Tension between two accelerating forces.

[Notyou]

Homework Statement

A 6000kg helicopter accelerates upward at .6m/s^2 while lifting a 1500kg car. What is the tension in the cable (ignore the cable mass) that connects the car to the helicopter?

Homework Equations

F=MA

The Attempt at a Solution

Alright... so here's what I've been trying to do. The acceleration that is the acceleration due to gravity plus .6m/s^2 which gives an acceleration of -9.2. From there I would multiply the acceleration by mass to get the force of the helicopter and the car. So for the helicopter the force I get is 55200N and for the car it is 13000N. I add those forces together and get... the wrong answer. The answer is supposed to be 15600N and I can't figure out how.

I have a test coming up and I can't seem to do any tension problems to save my life; any help at all would be greatly appreciated.

 

[Doc Al]

Do it step by step. What forces (in what directions) act on the car? Apply F = ma.

 

[Redbelly98]

The acceleration is +0.6m/s^2, as given in the problem statement. That can be used to find the net force on either the car or helicopter.

I suggest looking at the car and drawing a free body diagram for it. What would the values of all the forces be, to give a net force that causes a +0.6m/s^2 acceleration on the car?

edit: Hello Doc, you beat me by 2 minutes on this one.

 

[Notyou]

Alright. The forces working against the car in the negative direction would be the weight of the car x acceleration due to gravity. The forces working on the car in the positive direction would be the force of the helicopter x gravity. That seems to only be the case if the whole scenario were stationary... so I really don't know how to factor in the acceleration of the helicopter.

Edit: Still stuck. I have a force of 58800N acting on the car from the positive y direction and a force of 14700N acting on the car in the negative y direction. That's without taking the acceleration of the helicopter into consideration. If I take the acceleration of the helicopter into consideration I have no clue what to do.

 

[Doc Al]

The forces working against the car in the negative direction would be the weight of the car x acceleration due to gravity.

Edit: Oops... that's not right. The force is the weight of the car, which is its mass x the acceleration due to gravity. That's what I assumed you meant, but that's not what you said. Careful!

The forces working on the car in the positive direction would be the force of the helicopter x gravity.

When analyzing the car, we care about forces on the car, not the helicopter. What's pulling up on the car? Hint: It's what you're trying to solve for!

That seems to only be the case if the whole scenario were stationary... so I really don't know how to factor in the acceleration of the helicopter.

The acceleration of the helicopter is only relevant when you analyze forces on the helicopter. But we're analyzing forces on the car.

 

[Redbelly98]

Alright. The forces working against the car in the negative direction would be the weight of the car x acceleration due to gravity.

No, the force in the negative direction is the weight of the car, period. "weight of the car x acceleration due to gravity" is not even a force, so that statement makes no sense.

[EDIT] unless you meant "mass of the car x acceleration due to gravity", which is the weight, and is correct.

As for the positive direction: what is in actual, physical contact with the car?

 

[Notyou]

The rope is pulling on the car in the positive direction... and that force would be equal to the force of the weight due to Newton's third law correct?

 

[Doc Al]

The rope is pulling on the car in the positive direction...

Right. That's the tension in the rope, which is what you're trying to find.

and that force would be equal to the force of the weight due to Newton's third law correct?

Nope! The 3rd law pair to "the rope pulling on the car" tension force is "the car pulling down on the rope" with an equal force. Since weight is "the Earth's gravitational force on the car", the third law pair is "the car's gravitational force on the earth".

Just call the tension "T" and set up Newton's 2nd law. What's the sum of those two forces on the car?

 

[Notyou]

I got it now. The weight of the helicopter does not matter in this question. The acceleration of the car is 9.8 plus .6 acting in the positive direction. So... force would be the mass of the car times 10.4. Thank you so much!

 

[Redbelly98]

I repeat:

The acceleration is +0.6m/s^2, as given in the problem statement.

 

[Doc Al]

The weight of the helicopter does not matter in this question.

This is true.

The acceleration of the car is 9.8 plus .6 acting in the positive direction. So... force would be the mass of the car times 10.4.

While you "got the right answer", your thinking is off.

As Redbelly98 emphasizes, the acceleration is given as 0.6 m/s² upward. Here's how to properly get the answer:

What forces act on the car? (1) Tension, acting up (+T); (2) weight, acting down (-mg).

The net force on the car: T - mg

The acceleration of the car: +0.6 m/s²

Apply Newton's 2nd law: T - mg = ma

Thus: T = ma + mg