jet no longer accelerates even though it could very well be moving at a constant velocity. If P < F or D, the block or jet accelerates in a negative direction (a < 0), which we call deceleration.

A is false because P > F or D and P < F or D are feasible; the block and jet would accelerate or decelerate for example. If P = F or D, then the block/jet would be at a constant velocity (which includes v = 0 because 0 is a constant).

B is only partially true so that makes it false. Drag does increase with the square of the velocity because D = 1/2 rho Cd A v^2; where v is the velocity. But kinetic friction is just F = kN; where N is the normal weight of the sliding whatever. No velocity involved here.

C is false because, a = (P - F)/m or a = (P - D)/m; and if P > F or D, then a > 0 but F and D < 0 because of the minus signs, they are acting in the direction opposite to a. In fact if P = F, we have a = 0 and there is no direction (or magnitude) for the acceleration even though both P and F or D still have direction (and magnitude).

E is false because when P < D or F we have a < 0, which means negative acceleration which we call deceleration. Since D < 0 and F < 0 and a < 0 in this case, the drag and friction are acting in the same direction as the deceleration.