Drop Test: Mass vs Horizontal Component

[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 occurred 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?

 

[Doc Al]

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.

 

[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.

 

[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?

 

[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.

 

[Doc Al]

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.)

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?

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.

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.

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.

 

[what]

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

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

 

[pmb_phy]

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 occurred 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?

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

 

[atomant]

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

 

[pmb_phy]

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

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

 

[Mmx]

Both object with different masses fall and the same time and hit at the ground at the same time. If I am 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. I am can't really remember how to counting? Anyone?

 

[pmb_phy]

Both object with different masses fall and the same time and hit at the ground at the same time. If I am 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. I am can't really remember how to counting? Anyone?

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

 

[russ_watters]

Both object with different masses fall and the same time and hit at the ground at the same time. If I am 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. I am can't really remember how to counting? Anyone?

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.

 

[Mmx]

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.

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 Earth's mid point. If the object is throw higher place then the gravitation force become smaller value? Corrrect me if I am wrong? Sorry my physics is malay so is kinda hard for me to descibed in Malay.

 

[ZapperZ]

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 Earth's mid point. If the object is throw higher place then the gravitation force become smaller value? Corrrect me if I am wrong? Sorry my physics is malay so is kinda hard for me to descibed in Malay.

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.

 

[russ_watters]

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.

 

[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 vacuum 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.

 

[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?

 

[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?

 

[ZapperZ]

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?

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.

 

[ZackQuantum]

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?

Now it is more of a case of an objects weight determining it's ability to overcome air resistance and imperfections of a given surface. It would be a case of attempting to stop a toy truck vs a freight train, one is obviously going to be more susceptible to external resistance