Question

Suppose your car was mired deeply in the mud and you wanted to use the method illustrated in Figure 4.37 to pull it out. (a) What force would you have to exert perpendicular to the center of the rope to produce a force of 12,000 N on the car if the angle is 2.00°? In this part, explicitly show how you follow the steps in the Problem-Solving Strategy for Newton’s laws of motion. (b) Real ropes stretch under such forces. What force would be exerted on the car if the angle increases to 7.00° and you still apply the force found in part (a) to its center?

Answer 1

To solve part (a), use the equation force = applied force / sin(angle). The force exerted perpendicular to the center of the rope is 349,110 N. For part (b), use the same equation with the new angle and force found in part (a) to find the force exerted on the car, which is 49,815 N.

Step-by-step explanation:

To solve part (a) of this problem, we can use the problem-solving strategy for Newton's laws of motion. First, we need to identify the known and unknown quantities. The known quantities are the force applied to the car (12,000 N) and the angle of the rope (2.00°). The unknown quantity is the force exerted perpendicular to the center of the rope.

The force exerted perpendicular to the center of the rope can be found using the equation: force = applied force / sin(angle). Plugging in the values: force = 12,000 N / sin(2.00°) = 349,110 N.

To solve part (b) of the problem, we can use the same equation with the new angle (7.00°) and the force found in part (a). Plugging in the values: force = 12,000 N / sin(7.00°) = 49,815 N.