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Answer :
Final answer:
a) The total force resisting the motion is 1000 N.
b) The force in the hitch between the car and the trailer is 200 N.
Explanation:
(a) To determine the total force resisting the motion of the car, boat, and trailer, we need to consider the individual forces acting on the system. The force exerted by the car on the road is 2000 N, and the mass of the car is 1200 kg. The boat plus trailer has a combined mass of 800 kg. Using Newton's second law, F = ma, we can calculate the force resisting the motion of the car, boat, and trailer.
The force exerted by the car is equal to the sum of the forces resisting the motion:
F_resistance = F_car - F_net
F_resistance = 2000 N - (m_total * a)
By substituting the given values, we get:
F_resistance = 2000 N - ((1200 kg + 800 kg) * 0.5 m/s^2)
F_resistance = 2000 N - (2000 kg * 0.5 m/s^2)
F_resistance = 2000 N - 1000 N
F_resistance = 1000 N
Therefore, the total force resisting the motion of the car, boat, and trailer is 1000 N.
(b) If 80% of the resisting forces are experienced by the boat and trailer, then the remaining 20% is experienced by the car. Let F_total be the total force resisting the motion:
F_total = 1000 N
80% of F_total is experienced by the boat and trailer:
F_boat_trailer = 0.8 * F_total = 0.8 * 1000 N = 800 N
The force in the hitch between the car and the trailer is the remaining 20% of F_total:
F_hitch = 0.2 * F_total = 0.2 * 1000 N = 200 N
Therefore, the force in the hitch between the car and the trailer is 200 N.
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