An elevator (cabin mass 600 kg) is designed for a maximum load of 2700 kg, and to reach a velocity of 3.4 m/s in 5 s. For this scenario, what is the tension the elevator rope has to withstand?
I know I have to multiply the mass by the acceleration. I'm having a hard time deciphering what exactly I need to use. Please help! Thanks
so the maximum load (cabin plus cargo) is 3300 kg
the tension is the force that will accelerate the load to .68 m/s²
this is against gravity
so the tension overcomes gravity (mg) PLUS accelerates the load
t = m g + m a = m (g + a)
...= 3300 (9.81 + .68)
To find the tension the elevator rope has to withstand, we need to consider a few different forces acting on the elevator cabin.
First, let's calculate the acceleration of the elevator using the provided information. We have the initial velocity (0 m/s) and final velocity (3.4 m/s), as well as the time taken (5 s). The acceleration can be calculated using the formula:
acceleration = (final velocity - initial velocity) / time
Plugging in the values:
acceleration = (3.4 m/s - 0 m/s) / 5 s = 0.68 m/s²
Now, we can calculate the net force acting on the elevator using Newton's second law of motion, which states that the net force is equal to the mass times acceleration:
net force = mass × acceleration
The mass we use here is the sum of the cabin mass and the load mass:
mass = cabin mass + load mass = 600 kg + 2700 kg = 3300 kg
Plugging in the values:
net force = 3300 kg × 0.68 m/s² = 2244 N
The tension in the elevator rope must be equal to this net force. Therefore, the tension the elevator rope has to withstand is 2244 Newtons (N).