A 2009-kg elevator moves with an upward acceleration of 1.10 m/s22. What is the force exerted by the cable on the elevator?

To solve this problem, we need to use Newton's second law of motion, which states that the force acting on an object is equal to its mass times its acceleration (F = ma).

Step 1: Identify the given values. The mass (m) of the elevator is 2009 kg and the acceleration (a) is 1.10 m/s^2.

Step 2: Plug the given values into the formula. F = ma F = 2009 kg * 1.10 m/s^2

Step 3: Calculate the force (F). F = 2209.9 N

However, this is just the force required to accelerate the elevator upwards. We also need to consider the force of gravity acting on the elevator, which is the mass of the elevator times the acceleration due to gravity (9.8 m/s^2).

Step 4: Calculate the force of gravity. Force of gravity = mass * gravity Force of gravity = 2009 kg * 9.8 m/s^2 Force of gravity = 19688.2 N

Step 5: Add the force required to accelerate the elevator and the force of gravity to get the total force exerted by the cable. Total force = force to accelerate the elevator + force of gravity Total force = 2209.9 N + 19688.2 N Total force = 21898.1 N

So, the force exerted by the cable on the elevator is 21898.1 N.