How Is the Elevator's Acceleration Calculated Using Newton's Second Law?

[cheerspens]

Homework Statement

A 1000 kg elevator is held up by two cables. If each able exerts a force of 6000N upwards upon the elevator, find the elevator's acceleration.

Homework Equations

F_g=mg

F_NET=ma

The Attempt at a Solution

I started with a force diagram to help me and then I think I'm supposed to use the F_NET=ma formula. So I plugged in the variables as follows: (6000+6000)-F_ge=1000a
How do you solve for acceleration in this problem when I also need to find the Force that gravity exerts on the elevator (F_ge)?

Would the answer be 2.2m/s^2?

 

[rock.freak667]

F_ge would simply be the weight, mg, of the elevator.

 

[kerimek]

Yes, you are on the right track. In order to solve for the elevator's acceleration, you will need to use both Newton's 2nd Law (FNET = ma) and the equation for gravitational force (Fg = mg).

First, let's find the force of gravity acting on the elevator. We know that the mass of the elevator is 1000 kg, so we can plug that into the equation Fg = mg. This gives us Fg = (1000 kg)(9.8 m/s^2) = 9800 N.

Now, we can use this value for Fg in the FNET = ma equation. We know that the net force acting on the elevator is the sum of the upward forces (6000 N + 6000 N) minus the force of gravity (9800 N). This gives us:

FNET = (6000 N + 6000 N) - 9800 N = 2200 N

Now, we can plug this value for FNET into the FNET = ma equation to solve for the acceleration (a):

2200 N = (1000 kg)a

a = 2200 N / 1000 kg = 2.2 m/s^2

So, the elevator's acceleration is 2.2 m/s^2.