Answer to Question #102208 in Other for Kampamba

Question #102208
If the units of force, energy and velocity in a new system are 10N, 5J and 0.5m/s respectively ,find the units of mass ,length and time in that system
1
Expert's answer
2020-02-03T08:33:36-0500

"[Energy] = [Force]\\times [length]"

Units of energy:

"1J= 1N\\times m"


"[velocity] = \\frac{[lenght]}{[time]}"

Units of velocity:

"m\/s=\\frac{m}{s}"


"[Force ] = [mass] \\times[acceleration] = \\frac{[mass]\\times[velocity]}{[time]}= \\frac{[mass]\\times[length]}{[time]^2}"

Units of Force:

"1N = \\frac{1kg\\times m}{s^2}"


Obviously we can express length through force and energy

"[length] = \\frac{[Energy]}{[Force]}"

Unit of length = unit of energy divide by unit of force

"\\frac{5J}{10N}= \\frac{5N\\times m}{10N}=0.5m"


"[time] = \\frac{[length]}{[velocity]}"

Unit of time= unit of velocity divide by unit of length

"\\frac{0.5 m}{0.5\\frac{m}{s}} = 1s"


"[mass] =\\frac{[Force]\\times[time]^2}{[length]}"

"\\frac{10N\\times s^2}{0.5m}=\\frac{20{kg\\times m}\\times s^2}{m\\times s^2}= 20 kg"


Units of length 0.5 meters

Units of time 1 second

Units of mass 20 kilograms


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