What is the velocity of the balloon relative to earth ?

[leena19]

Homework Statement

In the figure: A balloon is attached to a ladder.
The ladder stands vertical on the ground.
The height of the ladder is 6m and there's a monkey at the base of the ladder

Q) The mass of the balloon is 50kg and mass of the monkey is 25kg.
The monkey starts to climb upwards with a constant speed of 0.5m/s

1)What is the velocity of the balloon relative to Earth ?
2)What is the velocity of the monkey relative to Earth ?
3)What is the velocity of the monkey relative to the balloon?
4)Find the timetaken to reach the top of the ladder
5)What's the displacement of the monkey relative to the earth?
6)What's the displacement of the balloon relative to the earth?
7)What's the displacement of the balloon relative to the balloon?
8)what's the increase in PE?
9)What's the total work done by the monkey?

Homework Equations

The Attempt at a Solution

1) \uparrowV (m,b) = velocity of monkey relative to balloon = 0.5
V(b,e) = v1 down
V(m,e) = v

V(m,e) = V(m,b) + V(b,e)
V(m,e) = 0.5 - v1 = vel' of monkey relative to earth.

But how do I find the magnitude of V(m,e) ?
I think I can manage to do the other parts of the question,if only I knew how to solve for V(m,e) . :(

Thanks in advance .

 

[kuruman]

It's a bit more complicated than what you have written down. Suppose the monkey and balloon system are initially at rest. Then the monkey starts climbing up. Will the balloon move? How can you find its speed? (Think center of mass). The same considerations apply when the balloon is moving with velocity v1.

 

[leena19]

Suppose the monkey and balloon system are initially at rest. Then the monkey starts climbing up. Will the balloon move?

Yes,when the monkey starts climbing,it exerts a downward force on the ladder causing the ladder to move down .

How can you find its speed? (Think center of mass).

I tried using centre of mass,but I end up with 2 unknowns.

Here's what I did,
Taking y as the reference distance from the top of the system,
Initially,when the monkey's at the bottom of the ladder
[25 * (6+y) + 50 * y/2 ]/75 = X --------(1) where X = COM

When monkey starts climbing up,
in 1 second,
the balloon moves down by a distance v1,
the monkey moves up by a distance 0.5-v1,sooo...

[ 25 * (6-(0.5-v1)) + y) + 50 (y+v1) ] / 75 = X -----------(2)

(1)=(2)
137.5 + 75v1 + 25y = 150

Not sure how to proceed from here

 

[kuruman]

Before we proceed any further, what does the picture show about the motion of the balloon? Is there a direction to the balloon's velocity v1? In other words is the balloon already moving when the monkey starts climbing?

 

[leena19]

Before we proceed any further, what does the picture show about the motion of the balloon? Is there a direction to the balloon's velocity v1? In other words is the balloon already moving when the monkey starts climbing?

The balloon doesn't seem to be moving in the picture,but its just a rough sketch that our teacher put up on the board for us to copy.
I could draw the pic, if needed.may take a few minutes

 

[kuruman]

No need for a picture. If the balloon is initially at rest, when the monkey starts climbing, the centre of mass should remain at rest. Can you write an expression for V_CM? (Note that the velocities of monkey and balloon must be relative to the Earth.) Then V_CM = 0.

 

[leena19]

No need for a picture. If the balloon is initially at rest, when the monkey starts climbing, the centre of mass should remain at rest. Can you write an expression for V_CM? (Note that the velocities of monkey and balloon must be relative to the Earth.) Then V_CM = 0.

Is V_CM the velocity of center of mass?

Here's the pic. anyway
http://img441.imageshack.us/img441/3106/balloon.png"

 

[kuruman]

Yes.

 

[leena19]

Well,if that's the case,I'm sorry I don't know to write an expression for V_CM.

One more hint,please...?

 

[leena19]

OK,I'm kinda desperate here.I have a physics exam the day after tomorrow and i have a lot more to revise,but I can't seem to concentrate in my studies without solving this problem,so anybody know how i could find expressions for V_CM?

Thanx

 

[kuruman]

V_{CM} = \frac{m_{1}v_{1}+m_{2}v_{2}}{m_{1}+m_{2}}

 

[leena19]

V_{CM} = \frac{m_{1}v_{1}+m_{2}v_{2}}{m_{1}+m_{2}}

Oh that's the conservation of momentum equation.i feel so stupid i completely missed it.

Anyway,this is what i get
\downarrow m₁v₁ - m₂v₂ = 0
50 * v1 = 25*v2
v2 = 2v1

Then,
2v₁ = 0.5 - v₁
3v₁=0.5
v₁= 1/6

Is this correct now?

THANK YOU!

 

[kuruman]

The number is correct, but the sign is wrong. Velocity v₁ is an algebraic quantity which might turn out positive or negative when you put in the numbers. You should start from

m₁v₁ + m₂v₂=0,

do the math and put in the numbers in the end. Then v₁ will come out negative indicating that the balloon is moving down while the monkey is climbing up. Note that

v₂=-2v₁.

I think you can finish the rest now.

 

[leena19]

Yeah.The rest are easy.

Thanks for the help,sir.
You're awesome!