The instruments attached to a weather balloon in the figure below have a mass(m) of 5.0 kg. The balloon is released and exerts an upward force(F) of 92 N on the instruments.

F = ma = 92 N,

5a = 92,
a = 92 / 5 =18.4 m/s

17.77

To determine the weight(W) of the instruments, use the equation:

W = m * g,

where m is the mass and g is the acceleration due to gravity.

Given that the mass of the instruments is 5.0 kg, we can substitute this value into the equation:

W = 5.0 kg * g.

To calculate the acceleration due to gravity, we can use the standard value of 9.8 m/s²:

W = 5.0 kg * 9.8 m/s².

Calculating the weight of the instruments gives:

W = 49.0 N.

Therefore, the weight of the instruments attached to the weather balloon is 49.0 N.

To understand how the force exerted by the balloon on the instruments can be calculated, we need to consider the concept of buoyancy.

When a balloon filled with gas is released, it rises upwards due to the difference in density between the gas inside the balloon and the surrounding air. This upward force is known as buoyant force.

According to Archimedes' principle, the buoyant force exerted on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. In this case, the fluid is air, and the object is the balloon filled with gas and the attached instruments.

So, the buoyant force (F_buoyant) acting on the balloon is equal to the weight of the air displaced by the balloon. This buoyant force is acting in the opposite direction to the force exerted by the balloon on the instruments.

Therefore, we can write the equation:

F_buoyant = F_balloon - F_gravity

Where:
F_buoyant = Buoyant force
F_balloon = Force exerted by the balloon on the instruments
F_gravity = Weight of the instruments

Given that the force exerted by the balloon on the instruments is 92 N and the mass of the instruments is 5.0 kg, we can find the weight of the instruments using the formula:

F_gravity = m * g

Where:
m = Mass of the instruments
g = Acceleration due to gravity (approximately 9.8 m/s^2)

Plugging in the values, we have:

F_gravity = 5.0 kg * 9.8 m/s^2

Calculating F_gravity, we find:

F_gravity = 49 N

Now we can substitute the values back into the initial equation:

F_buoyant = 92 N - 49 N

Simplifying further:

F_buoyant = 43 N

Therefore, the buoyant force acting on the instruments is 43 N.