# Mass and time

1. Feb 25, 2006

### atomant

I was thinking about a question where when 2 similar objects with different masses were dropped from the same height that they would hit tthe ground at the same time. It then occured to me if the same would happen if the objects were given a horizontal component. i.e if they were rolled off an object..would the still hit the ground at the same time?

Last edited: Feb 25, 2006
2. Feb 25, 2006

### Staff: Mentor

The vertical and horizontal motions are independent. As long as the two objects start falling with the same initial vertical speed (zero, in this case), their horizontal speed is irrelevant; they would fall through the same distance in the same time.

3. Feb 25, 2006

### rcgldr

As long as the horizontal component wasn't significant enough to have an effect from the curved surface of the earth. Because of the curvature of the earth, the object with the horizontal component lands just a bit (pico or nano-seconds) later.

4. Feb 25, 2006

### atomant

o.k, but if they were rolled of a surface..say a table, presuming that they were subjected to the same amount of force, wouldn't the object with the lightest mass travel faster than the other?. and hence wouldn't it roll off the table and hit the ground before the other object?

5. Feb 25, 2006

### what

They wouldn't be subject to the same net force, the frictional force would be lesser on the lighter object so it would accelerate towards the end of table faster and start falling at a different(earlier) time then the heavier object. In answer to your question, in that scenario, yes.

6. Feb 26, 2006

### Staff: Mentor

I thought the intent of the original question was "Does horizontal speed influence the rate of falling?" To that, the answer is simply no. (Subject to Jeff Reid's caveat, though.)

Assume, if you like, that the objects are balls rolling without slipping at the same speed. Obviously if the objects roll at different speeds, or start at different distances from the edge, then they will begin falling at different times and hit the ground at different times.

Balls rolling without slipping on a horizontal surface have zero net force and no acceleration. Of course, if the objects slide against friction along a horizontal surface, then the net force on each would depend on its mass ($F = \mu_k mg$), but the accelerations would be the same ($a = \mu_k g$). Assuming the same coefficient of friction for each, of course.

Last edited: Feb 26, 2006
7. Feb 26, 2006

### what

Right, I don't know why I missed that.

Edit: I think I've figured it out.... posted "Today, 12:13 AM"

Last edited: Feb 26, 2006
8. Feb 27, 2006

### pmb_phy

That's a good question. In Newtonian gravity the answer is that they'd hit the ground at the same time. In general relativity the gravitational force/acceleration is velocity dependant so you'd really have to calculate it to be sure. I can give it a try if you'd like (or find out from experts I know).

Pete

9. Feb 28, 2006

### atomant

That would be helpful to know. I always did like experimental physics.

10. Mar 1, 2006

### pmb_phy

I guess Doc al was write all along. The way to show this is by looking at the geodesic equation, i.e.

$$\frac{d^2x}{d\tau^2} = -\Gamma^1_{ \alpha \beta} U^{\alpha}U^{\beta}$$

(Latex doesn't seem to work????)
As you can see from this expression, acceleration depends on velocity in general. However after calculation there is no horizontal acceleration in the x-direcction. But you actually have to do this out to see it.

By the way. I had general relativity in mind when I posted my comments. Sorry.

Pete

Last edited by a moderator: Mar 13, 2006
11. Mar 1, 2006

### Mmx

Both object with different masses fall and the same time and hit at the ground at the same time. If im not wrong when the counting of this object the gravity force is not counted in it? But my teacher said that no matter 1 object is say like 10 N and 1 object 5 N fall at the same time in a height will both reach at the gound at the same time. Im cant really remember how to counting? Anyone?

12. Mar 1, 2006

### pmb_phy

In Newtonian mechanics that is correct. In GR the validity may depend on the gravitational field. In are in a uniform gravitational field and then the observer changes his frame of reference then it is no longer true; now there will be moving to different frames which then correspond to different gravitational field in which a falling object will be swept aside even when there is no initial velocity to the sides. This is called frame dragging.

Pete

13. Mar 1, 2006

### Staff: Mentor

Have you learned f=ma yet? An object with double the mass has double the weight and therefore double the force of gravity acting on it. By f=ma if you double the "f" and the "m", the "a" stays the same.

14. Mar 3, 2006

### Mmx

Im so confuse now? Are you talking about Newtonian mechanics or in general relativity? I got learn F=ma. But you said that object with double the mass have double the gravity? Should be gravity be a constant unit? the gravity value changes is base on how high the object from the earths mid point. If the object is throw higher place then the gravitation force become smaller value? Corrrect me if im wrong? Sorry my physics is malay so is kinda hard for me to descibed in Malay.

15. Mar 3, 2006

### ZapperZ

Staff Emeritus
Pay attention. Russ said "double the force of gravity acting on it". This is not "g", but "mg", as in Weight=mg. This is nothing but F=ma where F=Weight, a=g on the surface of earth.

Zz.

16. Mar 3, 2006

### Staff: Mentor

Yeah, we can leave general relativity out of this and just consider the ideal Newtonian freefall case. Also, there is no need to account for height and changes in "g" here, since both objects are at the same height.

17. Mar 4, 2006

### spiffing_abhijit

I am not satisfied with the first part of this question.We know that two bodies land at same time of differnt masses in vaccum but practically the surface area of the body ,the very negligible air resistance and the height is going to matter.The next part of the question is simple .If two bodies are thrown horizontally then the horizontal component is going to be zero as each body will make an angle of 90* with imaginary vertical plane and cos 90* is always zero.So they have to land at same time but there will be a difference of atleast a pico second if this experiment is conducted practically.

18. Mar 4, 2006

### atomant

Correct me if I am wrong but isn't there an equation a=mgμ0/M that relates acceleration to the friction of a surface. Hence wouldn't the equation read a=gμ0. Thus acceleration is independent of mass. So if two objects of different masses were to slide off a plank for example wouldn't they both fall at the same time?

19. Mar 13, 2006

### atomant

Also what abt when we Consider a hollow cylinder and a solid cylinder rolling down a hill. Both are released from rest at the same time. Which reaches the bottom first and why?
what would happen in the case, where the overall composition is different?

20. Mar 13, 2006

### ZapperZ

Staff Emeritus
But then, you do know that now, you're changing the topic of your own thread, don't you? [Is there a rule against hijacking one's own thread?] Your original intention included nothing about moment of inertia. This latest scenario you have described is easily explained simply by invoking such moment of inertia effects without the need for anything more exotic than that.

Zz.