# Two carts and their initial acceleration

1. Dec 4, 2003

### suyver

As promised in another thread: Riddle me this, riddle me that...

There are two carts on the table. For each cart, there is a rope attached on one side to the cart and via a pulley it is hanging over the edge of the table. On the other end of one rope a 5 kg weight is attached and on the other rope a person pulls with a force corresponding to 5 kg. Which cart has the highest initial acceleration?
a. The cart with the weight.
b. The cart with the person.
c. There is no difference.

I think that the cart with the person pulling the rope will have the highest initial acceleration. This is due to the difference between force and thrust: the person pulling the rope immedialtly applies a thrust to the system, while gravitation does not.

Any thoughts, anyone?

2. Dec 4, 2003

### Staff: Mentor

It depends on how hard the person is capable of pulling. If he can pull at more than 50N (the weight of the weight) then the initial accel of that cart he pulls on will be higher.

3. Dec 4, 2003

### whatgravity

There would be no difference in acceleration.

For there to be a difference, the person would have to change the amount of force he pulled with

4. Dec 4, 2003

### Staff: Mentor

This one's easy, suyver!

First, I assume you mean that the person pulls with a force equal to the weight of the 5 kg mass.

In any case, whichever exerts the greatest tension on the rope will create the greatest acceleration. For the cart plus weight case, the tension in the rope is always less than the weight of the hanging mass. In the cart plus person case, by stipulation, the tension in the rope equals the weight of the hanging mass.

So, the answer is b: the cart with the person accelerates most.
Agreed!
I'm not sure I get your point. In both arrangements the force is applied immediately; the hanging weight just applies less force.

5. Dec 4, 2003

### whatgravity

I don't get it. Why is the tension in the rope always less with the hanging mass? If the carts are frictionless, then wouldn't the tension in the rope connected to the hanging mass remain constant. The force from the weight is constant isn't it?

[?]

6. Dec 4, 2003

### Staff: Mentor

The tension remains constant, but it does not equal the weight of the mass. If it did, the mass wouldn't accelerate, would it?

7. Dec 4, 2003

### Staff: Mentor

How so? With an aceleration force, if the force is constant, the acceleration is constant.

Yes it is, but that mass has to accelerate the cart and ITSELF. When you pull on the rope(using Doc's stipulation on the force being the actual tension in the rope), you are only accelerating the cart.

8. Dec 4, 2003

### whatgravity

Ok, i think i get it now... In order for the person pulling to keep his pulling force at 50 N, he has to keep the rope tension at 50 N.

and the rope tension on the cart from the hanging mass is always less? This makes sense to me intuitively, but I still don't fully understand it.[b(] Is this because of F = (m + m2)a?

9. Dec 5, 2003

### suyver

Re: Re: Two carts and their initial acceleration

And still the first 3 answers were all different! That's the nice thing about physics: even classical mechanics can put one over on you...

Yes, that's what I ment. It's always hard to formulate such a configuration in another language. I agree with your answer, by the way.

I have, maybe, even another line of reasoning that also leads to answer B: In the case of cart+weight, both the cart and the weight will need to get an initial acceleration. The combined system will have a larger moment of inertia than the cart-only system. Therefore, the initial acceleration must be les in the combined system than in the cart-only system. I personally feel that this is a more insightfull argument. What do you think?

10. Dec 5, 2003

### Staff: Mentor

Re: Re: Re: Two carts and their initial acceleration

How right you are!
I think you have the right idea. In both cases, the external force (mg) is the same. In the cart+person case, that force accelerates the cart; but in the cart+weight case, that same force must accelerate both the cart and the weight. Same force--more mass--less acceleration: makes sense to me!