A weight is hung from the ceiling of an elevator by a massless string. under which circumstances will the tension in the cord be the greatest? smallest?
a.) The elevator rises with decreasing speed
b.) The elevator rises with increasing speed
c.) The elevator is at rest
d.) The elevator descends with increasing speed
e.) The elevator descends with decreasing spead.
The tension in the cord will be the greatest when the elevator accelerates upward with increasing speed (option b).
To understand why, let's consider the forces acting on the weight. The weight experiences two forces: the force due to gravity (its weight) pulling it downward and the tension force from the cord pulling it upward.
When the elevator accelerates upward with increasing speed, it means that the net force acting on the weight is greater than just the force due to gravity. This extra force is being provided by the tension in the cord. So, the tension in the cord needs to be larger in order to provide this additional upward force required to accelerate the weight.
On the other hand, the tension in the cord will be the smallest when the elevator descends with decreasing speed (option e). In this scenario, the net force acting on the weight is less than just the force due to gravity. Therefore, the tension in the cord needs to be smaller to balance out the weight and the downward force.
In options a, c, and d, the elevator is either at rest or has a constant speed, which means there is no net force acting on the weight other than the force due to gravity. Thus, the tension in the cord will be equal to the weight in these cases.
The tension in the cord is determined by the weight of the object and the acceleration it experiences.
a.) The elevator rises with decreasing speed: In this case, the tension in the cord will be greater than when the elevator is at rest but less than when the elevator is descending with increasing speed. The tension will be less than the weight of the object.
b.) The elevator rises with increasing speed: In this case, the tension in the cord will be greater than when the elevator is at rest or when the elevator rises with decreasing speed. The tension will be equal to the weight of the object plus the additional force due to the acceleration of the elevator.
c.) The elevator is at rest: When the elevator is at rest, there is no acceleration, so the tension in the cord will be equal to the weight of the object.
d.) The elevator descends with increasing speed: In this case, the tension in the cord will be greater than when the elevator is at rest or when the elevator rises with decreasing speed. The tension will be equal to the weight of the object plus the additional force due to the acceleration of the elevator.
e.) The elevator descends with decreasing speed: In this case, the tension in the cord will be greater than when the elevator is at rest but less than when the elevator descends with increasing speed. The tension will be less than the weight of the object.
So, the greatest tension in the cord occurs when the elevator is descending with increasing speed (option d), and the smallest tension occurs when the elevator is at rest (option c).