Final answer:
To convert 60 J/m to a system with 10 cm, 100 g, and 1 min as units, we need to use the conversion factor for joules in terms of the new base units. After converting to g·cm²/min², we find that 60 J/m is equal to 16666.8 g·cm/min² in the new system.
Step-by-step explanation:
To find the value of 60 J/m in a system with fundamental units of 10 cm, 100 g, and 1 min, we need to convert joules to the equivalent units in the given system, which has a base unit of energy of g⋅cm2/min2. First, we need to convert the known joule value into the base units. Since 1 J is equivalent to 1 kg⋅m2/s2, we need to express this in terms of 100 g (1 kg = 1000 g), 10 cm (1 m = 100 cm), and 1 min (1 min = 60 s).
To convert, we have:
- 1 J = 1 kg⋅m2/s2 = (1000 g)⋅(100 cm)2/(60 s)2
- 1 J = 1000000 g⋅cm2/3600 s2
- 1 J = 1000000/3600 g⋅cm2/min2
- 1 J = 277.78 g⋅cm2/min2
Now, to find the value of 60 J/m in the new system, we multiply 60 by the conversion factor for J to the new energy unit:
60 J/m × (277.78 g·cm2/min2)/(1 J) × (1 m / 100 cm) = 16666.8 g·cm/min2