Question

A hot air balloon weighing 30 N is tied to the ground by a string to prevent it from floating off the ground. The volume of the balloon is 20 m³, and the density of air is 1.3 kg/m³. a) What is the upthrust acting on the balloon? Take g = 10 m/s². b) What is the force exerted by the rope on the balloon?

Answer 1

The upthrust acting on the hot air balloon is calculated as 260 N using the given volume, air density, and gravity. The force exerted by the rope on the balloon is the tension, which is determined by subtracting the weight of the balloon (30 N) from the upthrust, resulting in a tension of 230 N.

Step-by-step explanation:

To answer the student's question regarding the forces acting on a hot air balloon:

Part A: Calculating Upthrust

To calculate the upthrust (buoyant force) on the balloon, we use Archimedes' principle, which states that the upthrust is equal to the weight of the air displaced by the balloon. The formula to calculate the upthrust is:

Upthrust = Volume of balloon × Density of air × g

Here, the volume of the balloon is given as 20 m³, the density of air is 1.3 kg/m³, and g (acceleration due to gravity) is 10 m/s². Therefore, we can calculate the upthrust as:

Upthrust = 20 m³ × 1.3 kg/m³ × 10 m/s² = 260 N.

Part B: Force Exerted by the Rope

The force exerted by the rope on the balloon is the tension in the rope. This force is the difference between the upthrust and the weight of the balloon. Thus, the tension (T) can be calculated as:

Tension = Upthrust - Weight of the balloon

Tension = 260 N - 30 N = 230 N.

Note: If there are any other external forces acting on the balloon, such as wind, they would also need to be accounted for in the total force exerted by the rope.