The cable supporting a 2123 kg elevator has a maximum strength of 25982 N. What maximum upward acceleration can it give the elevator without breaking?

Can someone give me step by step on how to solve this?

F = m a

25982 - m g = ma

25982 = 2123 (a + 9.81)

A car starts from rest and travels for 6.0 s with a uniform acceleration of +1.5 m/s2. The driver then applies the brakes, causing a uniform acceleration of -2.0 m/s2. If the brakes are applied for 3.0 s, how fast is the car going at the end of the braking period?

damon can u help me?

Hey Damon, i'm not sure if i calculated wrong, but was I supposed to do

(2123)(9.81a) = 20826.63a
then divide 25982a/20826.63?

Oh, nvm haha I'm an idiot. I got it THANKS A BUNCH!

care to help me out jin hwang?

To solve this problem, we need to use Newton's second law of motion and consider the forces acting on the elevator.

Step 1: Identify the forces involved:
In this case, the elevator is subject to two forces: the force of gravity pulling it downward and the tension force exerted by the cable pulling it upward. The maximum upward acceleration that the elevator can have without breaking the cable will be limited by the tension force.

Step 2: Calculate the force of gravity:
The force of gravity can be calculated using the equation F = m * g, where F is the force, m is the mass, and g is the acceleration due to gravity (approximately 9.8 m/s²). So, F_gravity = 2123 kg * 9.8 m/s².

Step 3: Calculate the maximum tension force:
The maximum tension force that the cable can withstand without breaking is given as 25982 N.

Step 4: Apply Newton's second law of motion:
According to Newton's second law, the net force acting on an object is equal to its mass multiplied by its acceleration. In this case, the net force is the tension force minus the force of gravity. So, F_net = F_tension - F_gravity.

Step 5: Calculate the maximum upward acceleration:
Set the net force equal to the product of the mass and the maximum acceleration:
F_net = m * a_max. Rearranging the equation, we have:
F_tension - F_gravity = m * a_max. Now substitute the known values into the equation:
25982 N - (2123 kg * 9.8 m/s²) = 2123 kg * a_max. Solve for a_max to find the maximum upward acceleration.

By following these steps, you should be able to find the maximum upward acceleration that the elevator can have without breaking the cable.