Can you please show all work!! Thank you!! Two drag forces act on a bicycle and

Question

Can you please show all work!! Thank you!!

Two drag forces act on a bicycle and rider: FD1 due to rolling resistance, which is essentially velocity independent; and FD2 due to air resistance, which is proportional to v2. For a specific bike plus rider of total mass 78 kg, FDl 4.0 N; and for a speed of 2.2 m/s, FD2 1.0 N. Show that the total drag force is Fd = 4.0 + 0.21 v2, where v is in m/s, and FD is in N and opposes the motion. Determine at what slope angle theta the bike and rider can coast downhill at a constant speed of 8.0 m/s.

Explanation / Answer

here,

(a)

Fd1 = 4 N

Fd2 is proprtional to v^2

let Fd2 = k*v^2

where k is a constant and v is the velocity of the particle

for Fd2 = 1 N , v = 2.2 m/s

1 = k * 2.2^2

k = 0.21 N

therefore , Fd2 = 0.21 *v^2

total drag force , Fd = Fd1 + Fd2

Fd = 4 + 0.21 v^2

hence ,proved

(b)

m = 78 kg

for constant speed v = 8 m/s

Fd = m*g*sin(theta)

4 + 0.21 * 8^2 = 78 *9.8 *sin(theta)

theta = 1.31 degree

the slope angle theta is 1.31 degree

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