Question

A 3200 lb vehicle is being designed with a drag coefficient of 0.35 and a frontal area of 50 ft2. If the vehicle is traveling at 70 miles per hour on a downhill grade of 2% at an air density of 0.002378 slugs/ft3, what tractive effort is required to overcome the vehicle resistance forces (in lb)?

Answer 1

Answer:209.73 lb

Step-by-step explanation:

Given

Weight of vehicle=3200 lb

frontal area
`=50 ft^2`

Velocity
`=70 mph\approx 102.67 ft/s`

`\rho =0.002378 slugs/ft^3`

Tractive effort is the sum of aerodynamic, Rolling and grade resistance

`F_D=(\rho )/(2)C_dA_fv^2`

`F_D=(0.002378)/(2)* 0.35* 50* (102.67)^2`

`F_D=219.33 lb`

Rolling Resistance

`F_R=F_(rl)\omega`

`F_(rl)`=Rolling resistance coefficient

`F_(rl)=0.01\left [ 1+(v)/(160)\right ]`

where v is in km/hr

`F_(rl)=0.01\left [ 1+(112.65)/(160)\right ]`

`F_(rl)=0.017`

`F_R=0.017* 3200=54.4 lb`

Grade resistance

`F_G=\omega G`

`F_G=3200* (2)/(100)=-64 lb` (beacuse of downward slope)

Total resistance
`=F_D+F_R+F_G=219.33+54.4-64=209.73 lb`