A helium balloon has a mass of 0.022 kg, which includes both the helium and the balloon itself. On this balloon, there is 0.290 N of buoyant force pushing the balloon upward. If I let go of the balloon, find the balloon's acceleration rate in the upward direction.





If we neglect air resistance, how long will it take for the balloon to reach a speed of 10 m/s?





Neglecting air resistance is a good approximation for heavy objects and slow-moving objects. Therefore, we should NOT neglect air resistance for a helium balloon once it starts moving. Let's say the balloon reaches its "terminal velocity" in the upward direction after about 2 seconds. What is the drag force acting on the balloon at this point?

To find the balloon's acceleration rate in the upward direction, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.

In this case, the net force acting on the balloon is the buoyant force pushing it upward, which is equal to 0.290 N. The mass of the balloon is given as 0.022 kg.

Using the formula F = ma, we can rearrange it to find the acceleration, a = F/m.

a = 0.290 N / 0.022 kg

a ≈ 13.18 m/s²

Therefore, the balloon's acceleration rate in the upward direction is approximately 13.18 m/s².

To find how long it will take for the balloon to reach a speed of 10 m/s, we can use the equation of motion v = u + at, where v is the final velocity, u is the initial velocity (which is 0 m/s since the balloon is initially at rest), a is the acceleration we just calculated, and t is the time taken.

Plugging in the values, we have:

10 m/s = 0 + (13.18 m/s²) * t

Simplifying, we find:

t ≈ 0.76 seconds

Therefore, it will take approximately 0.76 seconds for the balloon to reach a speed of 10 m/s.

Now, if we consider the case where the balloon reaches its "terminal velocity" after about 2 seconds, we know that the drag force (also known as air resistance) acting on the balloon is equal and opposite to the buoyant force. This is because at terminal velocity, the balloon stops accelerating and reaches a constant speed due to the balance between the upward buoyant force and the downward drag force.

Since the buoyant force is given as 0.290 N, the drag force acting on the balloon at this point is also 0.290 N.