Concept explainers
A 1 000-kg car is pulling a 300-kg trailer. Together, the car and trailer move forward with an acceleration of 2.15 m/s2. Ignore any force of air drag on the car and all frictional forces on the trailer. Determine (a) the net force on the car, (b) the net force on the trailer, (c) the force exerted by the trailer on the car, and (d) the resultant force exerted by the car on the road.
(a)
The net force on the car.
Answer to Problem 42P
The net force on the car is
Explanation of Solution
The free body diagram for the system is given by figure 1.
Write the expression for the net force along horizontal direction.
Here,
The car is having only horizontal acceleration.
Conclusion:
Substitute,
The net force is acting along forward direction.
Thus, the net force on the car is
(b)
The net force on the trailer.
Answer to Problem 42P
The net force on the car is
Explanation of Solution
Write the expression for the net force along horizontal direction.
Here,
Conclusion:
Substitute,
The net force is acting along forward direction.
Thus, the net force on the car is
(c)
The force exerted by the trailer on the car.
Answer to Problem 42P
The force exerted by the trailer on the car is
Explanation of Solution
According to the Newton’s third each and every action has equalled and opposite reaction. In the given problem, the force acting on the trailer given by the car is 645N. This force is directed along forward.
Thus, according to Newton’s third law, the trailer will also give same amount of force on the car. Hence, The force exerted by the trailer on the car is
(d)
The resultant force exerted by the car on the road.
Answer to Problem 42P
The resultant force exerted by the car on the road is
Explanation of Solution
Write the expression for the net force exerted by the road acting on the car.
Here,
Write the expression for the x-component of force.
Write the expression for the y-component of force.
Here,
Write the expression for the magnitude of the net force exerted by the road on the car by using (IV) and (V).
Here,
Write the expression for the magnitude of the net force exerted by the road on the car by using (IV) and (V).
Here,
Conclusion:
Substitute,
Substitute,
Here, the force with magnitude
Thus, according to Newton’s third law, the resultant force exerted by the car on the road is
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