A balloon lifting a heavy stone

In summary, a party balloon filled with helium is tied to a small stone by a light string to prevent it from flying away. When a child releases the balloon at ground level, it rises and lifts the stone off the ground. Using the "impulse approximation," the solution calculates the time it takes for the balloon to rise 1.5m and the velocity of the stone when it is lifted off the ground. It also considers the time for the stone to touch the ground again, taking into account the conservation of momentum. The method of using variables instead of numbers is recommended for easier identification of mistakes.
  • #1
jianghan
25
0

Homework Statement


A party balloon(of mass 0.0025kg when empty) is filled with helium to a volume of 0.0045m3. it is tied to a small stone of mass 0.015kg by a light string of length 1.5m to prevent it from flying away. a child holds the balloon at ground level and then releases it.
(ρair=1.20kg/m3 ρHe=0.178kg/m3)

(a)how long does it take for the balloon to rise 1.5m,that is,for the string to become taut?

(b)What is the velocity of the stone when it is lifted off the ground? you may assume the time needed to bring the stone to this velocity is very short(impulse approximation) once the string is taut, and the string remains taut throughout

(c)How long after lifting off will the stone touch the ground again?(neglect air resistance and treat the stone as a particle)

2. The attempt at a solution
part 1 is relatively easy,i have mtotal=0.00330kg,net upward force=0.0206N,a=6.24m/s2, t=0.693s which agrees with the given answer

not really understand part 2 as the net upward force acting on balloon is only 0.0206N,how can it then lift a stone with a weight of 0.147N?

for part 3,if the stone can be lifted,why would it touch the ground again?
 
Physics news on Phys.org
  • #2
I think it is the conservation of momentum for the part2, where

m(of balloon)v=m(of balloon and stone)v
v of balloon=at=4.32432, mass of balloon is 0.00330kg (as you calc-ed), mass of balloon+stone=0.0183kg, then you can solve for v.

as for part3, hmm...
 
  • #3
Did you read the question?

"it is tied to a small stone of mass 0.015kg by a light string of length 1.5m to prevent it from flying away."

If the upward force of the balloon could lift the stone indefinitely, then the stone isn't doing its job.

"(b)What is the velocity of the stone when it is lifted off the ground? you may assume the time needed to bring the stone to this velocity is very short (impulse approximation) once the string is taut, and the string remains taut throughout"

If the balloon is floating and accelerating upward, it is gaining momentum. If the balloon just flies up, makes the string taught, and nothing further moved, that would imply that the momentum disappears. The momentum obviously doesn't disappear, and the question tells you that. It tells you to use the "impulse approximation." Impulse is instantaneous momentum change.

jianghan said:
not really understand part 2 as the net upward force acting on balloon is only 0.0206N,how can it then lift a stone with a weight of 0.147N?

for part 3,if the stone can be lifted,why would it touch the ground again?

Have you ever tried this as a kid? It really does lift the stone.
 
  • #4
No,maybe the stones i used to tie my balloons to were all too heavy for this effect to be noticeable.

anyway,for part 3,my solution is as follows
maximum momentum=mballoon x at=0.0143 kgm/s
net downward force=0.1264N
time needed to "cancel" the upward momentum=0.0143/0.1264=0.113s
time needed to touch the ground again(achive the same downward momentum)=0.113x2=0.226s

is my method correct?
 
  • #5
Your method for part 3 is correct. However, your method for part 1 is incorrect, which led to an incorrect answer. Next time, try to do the problem with variables as opposed to numbers. It looks cleaner, and it's easier to identify where you went wrong.

In the setup of the problem, the balloon is tied to a string, which is tied to a stone. If the balloon is at ground level (the string is not taut), then the stone is on the ground, and there is no way for balloon to lift the stone. We assume that the string has no mass, so the only thing accelerating up is the balloon.

The only moving piece is the balloon, so the rock does not contribute to the total momentum of the apparatus. Therefore, the acceleration and time you calculated for part 1 is wrong, because it uses the total mass, not the mass of the balloon.
 
Last edited:
  • #6
Harrisonized said:
Your method for part 3 is correct. However, your method for part 1 is incorrect, which led to an incorrect answer. Next time, try to do the problem with variables as opposed to numbers. It looks cleaner, and it's easier to identify where you went wrong.

In the setup of the problem, the balloon is tied to a string, which is tied to a stone. If the balloon is at ground level (the string is not taut), then the stone is on the ground, and there is no way for balloon to lift the stone. We assume that the string has no mass, so the only thing accelerating up is the balloon.

The only moving piece is the balloon, so the rock does not contribute to the total momentum of the apparatus. Therefore, the acceleration and time you calculated for part 1 is wrong, because it uses the total mass, not the mass of the balloon.

Actually in my solution for part 1,"total mass" means the combined mass of balloon and helium, i did exclude mass of the stone, that's why my answer agrees with the given answer.
but thank you for your advice though
 

1. How does a balloon lift a heavy stone?

A balloon is able to lift a heavy stone because of the principle of buoyancy. When a balloon is filled with a gas, such as helium, it becomes less dense than the surrounding air. This creates an upward force, known as buoyancy, which allows the balloon to lift objects that are heavier than itself.

2. How much weight can a balloon lift?

The amount of weight a balloon can lift depends on the size and type of balloon, as well as the amount of gas it contains. However, in general, a standard party balloon filled with helium can lift about 14 grams of weight. Larger balloons, such as weather balloons, can lift much heavier loads, sometimes up to several hundred kilograms.

3. Can a balloon lift a stone that is heavier than itself?

Yes, a balloon can lift a stone that is heavier than itself as long as the buoyant force generated by the gas inside the balloon is greater than the weight of the stone. This is why helium balloons are often used to lift heavy objects, such as banners or cameras, for aerial photography.

4. What happens if the balloon pops while lifting a stone?

If the balloon pops while lifting a stone, the stone will fall to the ground due to the force of gravity. However, depending on the height at which the balloon popped, the stone may not fall straight down and could potentially cause damage or injury. This is why it is important to always handle balloons and their attached objects with care.

5. Are there any limitations to using a balloon to lift a heavy stone?

Yes, there are several limitations to using a balloon to lift a heavy stone. The first limitation is the amount of weight the balloon can lift, as discussed in question 2. Additionally, balloons can be affected by wind and weather conditions, which can make it difficult to control their movement. Also, the strength of the material used to attach the stone to the balloon must be carefully considered to ensure it can withstand the weight without breaking. Finally, using a balloon to lift a heavy stone can be dangerous and should only be done by trained professionals with proper safety measures in place.

Hot Threads

Recent Insights

Back
Top