Question

An elevator weighing 8400 lb is pulled upward by a cable with an acceleration of 8.00 ft/s^2. What is the tension (in pounds) in the cable?

Answer 1

say I've tried T= m(g+a) and that's not right.

Answer 2

What answer are you getting?

Answer 3

149520 pounds but its wrong

Answer 4

Is the answer 10,500 lbs?

Answer 5

yes that was the answer! can you explain how you got it though?

Answer 6

Sure! I just wanted to run it by you first because I'm not used to working with these units!

Let me first clear up the units. First, you need to realize that the pounds mentioned in the question are units of FORCE, not of mass. When we talk about weight, we're talking about a force (specifically, the force of gravity). In SI units, we would something something weighs x newtons (it wouldn't technically be correct to say something "weighs" x kilograms).

You know the general equation for force is F=ma. In this case, F is measured in pounds (of force), m is measure in pounds (of mass...confusing right?), and a is measure in ft/s^2.

So let's go back to your equation, which is correct:

T = mg + ma

In this case, mg = 8400 lbs. Remember, the 8400 lbs of WEIGHT is talking about a FORCE. The trouble is the ma. We know a = 8 ft/s^2 from the question, so we just need to find m. We can do that using mg, because we know that g = 32 ft/s^2. Since m*32 = 8400, m = 8400/32 --> 262.5 pounds (of MASS).

So going back to our equation for tension:

T = 8400 + 262.5(8) = 10 500 pounds (of FORCE)

You just need to keep track of the units! When working in pounds it can be kind of confusing for this reason. Anyways...let me know if that made sense or if you have any other questions!

Answer 7

made so much more sense! thanks a lot :D