A snowplow mounted on a truck clears a path 35m wide through

A snowplow mounted on a truck clears a path 3.5[m] wide through heavy snow. The snow is 0.2 [m] deep and the density is 200 [kg/m^3]. The truck travels at 50 [km/h]. The snow is discharged at a 45 degree angle from the direction of travel and 45 degree on the horizontal. Estimate the force required to push the plow (in the direction of travel)

Solution

Calculate the area of the path cleared by the plow.

A= (0.2 m) (3.5 m) = 0.7 m²

From the Reynolds Transport Theorem, the force required to push the plow is given by -
F = [ U*(-U)*density*A] - [U*U*density*A*(1+cos 45^o)]
=-U²*density*A (1+cos 45^o)
   =-(13.89 m/s)² (200 kg/m³) (0.7 m²) (1+cos 45^o)
   = -46103.158 N

Thus the force required to push the plow is -46103.158 N.