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Mechanics 1 - Vertical motion - I just don't get it

Everyone in our Maths class does physics, other than me and one other person...I just don't get this typic...and the teacher doesn't explain it to us properly...she just dictates notes to us and doesn't even go through an example!

Please could someone help me with the following questioning, going through each bit step by step and explaining the science behind it - that's the bit I really do not understand, being a linguist and all:confused:

4) A balloon of total mass 420 kg is descending with a constant acceleration of 0.4 m/s/s. Find the uprhtust acting on the balloon. When the balloon is moving at 1.5 m/s, enough ballast is released for the balloon to fall with a decleration of 0.2 m/s/s. Calculate:

a) how much ballast was released,
b) the time for which the balloon continues to fall before it begins to rise.

I managed to find the upthrust (not sure if it was for the right reasons)... I got 3948 N

Help would be much appreciated:biggrin:
I assume you can picture a balloon of mass 420kg accelerating downwards with an acceleration of 0.4m/s^2. Newton's second law states that the resultant force is equal to mass times acceleration: F = ma. Drawing a force diagram is essential in these problems, and in most of mechanics.

You have a balloon, with weight acting downwards, upthrust acting upwards, and a downward acceleration of 0.4. So, the resultant force down is (weight) - (upthrust), which will be equal to mass * acceleration.
Weight = 420g, or 420*9.8 (mass * acceleration due to gravity... g = 9.8 on Earth)
Upthrust... let's call it T.
420g - T = 420*0.4
and solve for T.

(You got that bit right. :smile:)

When the balloon is moving at 1.5m/s, its acceleration is 0.2m/s^2. Its upthrust at that instant is 3948N. Call the mass of the balloon m.
Same as before:
mg - 3948 = m(0.2)
m = 3948/9.6 = 411.25
So 8.75kg was released.

Does this help? :smile:
The answer in the back of the book is 25.2kg :s
I managed to get 25.2 by doing this:

3948 - 9.8m = 0.2m
3948 = 10m
m = 394.8 kg

420 - 394.8 = 25.2 kg

But that was just by messing about with the equations, I DO NOT UNDERSTAND the reasons behind it... why in that order?
Reply 4
You have deceleration, which is upwards - in the same dirn as the upthrust. So you have,

T - m'g = m'd
3948 - 9.81m' = 0.2m'
3948 = 10.01m'
m' = 394.4 - the new mass of the baloon

mass released = 420 - 394.4 = 25.6 kg

Edit: removed deliberate mistake :smile:
Reply 5
Since you have a deceleration, then the net force on the balloon must be acting upwards. So the upthrust, acting up, must be greater than the weight, acting down. The deceleration is the also in the same direction as the upthrust.
If you consider downwards as positive, then you could write your equation as

m'g - T = - m'd

which is just the same as

T - m'g = m'd
Thanks - that makes it a little clearer. Where you've put 0.3, do you mean 0.2?

and I have no idea how to do b). I think you may use the v= u + at thing, not sure how to work all of that out, though
Reply 7
eh yeah, well spotted - you got the deliberate mistake <crawls off>
Thanks.

Still haven't managed to do part B). eek.
Reply 9
friendsfanatic
Thanks - that makes it a little clearer. Where you've put 0.3, do you mean 0.2?

and I have no idea how to do b). I think you may use the v= u + at thing, not sure how to work all of that out, though

Yes, you would use the v = u + at thing.

u = initial velocity = 1.5 m/s
v = final velocity = 0 (balloon at rest)
a = -0.2 m/s² (a is negative accln, or d is a +ve deceln and a = -d)
t = ?

Under the deceleration, the balloon will slowly come to rest. It will halt, then slowly start to rise upwards.
Thank you so much. I'm beginning to, finally, understand this topic a bit more. I dunno why I find it so hard - I guess it's the applying/science-y bit. I mean, core 4 is meant to be harder than M1, but I don't have a problem with it really. Thanks once again.
Reply 11
only to 1d.p because it is m1
Reply 12
Original post by jasperD
only to 1d.p because it is m1


Welcome to TSR jasper.

Please don't bump threads that are 5 years old!
bump
this says 15 years ago and here i am today in year 12 struggling with the exact same question