A blimp is filled with 380 m3 of helium. How big a payload (in kg) can the blimp lift? (The density of air is 1.29 kg/m3 and the density of helium is 0.18 kg/m3)
A blimp is filled with 380 m3 of helium. How big a payload (in kg) can the blimp lift? (The density of air is 1.29 kg/m3 and the density of helium is 0.18 kg/m3)
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![**Problem Statement:**
A blimp is filled with 380 m³ of helium. How big a payload (in kg) can the blimp lift?
**Given:**
- The density of air is 1.29 kg/m³.
- The density of helium is 0.18 kg/m³.
**Solution Overview:**
To solve this problem, we need to determine the buoyant force acting on the blimp, which can be used to lift a payload. The buoyant force is equal to the weight of the air displaced by the helium. The net lift of the blimp is the difference between the weight of the displaced air and the weight of the helium.
**Step-by-Step Calculation:**
1. Calculate the weight of the air displaced:
\[
\text{Weight of displaced air} = \text{Volume} \times \text{Density of air} = 380 \, \text{m}^3 \times 1.29 \, \text{kg/m}^3
\]
2. Calculate the weight of the helium:
\[
\text{Weight of helium} = \text{Volume} \times \text{Density of helium} = 380 \, \text{m}^3 \times 0.18 \, \text{kg/m}^3
\]
3. Calculate the net lift (buoyant force - weight of helium):
\[
\text{Net lift} = \text{Weight of displaced air} - \text{Weight of helium}
\]
This net lift represents the maximum payload the blimp can support.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F53de9b21-b783-4351-a637-bc1fa6100b57%2F252ae9ac-e019-4135-add8-9c53df1c76aa%2Fszj9gfl_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A blimp is filled with 380 m³ of helium. How big a payload (in kg) can the blimp lift?
**Given:**
- The density of air is 1.29 kg/m³.
- The density of helium is 0.18 kg/m³.
**Solution Overview:**
To solve this problem, we need to determine the buoyant force acting on the blimp, which can be used to lift a payload. The buoyant force is equal to the weight of the air displaced by the helium. The net lift of the blimp is the difference between the weight of the displaced air and the weight of the helium.
**Step-by-Step Calculation:**
1. Calculate the weight of the air displaced:
\[
\text{Weight of displaced air} = \text{Volume} \times \text{Density of air} = 380 \, \text{m}^3 \times 1.29 \, \text{kg/m}^3
\]
2. Calculate the weight of the helium:
\[
\text{Weight of helium} = \text{Volume} \times \text{Density of helium} = 380 \, \text{m}^3 \times 0.18 \, \text{kg/m}^3
\]
3. Calculate the net lift (buoyant force - weight of helium):
\[
\text{Net lift} = \text{Weight of displaced air} - \text{Weight of helium}
\]
This net lift represents the maximum payload the blimp can support.
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