A 1100-kg car pulls a boat on a trailer. (a) what total force resists the motion of the car, boat, and trailer, if the car exerts a 1900-n force on the road and produces an acceleration of 0.550 m/s2 ? the mass of the boat plus trailer is 700 kg. (b) what is the force in the hitch between the car and the trailer if 80% of the resisting forces are experienced by the boat and trailer?
R = total resistive force. 80% of this force is experienced by the boat and trailer. T = the force in the hitch between the car and the trailer.
Overall motion: Total mass = 1100 + 700 = 1800 kg Acceleration = 0.55 m/s² Driving force = 1900 N Resisting force = R N Therefore (1900 - R N) = (1800 kg)*(0.55 m/s²) 1900 - R = 990 R = 910 N 0.2R = 182 N 0.8R = 728 N
Consider the motion of the car: Driving force = 1900 N Resistive force = 0.2R = 182 N Force in the hitch = T NAcceleration = 0.55 m/s² Mass = 1100 kg Therefore 1900 - 0.2R - T = 1100*0.55 1900 - 182 -T = 605 T = 1113 N
Answer: R = 910 N, the total resistive force. T = 1113 N, the force in the hitch between the car and trailer.
