An elevator weighing 10 000N is supported by a steel cable. Determine the tension in the cable when the elevator is accelerated upward at 3.0 m/s2
A) 7.0kN
B) 10.0 kN
C)11.6 kN
D) 13.1 KN
E) 40.0 kN
13.1
Tension = M(a + g) = M g + M a
= 10,000 ( 1 + (a/g)) = ?
To determine the tension in the cable, we need to consider the forces acting on the elevator.
There are two forces acting on the elevator:
1. The weight of the elevator, which is equal to its mass multiplied by the acceleration due to gravity (9.8 m/s^2).
2. The tension in the cable, which is the force that opposes the weight and accelerates the elevator upward.
The weight of the elevator can be calculated using the formula:
Weight = mass x acceleration due to gravity
Given that the weight of the elevator is 10,000 N, we can rearrange the formula to solve for mass:
mass = weight / acceleration due to gravity
mass = 10,000 N / 9.8 m/s^2
mass ≈ 1,020.41 kg
Now, we can calculate the tension in the cable using the formula:
Tension = mass x acceleration
Tension = 1,020.41 kg x 3.0 m/s^2
Tension ≈ 3,061.23 N
Converting the tension from newtons to kilonewtons:
Tension ≈ 3,061.23 N / 1000
Tension ≈ 3.06 kN
Therefore, the tension in the cable when the elevator is accelerated upward at 3.0 m/s^2 is approximately 3.06 kN.
The correct answer is not listed among the options provided.
To determine the tension in the cable when the elevator is accelerated upward at 3.0 m/s², we first need to calculate the net force acting on the elevator.
The net force acting on an object can be calculated using Newton's second law of motion (F = ma), where F represents the net force, m represents the mass of the object, and a represents the acceleration.
Given that the weight of the elevator is 10,000 N, we can convert it to mass using the formula:
Weight (W) = mass (m) * gravitational acceleration (g)
10,000 N = m * 9.8 m/s²
Dividing both sides by 9.8 m/s², we get:
m = 10,000 N / 9.8 m/s² ≈ 1,020.41 kg
Now that we know the mass of the elevator, we can calculate the net force using Newton's second law:
F = ma
F = 1,020.41 kg * 3.0 m/s²
F ≈ 3,061.23 N
Therefore, the tension in the cable is approximately 3,061.23 N.
To convert this to kilonewtons (kN), divide by 1,000:
Tension = 3,061.23 N / 1,000 = 3.06 kN
Therefore, the correct answer is not listed among the given options.