Elevator Tension Calculation: Finding Force with Fnet and Newton's Laws

[t00kool]

Homework Statement

An elevator with a mass of 650 Kg supported by steel cable. What is the tension in the calbe when the elevator is accelerated upward at the rate of 3.00 m/s^2

Homework Equations

well he gives the equations that we can use as: Fnet=ma, w=mg and g=9.8m/s^2
I don't know what W means. Also he never taught us how to find tension.

The Attempt at a Solution

Well I used Fnet: 650KG * 3.00m/s^2= ANS.

If this is right can someone explain to me how.


x

Please Help.

 

[rock.freak667]

The Attempt at a Solution

Well I used Fnet: 650KG * 3.00m/s^2= ANS.

If this is right can someone explain to me how.

well the resultant acceleration is 3 ms$^{-2}$
so the net force,$F_{net}=650*3=1950N$

The weight of the elevator is W.
The tension in the cables holding the elevator is T.

If the weight is acting down and tension is acting up, and the resultant of these 2 is in an upward direction. What would be an equation relating the the resultant (net) force, the tension and weight?

 

[Moetasim]

Hello,

Thank you for your question. I am happy to assist you in understanding how to calculate the tension in the cable of an elevator using Fnet and Newton's Laws.

First, let's define some of the terms and equations that are relevant to this problem:

- Fnet: This stands for the net force acting on an object, which is equal to the mass of the object (m) multiplied by its acceleration (a). This can be expressed as Fnet = ma.

- W: This stands for weight, which is the force of gravity acting on an object. It is equal to the mass of the object (m) multiplied by the acceleration due to gravity (g). This can be expressed as W = mg.

- Tension: This is the force that is transmitted through a string, rope, or cable when it is pulled tight by forces acting on either end. In this case, the tension is the force in the steel cable that is supporting the elevator.

Now, let's use these equations to solve the problem. First, we need to find the weight of the elevator, which is equal to its mass (m) multiplied by the acceleration due to gravity (g). So, using the given mass of 650 kg, the weight of the elevator is:

W = mg = 650 kg * 9.8 m/s^2 = 6370 N

Next, we need to find the net force (Fnet) acting on the elevator. Since the elevator is accelerating upward at a rate of 3.00 m/s^2, the net force is equal to the mass (m) multiplied by the acceleration (a).

Fnet = ma = 650 kg * 3.00 m/s^2 = 1950 N

Finally, we can use Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. In this case, the action is the force of gravity pulling the elevator down (W) and the reaction is the tension in the cable pulling the elevator up (T).

So, we can set up an equation:

T - W = Fnet

Substituting the values we found for W and Fnet, we get:

T - 6370 N = 1950 N

Solving for T, we get:

T = 1950 N + 6370 N = 8320 N

Therefore, the tension in the cable is 8320