A 2011 kg elevator moves with an upward acceleration of 1.9 m/s2. What is the tension in the cable that supports the elevator?
To find the tension in the cable that supports the elevator, you can use Newton's second law of motion.
The formula for tension in this case is given by:
Tension = mass * (acceleration + gravity)
where:
mass = mass of the elevator = 2011 kg
acceleration = upward acceleration of the elevator = 1.9 m/s^2
gravity = acceleration due to gravity = 9.8 m/s^2 (assuming the elevator is near the surface of the Earth)
Substituting the given values into the formula:
Tension = 2011 kg * (1.9 m/s^2 + 9.8 m/s^2)
Tension = 2011 kg * 11.7 m/s^2
Tension = 23,526.7 N
Therefore, the tension in the cable that supports the elevator is 23,526.7 Newtons.
To determine the tension in the cable that supports the elevator, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration. In this case, the elevator is moving upwards, so we need to consider the tension in the cable as the net force.
The formula to calculate the net force is:
Net force = mass × acceleration
Given:
Mass of the elevator (m) = 2011 kg
Acceleration (a) = 1.9 m/s^2
Substituting these values into the formula, we get:
Net force = 2011 kg × 1.9 m/s^2
Now, we need to recognize that the tension in the cable (T) is the opposing force to the gravitational force acting on the elevator. The gravitational force can be calculated using the formula:
Gravitational force = mass × gravitational acceleration
Gravitational acceleration (g) is approximately 9.8 m/s^2 on Earth.
Substituting the known values, we have:
Gravitational force = 2011 kg × 9.8 m/s^2
Since the elevator is moving upwards with an acceleration of 1.9 m/s^2, the tension in the cable will be greater than the gravitational force. Hence, the net force can be calculated as the difference between the tension and the gravitational force:
Net force = T - (2011 kg × 9.8 m/s^2)
However, since the elevator is accelerating upwards, the net force can also be calculated using the formula:
Net force = mass × acceleration
Applying this formula, we have:
Net force = 2011 kg × 1.9 m/s^2
Since both equations represent the net force acting on the elevator, we can equate them:
T - (2011 kg × 9.8 m/s^2) = 2011 kg × 1.9 m/s^2
Now we can solve for T, which represents the tension in the cable. By rearranging the equation, we get:
T = (2011 kg × 1.9 m/s^2) + (2011 kg × 9.8 m/s^2)
By calculating this expression, you will find the tension in the cable that supports the elevator.