A hot air balloon with a mass of 18.0 kg is accelerating upward at 1.80 m/s^2 (Anet = 1.80 m/s^2). What is the weight and buoyant force acting on the balloon?
W=18*10N=180N B-W=Ma B-180N=(18)(1.8) B=32.4+180=212.4N
To find the weight and buoyant force acting on the balloon, we need to use the following equations:
1. Weight (W) = mass (m) * acceleration due to gravity (g)
2. Buoyant force (Fb) = density (ρ) * volume (V) * acceleration due to gravity (g)
Step 1: Find the weight (W):
The weight of an object is given by the formula W = m * g, where m is the mass and g is the acceleration due to gravity.
Given:
Mass of the balloon (m) = 18.0 kg
Acceleration due to gravity (g) = 9.8 m/s^2
Using the formula:
W = m * g,
W = 18.0 kg * 9.8 m/s^2,
W = 176.4 N.
Therefore, the weight of the balloon is 176.4 Newtons.
Step 2: Find the buoyant force (Fb):
The buoyant force on an object is given by the formula Fb = ρ * V * g, where ρ is the density of the fluid, V is the volume of the fluid displaced by the object, and g is the acceleration due to gravity.
Given:
Acceleration of the balloon (Anet) = 1.80 m/s^2
But the acceleration we know is the net acceleration, which is the difference between the upward buoyant force and the downward force of gravity.
Since the balloon is accelerating upward, the buoyant force is greater than the weight. So, we need to solve for the net buoyant force (Fb net):
Fb net = W - m * Anet,
Fb net = 176.4 N - (18.0 kg * 1.80 m/s^2),
Fb net = 176.4 N - 32.4 N,
Fb net = 144.0 N.
Therefore, the net buoyant force acting on the balloon is 144.0 Newtons.
Now, since the buoyant force is always equal to the weight of the fluid displaced by the object, the buoyant force is equivalent to the net buoyant force:
Fb = Fb net = 144.0 N.
Therefore, the buoyant force acting on the balloon is 144.0 Newtons.