An elevator in a tall building is allowed to reach a maximum speed of 3.55 m/s going down. What must the tension be in the cable to stop this elevator over a distance of 2.30 m if the elevator has a mass of 1270 kg including occupants?
(in N)
To solve this problem, we need to calculate the tension in the cable required to stop the elevator.
First, let's calculate the acceleration of the elevator. We can use the equation of motion:
v^2 = u^2 + 2as
Where:
v = final velocity (0 m/s, since the elevator needs to stop)
u = initial velocity (3.55 m/s)
s = distance (2.30 m)
Rearranging the equation, we get:
a = (v^2 - u^2) / (2s)
Substituting the values, we get:
a = (0^2 - 3.55^2) / (2 * 2.30)
Next, we can calculate the net force acting on the elevator using Newton's second law of motion:
F_net = ma
Where:
F_net = net force
m = mass of the elevator (1270 kg)
a = acceleration (calculated in the previous step)
Now, we know that the net force acting on the elevator is equal to the tension in the cable, so:
Tension = F_net
Substituting the values, we get:
Tension = m * a
Finally, we can calculate the tension in the cable:
Tension = 1270 kg * acceleration
Therefore, the tension in the cable is equal to 1270 kg multiplied by the calculated acceleration in Newtons (N).