An elevator suspended by a vertical cable is moving downward but slowing down. The tension in the cable must be
A greater than the weight of the elevator.
B equal to the weight of the elevator.
C less than than the weight of the elevator.
The correct answer and explanation is:
The correct answer is A: greater than the weight of the elevator.
When the elevator is moving downward but slowing down, it is experiencing a deceleration, which means there is an upward force acting on it that opposes the downward motion. To understand why the tension in the cable must be greater than the weight of the elevator, we need to consider the forces acting on the elevator.
- Gravitational force (weight): The weight of the elevator is the force pulling it downward due to gravity. It is equal to the mass of the elevator multiplied by the acceleration due to gravity (W = mg).
- Tension force: The tension in the cable is the force exerted by the cable on the elevator, and it acts upward. The elevator is slowing down, meaning the downward velocity is decreasing. According to Newton’s second law of motion (F = ma), for an object to decelerate, the net force acting on it must be in the direction opposite to its motion.
In this case, the elevator is moving downward, so the net force must be upward. To achieve this, the tension in the cable must exceed the weight of the elevator. If the tension were exactly equal to the weight, the elevator would continue moving downward at a constant speed (no acceleration). If the tension were less than the weight, the elevator would accelerate downward instead of decelerating.
Therefore, in order for the elevator to slow down while moving downward, the tension in the cable must be greater than the weight of the elevator, creating an upward net force that causes the deceleration. This is why the correct answer is A: greater than the weight of the elevator.