Q&A - PSLE Science

[Way2GO]

Nebbermind:

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?

Bro where got chim.
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:

[creamyhorror]

Way2GO:

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.

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,

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...)

[verykiasumummy]

alamak all the grandmasters here so chim…


this is PSLE sci ya?? need not consider acceleration & velocity right??

i cannot say i’m good in sci, i must say i make every effort to read and remember the texts and the many different sci guides in my hse…

the 2 objects, 1 heavier than the other, when released from the same height, they possess the same GPE as in gravitational potential energy. in pri sci, GPE is a type of potential energy due to the increased in height that the object is placed off the ground. in this case, both balls are at the same height, hence possess equal GPE.

however gravitational force, or gravity as all u mean, acting on the heavier ball will be higher due to its greater mass, hence the heavier ball will reach the ground first.

correct me if i miss out any keywords… but there is a difference in the time that each of the ball takes to reach the ground…

[verykiasumummy]

creamyhorror, i think u r right to say both balls have the same acceleration, but due to the gravity acting on the heavier ball is higher, the heavier ball should reach the ground first. u can do a simple experiment by placing a cola can with drink inside and the other empty… the one with drink which is heavier will reach the ground first…


pri students are supposed to assume that way… heavier one will reach ground first… they are not supposed to assume no friction or no air resistance, because that cannot be practically done.

my dd’s sci tutor came with an explanation to explain this some time ago. she said for example, a helium balloon can lift up and carry with it maximum 10g, so we say that to lift up 100g, we need 10 helium balloons. if the object gets heavier, say 200g, we need more balloons to lift the object up which is the same as the amount of force applied to move things, the heavier it is, the more force required to move or stop it.

i cannot say about the equations that u all have mentioned, whether they are right or wrong, i long forgotten about them though i was good in sci during my days… i deleted those memory to learn all about pri sci so as to coach my dc along… hope i didnt say anything wrong…

[Nebbermind]

verykiasumummy:

alamak all the grandmasters here so chim...


this is PSLE sci ya?? need not consider acceleration & velocity right??

i cannot say i'm good in sci, i must say i make every effort to read and remember the texts and the many different sci guides in my hse...

the 2 objects, 1 heavier than the other, when released from the same height, they possess the same GPE as in gravitational potential energy. in pri sci, GPE is a type of potential energy due to the increased in height that the object is placed off the ground. in this case, both balls are at the same height, hence possess equal GPE. - (1)

however gravitational force, or gravity as all u mean, acting on the heavier ball will be higher due to its greater mass, hence the heavier ball will reach the ground first. (2)

correct me if i miss out any keywords.. but there is a difference in the time that each of the ball takes to reach the ground..

(1) If they have different mass and all else remains the same, the GPE (which I presume is defined by 'mgh') will be different.

(2) As shown above, final velocity of the object is not dependent on mass but on 'g' & 'h' which are constants if the diff objects are at the same height. So all objects will travel at the same V and reach the ground at the same time.

[Nebbermind]

verykiasumummy:

creamyhorror, i think u r right to say both balls have the same acceleration, but due to the gravity acting on the heavier ball is higher, the heavier ball should reach the ground first. u can do a simple experiment by placing a cola can with drink inside and the other empty... the one with drink which is heavier will reach the ground first..


pri students are supposed to assume that way.. heavier one will reach ground first... they are not supposed to assume no friction or no air resistance, because that cannot be practically done.

my dd's sci tutor came with an explanation to explain this some time ago. she said for example, a helium balloon can lift up and carry with it maximum 10g, so we say that to lift up 100g, we need 10 helium balloons. if the object gets heavier, say 200g, we need more balloons to lift the object up which is the same as the amount of force applied to move things, the heavier it is, the more force required to move or stop it.

i cannot say about the equations that u all have mentioned, whether they are right or wrong, i long forgotten about them though i was good in sci during my days... i deleted those memory to learn all about pri sci so as to coach my dc along... hope i didnt say anything wrong...

Pls do not confuse FORCE with ENERGY.

[Way2GO]

creamyhorror:

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.

u nail it with dis working. :salute:
can use dis to explain to kids fr conservation of energy POV.
:udaman:

[Way2GO]

Nebbermind:

verykiasumummy:

the 2 objects, 1 heavier than the other, when released from the same height, they possess the same GPE as in gravitational potential energy. in pri sci, GPE is a type of potential energy due to the increased in height that the object is placed off the ground. in this case, both balls are at the same height, hence possess equal GPE. - (1)

however gravitational force, or gravity as all u mean, acting on the heavier ball will be higher due to its greater mass, hence the heavier ball will reach the ground first. (2)

correct me if i miss out any keywords.. but there is a difference in the time that each of the ball takes to reach the ground..

(1) If they have different mass and all else remains the same, the GPE (which I presume is defined by 'mgh') will be different.

(2) As shown above, final velocity of the object is not dependent on mass but on 'g' & 'h' which are constants if the diff objects are at the same height. So all objects will travel at the same V and reach the ground at the same time.

verykiasumummy, Nebbermind is correct
GPE = mgh
therefore, d greater d mass or height, d higher d GPE.
g is a constant.

[verykiasumummy]

but pri sci dun learn velocity and acceleration.

[Way2GO]

creamyhorror:

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.

In dis problem, d assumption has to be made dat d balls hv similar mass distribution n r of d same size, for ur stated conclusion to be correct.
Coz for a spherical solid ball rolling down an inclined palne,
GPE = KE + M (where M is a function of moment of inertia * angular velocity)
For a solid sphere, moment of inertia = 2/5 * mr^2 where r is d radius of d ball.
Therefore size n radius matters.
if d problem was changed to one with balls of different mass distribution, eg a solid spherical ball vs a ball with just a spherical shell, d solution wld be different.

creamyhorror:

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...)

Agree.
Why not? u r gud.