Compare the efficiencies of a ramp that uses 2,000 joules of energy to do 1,200 joules of work and a lever that uses 102 kJ of energy to do 98 kJ of work and identify the machine with the higher efficiency.
To compare the efficiencies of the ramp and the lever, we need to use the formula for efficiency:
Efficiency = (Useful output energy / Input energy) * 100
Let's calculate the efficiency for both the ramp and the lever.
For the ramp:
Input energy = 2,000 joules
Useful output energy = 1,200 joules
Efficiency of the ramp = (1,200 / 2,000) * 100 = 60%
For the lever:
Input energy = 102 kJ = 102,000 joules
Useful output energy = 98 kJ = 98,000 joules
Efficiency of the lever = (98,000 / 102,000) * 100 = 96.08%
Comparing the two efficiencies, we can see that the lever has a higher efficiency (96.08%) compared to the ramp (60%). Therefore, the lever is more efficient in converting input energy into useful work.
To compare the efficiencies of the ramp and the lever, we can use the efficiency formula:
Efficiency = (Work Output / Energy Input) * 100%
For the ramp:
Work Output = 1,200 joules
Energy Input = 2,000 joules
Efficiency (ramp) = (1,200 joules / 2,000 joules) * 100%
= 0.6 * 100%
= 60%
For the lever:
Work Output = 98 kJ (kilojoules = 1,000 joules)
Energy Input = 102 kJ
Efficiency (lever) = (98 kJ / 102 kJ) * 100%
= 0.96 * 100%
= 96%
Comparing the efficiencies, we can see that the lever has the higher efficiency (96%) compared to the ramp (60%).