Question

The drag force pushes opposite your motion as you ride a bicycle. If you double your speed, what happens to the magnitude of the drag force? a.The drag force goes up by a factor of 4 b.The drag force stays the same. c.The drag force decreases. d.The drag force doubles as well

Answer 1

F_d,1 / F_d,o = 4 , Option A

Step-by-step explanation:

Given:

- The velocity of the bike V_o is doubled to 2*V_o

Find:

what happens to the magnitude of the drag force?

Solution:

- The expression of the Drag force as a function of objects area, coefficient of drag, velocity and density of medium is given by:

F_d = 0.5*C_d*A*p*V^2 / 2

- In our case the force of drag with speed V_o is:

F_d,o = 0.5*C_d*A*p*V_o^2 / 2

- force of drag with speed 2V_o is:

F_d,1 = 2*C_d*A*p*V_o^2 / 2

- Take the ratio of F_d,1 to F_d,o:

F_d,1 / F_d,o = (2*C_d*A*p*V_o^2 / 2) / (0.5*C_d*A*p*V_o^2 / 2)

We get: F_d,1 / F_d,o = 4

Hence, by doubling the speed the magnitude of drag force is increased by a factor of 4.