An elevator, with a total mass of 454 kg, accelerates downward at 3.51 m/s2. During this time, the tension in the elevator cable is
T= F = m*a = 454 * 3.51 = 1594 N.
Well, look at Mr. Gravity pulling some pranks on the elevator! Now, let's see what's going on here. We have an elevator going down with an acceleration of 3.51 m/s². In this gravity dance, we need to find the tension in the cable. So, hang on tight!
To figure out the tension, we need to consider the forces at play here. We have the weight of the elevator pulling it downward and the tension in the cable pulling it up to balance it out. Newton's second law comes into play, so let's get calculating!
The weight of the elevator can be calculated using the formula:
Weight = mass * acceleration due to gravity
Now, since the elevator is accelerating downwards, we need to take into account the net force acting on it. The net force is given by:
Net Force = mass * acceleration
The net force can also be calculated as the difference between the tension and the weight. So, we can set up the equation:
Tension - Weight = mass * acceleration
Now, we can rearrange the equation to solve for tension:
Tension = Weight + mass * acceleration
Using the given values, we can substitute them into the equation:
Weight = mass * acceleration due to gravity
Weight = 454 kg * 9.8 m/s² (assuming acceleration due to gravity is 9.8 m/s²)
Now, plug in the values:
Tension = (454 kg * 9.8 m/s²) + (454 kg * 3.51 m/s²)
And voila! Just work that out and you'll have the tension in the cable. But hey, don't pull on my strings, check your math too!
To calculate the tension in the elevator cable, we can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration.
In this case, the net force acting on the elevator is the tension in the cable pulling it upwards, which opposes the gravitational force pulling it downwards. We can set up the equation as follows:
Net force = mass x acceleration
The mass of the elevator is given as 454 kg, and the acceleration is given as 3.51 m/s². Plugging these values into the equation, we get:
Net force = 454 kg x 3.51 m/s²
Net force = 1590.54 N
Therefore, the tension in the elevator cable is 1590.54 N.
To determine the tension in the elevator cable, we need to consider the forces acting on the elevator.
The force of gravity pulling the elevator downwards can be calculated using Newton's second law of motion, F = m * a, where F represents the force, m represents the mass, and a represents the acceleration.
Given that the mass of the elevator is 454 kg and the acceleration is 3.51 m/s^2, we can calculate the force of gravity.
F_gravity = m * a
F_gravity = 454 kg * 3.51 m/s^2
F_gravity = 1596.54 N
The tension in the elevator cable is equal in magnitude but opposite in direction to the gravitational force. So the tension in the cable is also 1596.54 N, but directed upwards to counteract the force of gravity.
Therefore, the tension in the elevator cable is 1596.54 N.