Air balloon acceleration and mass of ballast that must be droppped

[JLPG]

Homework Statement

A research balloon of total mass 220 kg is descending vertically with a downward acceleration of 4.3 m/s2. How much ballast must be thrown from the car to give the balloon an upward acceleration equal to 0.8 m/s2, presuming that the upward lift of the balloon does not change.
HINT: One body with two situations again. Draw sepatate FBD before and after the ballast is thrown out. Two equations from two FBDs.

Homework Equations

F=ma

The Attempt at a Solution

I don't know what forces I need to plug in which formula.

 

[Andrew Mason]

Homework Statement

A research balloon of total mass 220 kg is descending vertically with a downward acceleration of 4.3 m/s2. How much ballast must be thrown from the car to give the balloon an upward acceleration equal to 0.8 m/s2, presuming that the upward lift of the balloon does not change.
HINT: One body with two situations again. Draw sepatate FBD before and after the ballast is thrown out. Two equations from two FBDs.

Homework Equations

F=ma

The Attempt at a Solution

I don't know what forces I need to plug in which formula.

Can you figure out what Fb, the buoyancy force, is initially? (hint: it is the force that reduces what would otherwise be a downward acceleration of g).

What, if any, is the change in Fb - the buoyancy force on the balloon between the initial and final state?

If you answer that correctly you should be able to work out the mass change needed.

AM

 

[JLPG]

I've never heard of buoyancy force before, but would it be 9.8(220)? I don't think that makes any sense.

 

[Andrew Mason]

I've never heard of buoyancy force before, but would it be 9.8(220)? I don't think that makes any sense.

Do a freebody diagram.

We know that gravity acts. What is the magnitude of the force of gravity? Draw that vector pointing down.

What is the net force (hint: f = ma)? Draw that vector.

Now we just need to know what the other force is that, when added to the gravity force, results in the net force (ie the upward lift or buoyancy force).

Since the balloon is initially accelerating at -4.3 m/sec^2 and not -9.8 m/sec^2 what can you say about the magnitude of the upward force (the buoyancy force) on the balloon? (ie: the gravity vector + this buoyancy force vector = the net force).

Do the same thing for the final state (upward acceleration of .8 m/sec^2) assuming that upward force remains the same.

AM

 

[Nickie]

To solve this problem, we can use the equation F=ma, where F is the net force acting on the balloon, m is the mass of the balloon, and a is the acceleration of the balloon. In this case, we have two situations: before and after the ballast is thrown out.

Before the ballast is thrown out, the net force acting on the balloon is the weight of the balloon, which is equal to its mass (m) multiplied by the acceleration due to gravity (g). Therefore, we can write the equation as F=mg.

After the ballast is thrown out, the net force acting on the balloon is the upward lift force minus the weight of the balloon. Since we know that the upward lift force does not change, we can write the new equation as F= Lift - mg.

To find the amount of ballast needed, we need to find the difference between these two forces. We can set them equal to each other and solve for the mass of the ballast (m_b).

mg = Lift - mg

2mg = Lift

m_b = Lift / 2g

Therefore, the mass of the ballast that must be thrown out is equal to half of the upward lift force divided by the acceleration due to gravity. Plugging in the given values, we get:

m_b = (0.8 m/s^2) / (2 * 9.8 m/s^2)

m_b = 0.041 kg

Therefore, 0.041 kg of ballast must be thrown from the car to give the balloon an upward acceleration of 0.8 m/s^2.