To maintain a constant speed, the force provided by a car's engine must equal the drag force plus the force of friction of the road (the rolling resistance). The density of air is 1.2 kg/m3. (a) What are the drag forces in newtons at 80 km/h and 105 km/h for a Toyota Camry? (Drag area = 0.70 m2 and drag coefficient = 0.28.) at 80 km/h N at 105 km/h N (b) What are the drag forces in newtons at 80 km/h and at 105 km/h for a Hummer H2? (Drag area = 2.44 m2 and drag coefficient = 0.57.) at 80 km/h N at 105 km/h N

Toyota Camry

F_d = 51.852 N

F_d = 100.042 N

Hummer H2

F_d = 412.0888 N

F_d = 8351.755 N

Explanation:

Given:

- The density of air p_air = 1.2 kg/m^3

- The drag force equals car's engine force.

Find:

- What are the drag forces in newtons at 80 km/h and 105 km/h for a Toyota Camry? (Drag area = 0.70 m2 and drag coefficient = 0.28.)

- What are the drag forces in newtons at 80 km/h and at 105 km/h for a Hummer H2? (Drag area = 2.44 m2 and drag coefficient = 0.57.)

Solution:

- The formula for drag force is given as follows:

F_d = 0.5*C_d*p_air*A*V^2

Where,

A : The drag Area m^2

C_d: The drag coefficient

V: Velocity m/s

a) Toyota Camry

C_d = 0.28, A = 0.70 m^2, V = 80 km/h = 22.222 m/s

Then compute the F_d drag force:

F_d = 0.5*0.28*1.2*0.70 * (22.22) ^2

F_d = 51.852 N

C_d = 0.28, A = 0.70 m^2, V = 105 km/h = 29.1667 m/s

Then compute the F_d drag force:

F_d = 0.5*0.28*1.2*0.70 * (29.1667) ^2

F_d = 100.042 N

b) Hummer H2

C_d = 0.57, A = 2.44 m^2, V = 80 km/h = 22.222 m/s

Then compute the F_d drag force:

F_d = 0.5*0.57*1.2*2.44 * (22.22) ^2

F_d = 412.0888 N

C_d = 0.28, A = 0.70 m^2, V = 105 km/h = 29.1667 m/s

Then compute the F_d drag force:

F_d = 0.5*0.57*1.2*2.44 * (29.1667) ^2

F_d = 8351.755 N