Question 1) (KB.5) Convert: (A) 300 Lb.Ft To N.M, (B) 450 Lb/Ft3 To KN/M3, (C) 8 Ft/H To Mm/S. (10 Points) Question 2) (KB.5) If A Man Weights 200 Lb On Earth, Specify (A) His Mass In Slugs, (B) His Mass In Kilograms, And (C) His Weight In Newton. If The Man Is On The Moon, Where The Acceleration Due To Gravity Is Gm = 5.30 Ft/S?, Determine (D) His Weight In
The Correct Answer and Explanation is :
Question 1
Let’s work through the unit conversions for the first question step by step.
(A) Convert 300 Lb.Ft to N.M:
1 Lb.Ft (pound-foot) is equal to 1.35582 Newton-meters (N.m).
So, we can calculate as:
[
300 \, \text{Lb.Ft} \times 1.35582 \, \text{N.m/Lb.Ft} = 406.746 \, \text{N.m}
]
Thus, 300 Lb.Ft is approximately 406.75 N.m.
(B) Convert 450 Lb/Ft³ to kN/m³:
1 Lb/Ft³ is equal to 16.0185 kg/m³, and since 1 kg = 9.81 N, we get:
[
450 \, \text{Lb/Ft}^3 \times 16.0185 \, \text{kg/m}^3 = 7208.325 \, \text{kg/m}^3
]
Now convert kg to N/m³ (multiply by 9.81):
[
7208.325 \, \text{kg/m}^3 \times 9.81 \, \text{N/kg} = 70,717.28 \, \text{N/m}^3
]
Finally, convert to kN/m³ (divide by 1000):
[
70,717.28 \, \text{N/m}^3 \div 1000 = 70.717 \, \text{kN/m}^3
]
Thus, 450 Lb/Ft³ is approximately 70.72 kN/m³.
(C) Convert 8 Ft/H to mm/s:
To convert, we start by converting feet to millimeters and hours to seconds. There are 304.8 mm in a foot, and 3600 seconds in an hour.
[
8 \, \text{Ft/H} = 8 \times 304.8 \, \text{mm/3600 s} = \frac{2438.4}{3600} \, \text{mm/s}
]
[
8 \, \text{Ft/H} \approx 0.678 \, \text{mm/s}
]
Thus, 8 Ft/H is approximately 0.678 mm/s.
Question 2
Now, let’s calculate the answers for the second question.
(A) Man’s Mass in Slugs:
Weight (in pounds) = Mass (in slugs) × Gravity (in ft/s²). On Earth, gravity is 32.174 ft/s².
The weight of the man on Earth is 200 lb, so:
[
\text{Mass in slugs} = \frac{200 \, \text{lb}}{32.174 \, \text{ft/s}^2} = 6.21 \, \text{slugs}
]
Thus, the man’s mass is approximately 6.21 slugs.
(B) Man’s Mass in Kilograms:
We know 1 slug = 14.5939 kg. Therefore:
[
6.21 \, \text{slugs} \times 14.5939 \, \text{kg/slug} = 90.5 \, \text{kg}
]
So, the man’s mass is approximately 90.5 kg.
(C) Man’s Weight in Newtons on Earth:
1 lb = 4.44822 N, so:
[
200 \, \text{lb} \times 4.44822 \, \text{N/lb} = 889.644 \, \text{N}
]
Thus, the man’s weight on Earth is approximately 889.64 N.
(D) Man’s Weight on the Moon:
On the Moon, the acceleration due to gravity is 5.30 ft/s², so we calculate the weight using the formula:
[
\text{Weight} = \text{Mass in slugs} \times \text{Gravity on the Moon}
]
[
\text{Weight on the Moon} = 6.21 \, \text{slugs} \times 5.30 \, \text{ft/s}^2 = 32.87 \, \text{lb}
]
To convert this to Newtons, multiply by 4.44822:
[
32.87 \, \text{lb} \times 4.44822 \, \text{N/lb} = 146.32 \, \text{N}
]
Thus, the man’s weight on the Moon is approximately 146.32 N.
Summary Explanation:
In these questions, we perform unit conversions between commonly used units in physics, such as pounds to Newtons and feet to meters. For the second question, we also apply the concept of weight and mass and use the relationship between them (where weight = mass × acceleration due to gravity). By using specific conversion factors, we can calculate the mass in slugs and kilograms and then convert the weight from pounds to Newtons, considering the different gravitational accelerations on Earth and the Moon.
Let me now generate an image that summarizes these conversions for visual clarity.
Here is the educational diagram illustrating the unit conversions and calculations for both questions. It includes the conversions for pounds to Newton-meters, pounds per cubic foot to kiloNewtons per cubic meter, and feet per hour to millimeters per second, as well as the weight and mass conversions for the man on Earth and the Moon. Let me know if you need further clarifications!