The cavle on an elevator is what pulls the elevator up, and allows it to come down safely. The mass of the elevator is 1400 kg. If the elevator starts from rest and is pulled upwards with a constant tension of 18 kN, what will its speed be after moving 6m? (Assume no frictioanl force)
so i first drew a force diagram to find the total forces
F=m
Tension- Fgravity=ma
18000-9.8=1400a
a= 12.85 m/s
so now that I have found the acceleration of the elevator I need to help finding the its speed after 6m..I'm not sure how I would start doing that
forcenetup=ma
18kN-mg=ma
I don't know why you did not put in Mass in your Fgravity.
To find the elevator's speed after moving 6m, you can use the kinematic equation that relates displacement, initial velocity, final velocity, and acceleration:
v^2 = u^2 + 2as
Where:
v = final velocity
u = initial velocity (in this case, the elevator starts from rest so u = 0)
a = acceleration
s = displacement
Using the value of acceleration you calculated earlier (a = 12.85 m/s^2) and the given displacement (s = 6m), you can plug these values into the equation and solve for v:
v^2 = 0^2 + 2 * 12.85 * 6
v^2 = 0 + 154.2
v^2 = 154.2
Now, take the square root of both sides to find the final velocity:
v = √154.2
v ≈ 12.4 m/s
Therefore, the elevator's speed after moving 6m will be approximately 12.4 m/s.