Q&A - PSLE Science

[verykiasumummy]

i’m sorry… creamyhorror, way2go, nebbermind…


my mistake… i had mistaken and mixed up with impact of the object…

thks to creamyhorror, i have that same book as u and i saw that quote too. i was still thinking that the GPE on both object is the same, but the impact of the object landing on the ground will be different. the heavier object will have a greater impact, hence i mix it up that the heavier object will also fall faster…

sorry, my mistake…

the question my ds1 had was about 2 boxes, one with 5kg, and the other 20kg, similar size and material. when the 5kg was dropped from a certain height, the box did not tear apart, but the 20kg box was torn apart when it landed on the ground due to the greater impact it had because of a greater mass.

i’m really getting old…

[atutor2001]

Nebbermind:

W2G

Donch quite get u.

PE = mgh, KE = ½ mv²

Assuming the balls begin with v=0, and h=0 at the end of the slope, then

mgh = ½ mv²
=> gh = ½ v²

Since g and h are constant, v must be the same.

Lets put in frictional losses to the equation :

mgh = ½ mv² (without friction)
mgh = ½ mV2² + heat + sound (with friction)

Reduction in speed = v² - V2² = 2(heat + sound)/m

So the reduction in speed is inversely proportional to the mass of the object if there is friction.

That is, the reduction in speed will be smaller if the mass is big and vice versa.

For a \"free falling object\" the (heat + sound) is negligible as it is due to air resistance, so the final speed is about the same.

However, for a ball rolling down a ramp, the (heat + sound) depends on the surface texture and the length of the ramp.

If it is a smooth short ramp then the final velocity should be about the same. However, if the ramp is long and rough, frictional loss is quite substantial. Therefore, the ball with a bigger mass will reach the bottom first because the reduction in velocity of the bigger mass is less.

[Ares23]

all these equations are ‘O’ level physics/sec 3 IP syllabus…

[atutor2001]

Ares23:

all these equations are 'O' level physics/sec 3 IP syllabus...

The problem with Pr Science is that they like to question concepts that are quite chim. Like this question, there will be different outcome for different conditions. We need these equations to understand better. However, Pr school kids will not learn these equations until much later. So how to make them learn with understanding when they are not even well verse with the basics?

By the way, those equations are only for kiasu parents' discussion. Not meant for the children to learn.

[creamyhorror]

verykiasumummy:

thks to creamyhorror, i have that same book as u and i saw that quote too. i was still thinking that the GPE on both object is the same, but the impact of the object landing on the ground will be different. the heavier object will have a greater impact, hence i mix it up that the heavier object will also fall faster...

No problem, it's easy to get confused on these topics if you haven't reviewed them in some time

atutor2001:

Lets put in frictional losses to the equation :

mgh = ½ mv² (without friction)
mgh = ½ mV2² + heat + sound (with friction)

Reduction in speed = v² - V2² = 2(heat + sound)/m

So the reduction in speed is inversely proportional to the mass of the object if there is friction.

The following is just physics chat between people long past their exams

I don't think you can conclude this, not without knowing the function for (heat+sound). If we say x is the energy lost as heat and sound, then the relationship is

v^2 - u^2 = 2x/m

But if x is a function of m (i.e. it depends on m), then the inverse-proportional relationship is not certain. You'd have to assume x was independent of m in order to argue that the velocity difference is inversely proportional to m.

To analyse how mass affects the velocity, you could probably find an equation for air resistance (drag) and then subtract that from the force due to gravity. That should give you an acceleration-velocity (differential) equation, and then you'd have to solve for velocity as a function of time. If m is involved in that final equation, then velocity depends on m. But I'm not feeling particularly interested in finding that out myself

[atutor2001]

creamyhorror:

atutor2001:

Lets put in frictional losses to the equation :

mgh = ½ mv² (without friction)
mgh = ½ mV2² + heat + sound (with friction)

Reduction in speed = v² - V2² = 2(heat + sound)/m

So the reduction in speed is inversely proportional to the mass of the object if there is friction.

The following is just physics chat between people long past their exams

I don't think you can conclude this, not without knowing the function for (heat+sound). If we say x is the energy lost as heat and sound, then the relationship is

v^2 - u^2 = 2x/m

But if x is a function of m (i.e. it depends on m), then the inverse-proportional relationship is not certain. You'd have to assume x was independent of m in order to argue that the velocity difference is inversely proportional to m.

To analyse how mass affects the velocity, you could probably find an equation for air resistance (drag) and then subtract that from the force due to gravity. That should give you an acceleration-velocity (differential) equation, and then you'd have to solve for velocity as a function of time. If m is involved in that final equation, then velocity depends on m. But I'm not feeling particularly interested in finding that out myself

Thank you for the enlightenment. You are correct that rolling friction force does depends on mass and should cancel off. So if 2 objects of the same surface texture but of different mass roll down a ramp, the time to reach the bottom would be the same. The time taken should only depends on the coefficient of rolling friction. That is, if their surfaces are different, then the time taken will not be the same.

However, for free falling object, I tried googling and it appears that drag force is not dependent on the mass of the ball. Well it is beyond me to understand such thing now. Thanks for giving a knock on my rusty brain.

[creamyhorror]

atutor2001:

Thank you for the enlightenment. You are correct that rolling friction force does depends on mass and should cancel off. So if 2 objects of the same surface texture but of different mass roll down a ramp, the time to reach the bottom would be the same. The time taken should only depends on the coefficient of rolling friction. That is, if their surfaces are different, then the time taken will not be the same.

I see, this is interesting to know.
[quote]However, for free falling object, I tried googling and it appears that drag force is not dependent on the mass of the ball.[/quote]Intuitively, I'd guess that drag force wouldn't be dependent on mass, because drag occurs at the surface of the object, where the fluid particles are hitting the surface. The mass of the whole object therefore shouldn't matter. If the object were moving sideways (like an airplane), the drag force would depend on how fast it was hitting the air particles, not on how massive it was.

Sorry ah, I go ahead and work this out a bit. Once you combine drag force (Fdrag = -kv^2) with the pull of gravity, you get

net force = ma
Fgrav + Fdrag = ma
mg + Fdrag = ma
g + Fdrag/m = a
g - kv^2/m = a (where k is a constant)

Reading the above equation: For any particular velocity v, a greater m implies a greater acceleration. In other words, at any speed, a more massive object has a greater acceleration than a less massive one. A greater acceleration means the object speeds up faster. Thus, when air resistance is added into the equation, heavier objects actually fall faster (assuming all else, e.g. shape/area, is held constant).

I think this will extend to objects rolling down ramps as well. If air resistance is significant, then massive objects should roll faster. The effect will probably be pretty small unless you're rolling things down the Great Pyramid of Egypt.

This is really far from P6 Science, but I hope fellow posters will forgive us since it's after PSLE and no one will be doing much discussion for some time. :oops:
[quote]Well it is beyond me to understand such thing now. Thanks for giving a knock on my rusty brain.[/quote]No worries, interpreting formulae is often tricky and it took some thinking on my part too. It's quite fun sometimes.

[atutor2001]

creamyhorror:

......


I think this will extend to objects rolling down ramps as well. If air resistance is significant, then massive objects should roll faster. The effect will probably be pretty small unless you're rolling things down the Great Pyramid of Egypt....

Thank you for the explanation. You are very good in physics. I have not considered from this angle.

My apology to those who dislike physics for going off topic.

[verykiasumummy]

so does it mean that the heavier object will reach the ground first no matter whether is rolling down the ramp or free falling from a height??

[creamyhorror]

@atutor2001: Thanks! Physics puzzles are fun to think about.

verykiasumummy:

so does it mean that the heavier object will reach the ground first no matter whether is rolling down the ramp or free falling from a height??

That's what I think, but I haven't done calculations for the rolling case to confirm it. The basic idea from interpreting that last equation I gave is that air resistance depends only on speed, not mass. Therefore, comparing objects at the same speed, heavy objects can \"overcome\" air resistance more easily than light ones - they're slowed down less by air resistance. So they accelerate faster than light objects.

Still, it's important to keep sight of the original principle, which is that objects fall (accelerate) at the same rate, regardless of their masses.