## Question

secondary 4 | Physics

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##### Candice Lim

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Hi,
Qn : When two objects are hit vertically upwards at the same speed (with effect of air resistance), why does the object with smaller mass travel a shorter distance before reaching ground?

Kindly advise, thank you so much.

Date Posted: 2 years ago
Views: 1425
David Tan
2 years ago
The 2 objects have same speed but different masses, thus the smaller object have smaller momentum according to formula p = mv. Due to smaller momentum, smaller net force acts on it thus the shorter distance travelled.
Ref: https://en.wikipedia.org/wiki/Momentum
Candice Lim
2 years ago
oic, thank you so much Mr Tan :)
NotATutor
2 years ago
When air-resistance comes in, there area a few other factors affecting this.
1. size of the objects. It doesn't always imply smaller mass, smaller size. Big surface area greater resistance
2, surface texture of the objects. rough surface create more drag.
3. shape of the objects. I guest you heard of streamline body is designed to provide small drag against motion.
Candice Lim
2 years ago
Understood.
Thanks Mr Yong.
NotATutor
2 years ago
Just uploaded a more detailed analysis for your reference. Momentum cannot explain the effect. You many also want to add in some energy consisderation.
David Tan
2 years ago
The downward portion makes sense since larger mass means higher terminal vel but the upward portion makes no sense. Smaller mass means less gravity is acting on it meaning smaller mg so how can it be travelling shorter distance upward? The larger mass object will travel a shorter distance upward due to bigger pull of gravity acting on it. The bigger a for smaller object only makes sense if it is in the upward direction because mg + kv = ma where weight and drag are cancelled out by upward force.
NotATutor
2 years ago
Hello, I quote what you had written: (The larger mass object will travel a shorter distance upward due to bigger pull of gravity acting on it.} ... What you imply is the point 2 of the question is not correct.... ? Isn't it?
In your msg, it keep saying make sense or does not make sense. This is science. We use facts/theory to prove phenomenon. Perhaps, it will be better to pin point what is wrong with the proven expression a = g + kv/m... It tells us that the smaller the m, the bigger the kv/m and the bigger the downward acc. So the mass slow down fast. I do not invent this expression. This expression is derived out. You can point out which step of the derivation has problem?
David Tan
2 years ago
I said it will travel a shorter distance UPWARD and that is assuming the same force was applied which in this case is not because they have the same velocity but different mass, thus the object with larger mass requires a larger force to give the same vel upwards with larger inertia. This means the smaller object had a smaller force applied to it which means it has less inertia thus shorter distance travelled upwards. I am using science facts and common sense instead of blindly following eqns without understanding them and just because the expression was derived elsewhere doesn't mean you applied them correctly. Assuming kv is same for both objects, the mg of the larger object means a larger force needs to be applied for same v thus the f=ma upwards is larger.
NotATutor
2 years ago
Is force inertia.?
NotATutor
2 years ago
Sorry.. i try to but fail to understand what have you tried to say. Anyway, it is ok. You just teach what you want. Good night. Have a good rest and receive a good week ahead. Cheers.!
David Tan
2 years ago
Refer to https://www.physicsclassroom.com/class/newtlaws/Lesson-1/Newton-s-First-Law
David Tan
2 years ago
Thanks cheers.
J
2 years ago
Don't bother with this Yong Kc, David. Always misreading others' comments and only thinking he is right.

When corrected, he just brushes it off and says you're wasting his time.

When his working is wrong and that is pointed out to him, he will subtly and quietly delete his post without acknowledging the error.

Or, he simply ignores it.

When a term is vague and has different definitions interpretations, usage and conventions, he will only look at his own chosen one and ignore other possibilities

This person is not a verified tutor and his credibility is a big question mark.

Don't bother.