Question

how many dyne are equivalent to 15 kgf? calculate by using using the method of dimensional analysis.

Answer 1

Force = mass * acceleration. 1Newton =1kg*1m/s^2
1Dyne = 1g*1cm/s^2 
Work is force * distance => dyne * distance has units of 25gcm/s^2 * cm (distance) 
So that will be 25gcm^2/s^2 
Now multiply by conversion factors which remember all have a magnitude of 1 
25gcm^2/s^2 * (1kg/1000g)(1m/100cm)(1m/100cm) 
Notice the the grams cancel because I have one in the numerator and one in the denominator, leaving kg. Notice that the cm^2 cancel because I have cm^2 in the denominator, leaving m^2 
I also have 1000*100*100 = 10^7 in the denominator which is 10^-7 in the numerator 
So 25gcm^2/s^2 = 25*10^-7kgm^2/s^2