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Chapter 9: Problem 20

Two masses hang from two strings of equal length that are attached to the ceiling of a car. One mass is over the driver's seat; the other is over the passenger's seat. As the car makes a sharp turn, both masses swing away from the center of the turn. In their resulting positions, will they be farther apart, closer together, or the same distance apart as they were when the car wasn't turning?

Short Answer

Expert verified
Answer: During a sharp turn, the distance between the two masses hanging from strings will increase as they swing away from the center of the turn due to the net force acting on them.

Step by step solution

01

Visualize the problem

Picture the car in the stationary scenario, with two masses hanging from the ceiling by strings of equal length. When the car is not turning, the masses will be hanging straight down due to gravity, and the distance between them will be equal to the distance between the points of attachment to the ceiling. Now imagine the car making a sharp turn. As it does so, both masses will swing away from the center of the turn due to the centripetal force acting on them. Our goal is to determine whether they will be farther apart, closer together, or the same distance apart as they were when the car wasn't turning.
02

Analyze the forces on the masses

Let's consider the forces acting on the masses during the turn. Each mass will experience two forces: gravitational force (Fg) acting vertically downward and the centripetal force (Fc) acting horizontally towards the center of the turn. The net force (Fnet) acting on each mass will be the vector sum of these two forces.
03

Determine the direction of net force

The net force (Fnet) will act at an angle with respect to the vertical direction since it is the vector sum of the gravitational force (Fg) and the centripetal force (Fc) which act perpendicular to each other. This will cause the masses to swing away from the center of the turn, and the angle between the strings and the vertical direction will increase. This angle can be denoted as theta (θ).
04

Analyze the change in distance

Since both masses are swinging away from the center of the turn due to net forces acting on them, their horizontal components of displacement are in the same direction. The vertical components of displacement (strings length) remain constant. Therefore, the distance between the masses in their resulting positions will be greater than their original distance when the car was not turning.
05

Conclusion

After the car makes a sharp turn, the two masses hanging from the strings will be farther apart than they were when the car wasn't turning due to the net force causing them to swing away from the center of the turn.

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