What upward tension force (in Newtons) would allow a 1240-kg elevator to accelerate downwards (i.e., negative) at a rate of 4.29 m/s/s?
To find the upward tension force acting on the elevator, we need to consider the forces that are acting on it.
First, we have the weight of the elevator acting downwards. The weight can be calculated using the formula:
Weight = mass x acceleration due to gravity
Given that the mass of the elevator is 1240 kg and the acceleration due to gravity is approximately 9.8 m/s², we can calculate the weight of the elevator:
Weight = 1240 kg x 9.8 m/s²
Next, we need to consider the tension force acting upwards. Since the elevator is accelerating downwards, the net force acting on it in the upward direction must be equal to the tension force:
Net force = tension force - weight
We know that the net force is equal to the product of the mass and acceleration:
Net force = mass x acceleration
Rearranging the equation, we can solve for the tension force:
tension force = net force + weight
Substituting the known values, we can calculate the tension force:
tension force = (mass x acceleration) + (mass x acceleration due to gravity)
tension force = 1240 kg x (-4.29 m/s²) + 1240 kg x (9.8 m/s²)
Simplifying, we get:
tension force = (-5293.6 N) + (12152 N)
tension force = 6860.4 N
Therefore, the upward tension force required to allow the 1240-kg elevator to accelerate downwards at a rate of 4.29 m/s² is approximately 6860.4 Newtons.