Drop Test: Mass vs Horizontal Component

Click For Summary

Discussion Overview

The discussion revolves around the question of whether two objects with different masses, when dropped from the same height, will hit the ground at the same time, particularly when a horizontal component is introduced by rolling them off a surface. The scope includes concepts from classical mechanics and general relativity, exploring both theoretical and practical implications.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants assert that the vertical and horizontal motions are independent, suggesting that as long as the objects start falling with the same initial vertical speed, their horizontal speed does not affect the time to hit the ground.
  • Others introduce the idea that the curvature of the Earth could cause the object with a horizontal component to land slightly later, although this effect is described as negligible.
  • A participant questions whether the lighter object would roll off a table faster due to less friction, potentially hitting the ground before the heavier object, indicating a possible dependency on mass and friction.
  • Another participant clarifies that if both objects are rolling without slipping, they would have zero net force and no acceleration, but if they slide against friction, the net force would depend on their mass.
  • Some contributions reference general relativity, suggesting that gravitational force may depend on velocity, thus complicating the scenario beyond Newtonian mechanics.
  • Several participants express confusion regarding the relationship between mass, weight, and gravitational force, with discussions about the implications of Newton's second law (F=ma) and how it applies in different contexts.
  • There is mention of the practical effects of air resistance and surface area, indicating that in real-world scenarios, these factors could influence the outcome.

Areas of Agreement / Disagreement

Participants generally agree that in a vacuum, objects of different masses will fall at the same rate. However, there is disagreement regarding the effects of horizontal motion, friction, and the implications of general relativity, leading to multiple competing views on the topic.

Contextual Notes

Limitations include assumptions about ideal conditions (e.g., vacuum, no air resistance) and the varying effects of mass and surface interactions. The discussion also touches on the complexities introduced by general relativity, which are not fully resolved.

Who May Find This Useful

This discussion may be useful for students and enthusiasts of physics, particularly those interested in classical mechanics, general relativity, and the nuances of motion under varying conditions.

atomant
Messages
27
Reaction score
1
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?
 
Last edited:
Physics news on Phys.org
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.
 
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.
 
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?
 
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.
 
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.)

atomant said:
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.

what said:
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 ([itex]F = \mu_k mg[/itex]), but the accelerations would be the same ([itex]a = \mu_k g[/itex]). Assuming the same coefficient of friction for each, of course.
 
Last edited:
Right, I don't know why I missed that.

Edit: I think I've figured it out... posted "Today, 12:13 AM"
 
Last edited:
atomant said:
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 dependent 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
 
That would be helpful to know. I always did like experimental physics.:approve:
 
  • #10
atomant said:
That would be helpful to know. I always did like experimental physics.:approve:
I guess Doc al was write all along. The way to show this is by looking at the geodesic equation, i.e.

[tex]\frac{d^2x}{d\tau^2} = -\Gamma^1_{ \alpha \beta} U^{\alpha}U^{\beta}[/tex]

(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:
  • #11
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?
 
  • #12
Mmx said:
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
 
  • #13
Mmx said:
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.
 
  • #14
russ_watters said:
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.
 
  • #15
Mmx said:
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.
 
  • #16
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
I am not satisfied with the first part of this question.We know that two bodies land at same time of different 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.
 
  • #18
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
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
atomant said:
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.
 
  • #21
atomant said:
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
 

Similar threads

High School The Effect of Linear and Rotational Motion on Measured Weight
  • · Replies 10 ·
Replies
10
Views
1K
High School Testing the effect of Gravity at home....
  • · Replies 33 ·
2
Replies
33
Views
3K
High School Conservation of momentum and conservation of energy details
  • · Replies 30 ·
2
Replies
30
Views
3K
High School Energy changes that result when something drops from a height
  • · Replies 12 ·
Replies
12
Views
2K
Graduate Testing Newtonian Gravity: Collision of Two Masses
  • · Replies 17 ·
Replies
17
Views
3K
High School Same Mass Objects Dropped: Same Time?
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Accelerometer drop tests evaluation
  • · Replies 4 ·
Replies
4
Views
2K
High School Understanding Momentum: The Relationship Between Mass, Velocity, and Force
  • · Replies 29 ·
Replies
29
Views
3K
Graduate Counter-intuitive 2D collision
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad Would a Very Large Mass (e.g. the Moon) Fall with g?
  • · Replies 11 ·
Replies
11
Views
2K