by Unit conversion is a crucial aspect of physics, engineering, and scientific calculations, ensuring consistency and accuracy across different measurement systems. This article provides a fast and reliable method to convert 0.4 gram-centimeter per second (g·cm/s) to meganewton-minute (MN·min) in a step-by-step manner.
Units
Before proceeding with the conversion, it’s essential to understand the involved units:
- Gram-Centimeter per Second (g·cm/s):
This is a unit of momentum, where:- 1 gram (g) = 0.001 kilograms (kg)
- 1 centimeter (cm) = 0.01 meters (m)
- Momentum (p) is given as mass × velocity
- Meganewton-Minute (MN·min):
- 1 meganewton (MN) = 10⁶ newtons (N)
- 1 minute = 60 seconds
Thus, the goal is to express 0.4 g·cm/s in MN·min by converting mass and distance units appropriately.
Stepwise Conversion Process
Step 1: Convert g·cm/s to kg·m/s
Since: 1 g=0.001 kg,1 cm=0.01 m1 \text{ g} = 0.001 \text{ kg}, \quad 1 \text{ cm} = 0.01 \text{ m}1 g=0.001 kg,1 cm=0.01 m 0.4 g\cdotpcm/s=0.4×(0.001 kg)×(0.01 m/s)0.4 \text{ g·cm/s} = 0.4 \times (0.001 \text{ kg}) \times (0.01 \text{ m/s})0.4 g\cdotpcm/s=0.4×(0.001 kg)×(0.01 m/s) =0.000004 kg\cdotpm/s= 0.000004 \text{ kg·m/s}=0.000004 kg\cdotpm/s
Step 2: Convert kg·m/s to N·s
By Newton’s Second Law: 1 N=1 kg\cdotpm/s21 \text{ N} = 1 \text{ kg·m/s}^21 N=1 kg\cdotpm/s2
Thus, in terms of impulse: 1 N\cdotps=1 kg\cdotpm/s1 \text{ N·s} = 1 \text{ kg·m/s}1 N\cdotps=1 kg\cdotpm/s
So, 0.000004 kg\cdotpm/s=0.000004 N\cdotps0.000004 \text{ kg·m/s} = 0.000004 \text{ N·s}0.000004 kg\cdotpm/s=0.000004 N\cdotps
Step 3: Convert N·s to N·min
Since 1 minute = 60 seconds: 0.000004 N\cdotps×60=0.00024 N\cdotpmin0.000004 \text{ N·s} \times 60 = 0.00024 \text{ N·min}0.000004 N\cdotps×60=0.00024 N\cdotpmin
Step 4: Convert N·min to MN·min
Since 1 MN = 10⁶ N, we divide by 10610^6106: 0.00024 N\cdotpmin=2.4×10−10 MN\cdotpmin0.00024 \text{ N·min} = 2.4 \times 10^{-10} \text{ MN·min}0.00024 N\cdotpmin=2.4×10−10 MN\cdotpmin
Final Result
0.4 g\cdotpcm/s=2.4×10−10 MN\cdotpmin\boxed{0.4 \text{ g·cm/s} = 2.4 \times 10^{-10} \text{ MN·min}}0.4 g\cdotpcm/s=2.4×10−10 MN\cdotpmin
Conclusion
Converting gram-centimeter per second to meganewton-minute involves careful unit transformation. Using a systematic approach, we determined that 0.4 g·cm/s is equivalent to 2.4×10−102.4 \times 10^{-10}2.4×10−10 MN·min.
This conversion technique is essential in high-precision calculations across physics, mechanical engineering, and material sciences, ensuring accuracy in momentum and impulse-related problems.
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