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

most of them using statistics and defining how things are being measured