Q&A - PSLE Science
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Good luck to you kids, and to you mummies/daddies who are cheering for them. You should be in bed already!
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Yes should be in bed now. Need very careful thinking and clear mindset for tomorrow’s battle. A lot of application skills need to be applied.
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creamyhorror:
In general, if you ignore air friction, objects dropped from the same height fall with the same acceleration, regardless of their mass. This means that objects speed up at the same rate as they fall. A more massive ball will therefore reach the ground at the same time as a lighter ball dropped from the same height. This extends to objects rolling down a slope/ramp, if you ignore friction. So I'd say that both balls reach the ground at the same time.
Ball A with greater mass will reach the ground first.charsen:
[quote=\"vaidyanathan padmini\"]I just have a doubt.please help......
Two balls are placed on top of a ramp.ball A has a greater mass than ball B.which ball reaches the ground first?
Thanks in advance
Objects with greater mass will possess higher kinectic energy and hence A will travel faster than B.
(The gravitational potential energy (gpe) of the more massive object is higher, and after x seconds of falling it possesses more kinetic energy than the lighter object -- but that doesn't mean it's travelling faster than the lighter object. Kinetic energy is not the same as velocity.)
Let me know if this does not agree with your textbook or teachers
For parents/advanced students: http://www.batesville.k12.in.us/physics/phynet/mechanics/RotMechanics/fall_slide_roll.htm giving the evidence. The summary quote is as follows:[quote]This result says that the linear acceleration of the object down the ramp does not depend on the object's radius or mass, but it does depend on how the mass is distributed. Therefore, all spheres have the same acceleration on the ramp[/quote]Of course, at the primary school level it's unnecessary to go into the details. Just learn that objects with different masses fall through the air and roll down ramps with the same acceleration.[/quote]creamyhorror,
me think u mixed up acceleration with velocity here. d acceleration u refer to in ur post is gravity?
If u meant gravity, it is a given dat d same gravitational force acts on all objects.
If one looks at d question fr a P6 level understanding,
fr a purely conservation of energy point of view, GPE = KE
most P6s will likely reason dat d heavier ball possess greater KE n thus must travel faster or further.
(Since KE is a function of velocity squared, n d heavier ball possesses greater KE, where does d additional KE translate to, if not greater velocity or further distance travelled?)
d answer looks simple on d surface but d explanation requires a much deeper understanding of physics, which is really too much to ask of a P6.
Since it's a ball rolling down a slope, d rotational aspect of each ball must be taken into account. d rotational aspect is what u alluded to in 'distribution of mass'.
It is not a well thought-out question.
Don't u all like to hear d explanation/reasoning fr d teacher who set dis question - for d benefit of students who will come after d current batch? -
Way2GO:
W2G
creamyhorror,
me think u mixed up acceleration with velocity here. d acceleration u refer to in ur post is gravity?
If u meant gravity, it is a given dat d same gravitational force acts on all objects.
If one looks at d question fr a P6 level understanding,
fr a purely conservation of energy point of view, GPE = KE
most P6s will likely reason dat d heavier ball possess greater KE n thus must travel faster or further.
(Since KE is a function of velocity squared, n d heavier ball possesses greater KE, where does d additional KE translate to, if not greater velocity or further distance travelled?)
d answer looks simple on d surface but d explanation requires a much deeper understanding of physics, which is really too much to ask of a P6.
Since it's a ball rolling down a slope, d rotational aspect of each ball must be taken into account. d rotational aspect is what u alluded to in 'distribution of mass'.
It is not a well thought-out question.
Don't u all like to hear d explanation/reasoning fr d teacher who set dis question - for d benefit of students who will come after d current batch?
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. -
Nebbermind:
Good explanation, Nebbermind. I actually considered showing that equation but decided it might just end up confusing some students.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.
@Way2GO: In a sense, the more massive ball only has more kinetic energy because it has more mass. It doesn't speed up faster because it has more KE - it has more mass, so it gains KE faster. The cause is acceleration, the result is KE.
From a P6 point of view, all that students need to remember is: objects tend to fall with the same acceleration toward the Earth, regardless of their mass, when air resistance is ignored. This means that both heavy and light objects take the same time to fall to the ground, as demonstrated by Galileo's famous thought experiment about http://www.juliantrubin.com/bigten/galileofallingbodies.html. When this experiment was done on the Moon by an astronaut in 1972, a feather and a much heavier hammer fell to the ground at exactly the same time.
This is secondary-level knowledge, but it doesn't hurt to know it.
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Nebbermind:
Arh 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.
IMHO, u made a fundamental error to assume mass is d same in d two balls in ur deduction.
Let’s denote d heavier ball as 1, n lighter ball as 2.
For heavier ball, m1gh = ½ m1v1^2
For lighter ball, m2gh = ½ m2v2^2
g is a constant, h is d same, n d mass in each equation cancels each other out.
However, m1 > m2 n we know for certain KE1 > KE2, therefore we cannot simply conclude dat v1 = v2.
Dis problem lents itself easily to experiment for kids to visualized without all d theoretical mambo jumbo which I thot is beyond them at dis level n too much to expect of them to explain. Dat’s why I was interested for whoever came up with d question to explain the solution to d kids at their level fr a conservation of energy perspective or r hv d kids been taught dat acceleration due to gravity is independent of mass.
Let’s just discuss it for our understanding.
For a rolling object on an inclined plane, there is an additional rotational aspect day we need to include in d equation.
Dis aspect takes into account d moment of inertia and angular velocity. For simplicity, let’s denote dis as M.
D moment of inertia is different for different shape, size n mass distribution referred to by creamyhorror.
It was for dis reason dat I said d question was not well set-up, coz it just mentioned two balls but fail to specify dat d balls r of d same size n dat they r both solid or spherical shells, but it was left to d child’s assumption dat they must both be solid spherical balls of d same size, n friction is not at play.
If d two balls are exactly d same in size, shape except mass, we can drop dis term in our evaluation.
Dis is prolly wat creamyhorror meant when he said d radius n mass terms do not matter when an object rolls down a slope.
But these terms will matter in d calculation of M if d objects r of different shapes, sizes n mass distribution.
Otherwise d equation reduces to simply mgh = ½ mv2
At d top of d slope, d heavier ball will start with greater inertia. Both balls will gather speed as they roll down d slope. If u plot d velocity vs time graph, it will not be a straight line, n d graphs for d two balls will not be exactly d same. Since it is not a straight line, it means there is acceleration (not g, which is a constant) as d ball rolls along d slope. -
creamyhorror:
:celebrate: Gud for u.
Good explanation, Nebbermind. I actually considered showing that equation but decided it might just end up confusing some students.
I did d same by withholding dis discussion till after d Science paper so as not to confuse d kids.
However, I did ask my DS2 last nite for his answer, he said d heavier ball will reach d end of d slope first fr his understanding of conservation of energy.
He checked with his frenz in class today, two of them mentioned same speed but they didn't explain why.creamyhorror:
d acceleration u mentioned here is due to gravitational force, g? But dat is a constant for both balls.
@Way2GO: In a sense, the more massive ball only has more kinetic energy because it has more mass. It doesn't speed up faster because it has more KE - it has more mass, so it gains KE faster. The cause is acceleration, the result is KE.
In ur analysis, d velocity in d equation KE = 1/2 mv^2 has no effect on KE?creamyhorror:
d example u cite on free-falling objects in a vacuum is well known n its simpler to understand mathematically compared to a ball rolling down an inclined plane.
From a P6 point of view, all that students need to remember is: objects tend to fall with the same acceleration toward the Earth, regardless of their mass, when air resistance is ignored. This means that both heavy and light objects take the same time to fall to the ground, as demonstrated by Galileo's famous thought experiment about http://www.juliantrubin.com/bigten/galileofallingbodies.html. When this experiment was done on the Moon by an astronaut in 1972, a feather and a much heavier hammer fell to the ground at exactly the same time.
This is secondary-level knowledge, but it doesn't hurt to know it.
d observable evidence in free-falling objects having different masses dropped fr d same height is dat d object with heavier mass will hit d ground first.
Thus kids can be easily swayed by wat they hv experienced than an experimental result dat they hv not been previously exposed to.
d bone I was picking with d one setting d question is d kids hv to make many assumptions (eg no air friction, no difference in moment of inertia) to arrive at d answer dat both balls will reach d bottom of d slope at d same time AND IF they hv been taught dat acceleration due to gravity is independent of mass. -
W2G
What u very the chim leh. Once u go into rotational motion, I have to concede defeat!!
But hor…if the ball roll on the inclined plane, then there must be friction…yet another component to take care of.
Assume no friction…balls slide down…no moments…can? -
Nebbermind:
Bro where got chim.W2G
What u very the chim leh. Once u go into rotational motion, I have to concede defeat!!
But hor...if the ball roll on the inclined plane, then there must be friction...yet another component to take care of.
Assume no friction...balls slide down...no moments...can?
Question setter expecting kids to make too many assumptions to arrive at correct answer, tio bo?
u r rite one cannot ignore friction - without friction, ball cannot roll.
kids will be more confused! :slapshead:
if on one hand, assuming no friction to be in agreement with falling objects of different masses fall at d same rate,
n on d other, no friction - no roll. :slapshead: :slapshead: -
Way2GO:
Actually, he didn't assume mass was the same. He only examined the situation for a single object, not two objects. What he did was show that, for a single object with (any) mass m,
Arh Nebbermind,
IMHO, u made a fundamental error to assume mass is d same in d two balls in ur deduction.
Let’s denote d heavier ball as 1, n lighter ball as 2.
For heavier ball, m1gh = ½ m1v1^2
For lighter ball, m2gh = ½ m2v2^2
g is a constant, h is d same, n d mass in each equation cancels each other out.
However, m1 > m2 n we know for certain KE1 > KE2, therefore we cannot simply conclude dat v1 = v2.
change in GPE = change in KE
mgh = 1/2 mv^2
gh = 1/2 v^2
v^2 = 2gh
v = sqrt(2gh)
meaning that the final velocity v is a function of the distance fallen h, and not mass. Mass doesn't affect the final velocity of the object. Just calculate the actual value: when any object, of any mass, has fallen 1 metre, it will be travelling at
velocity = sqrt(2g*1) = 4.43 m/s (since g is a constant 9.8 m/s^2).
When it has fallen 2 metres,
velocity = sqrt(2g*2) = 6.26m/s.
So in your calculations we can certainly conclude that v1 = v2. At any distance h fallen, the velocity of a falling object will always be the same, no matter its mass.
Another approach to prove this would be to find the velocity of an object after it has fallen for a certain time. How do we find velocity? Velocity is the integral of acceleration with respect to time (sorry kids, you'll understand when you're older), and if acceleration is approximately the same (e.g. when the two objects are both near the Earth's surface), then
velocity = acceleration * time
Since acceleration due to gravity is g (9.8 m/s^2), the velocity is simply
velocity = g * time
velocity = 9.8 m/s * time
Every 1 second, the speed of a falling object increases by 9.8 m/s, regardless of its mass. So any two objects will increase in falling speed at the same rate (+9.8 m/s every second), causing them to fall at the same increasing speed.
(The above two lines of reasoning are more suited for upper secondary students. Younger students should just keep in mind the basic principle stated in words.)
[quote]Let’s just discuss it for our understanding.
For a rolling object on an inclined plane, there is an additional rotational aspect day we need to include in d equation.
Dis aspect takes into account d moment of inertia and angular velocity. For simplicity, let’s denote dis as M.
D moment of inertia is different for different shape, size n mass distribution referred to by creamyhorror.
It was for dis reason dat I said d question was not well set-up, coz it just mentioned two balls but fail to specify dat d balls r of d same size n dat they r both solid or spherical shells, but it was left to d child’s assumption dat they must both be solid spherical balls of d same size, n friction is not at play.
If d two balls are exactly d same in size, shape except mass, we can drop dis term in our evaluation.
Dis is prolly wat creamyhorror meant when he said d radius n mass terms do not matter when an object rolls down a slope.
But these terms will matter in d calculation of M if d objects r of different shapes, sizes n mass distribution.
Otherwise d equation reduces to simply mgh = ½ mv2
At d top of d slope, d heavier ball will start with greater inertia. Both balls will gather speed as they roll down d slope. If u plot d velocity vs time graph, it will not be a straight line, n d graphs for d two balls will not be exactly d same. Since it is not a straight line, it means there is acceleration (not g, which is a constant) as d ball rolls along d slope.[/quote]I think it's fair to assume that the balls have the same shape and are similar in mass distribution. Therefore, they will roll down the slopes with the same acceleration, even though their sizes/radii/moments of inertia are different. Solid balls of different masses will roll down ramps at the same rate, if other conditions are equal.
I wouldn't overthink the problem. The important idea/law here is that mass itself does not affect acceleration due to gravity, or acceleration down a ramp due to gravity. Students can learn about additional considerations like air resistance and mass distribution at a more advanced stage, especially through experimentation, but the basic principle should be given the most weight.
(I like teaching physics, maybe I should be a tutor...)
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