A particle is moving in a straight line under the action of a force of 685 dynes acting in the direction of motion. Find the work 𝑤 in ergs done by the force over a displacement of 390 centimeters. Take the acceleration due to gravity 𝑔 to be equal to 9.8 meters per square second.
We recall that work is the measure of energy transfer when a force 𝐹 moves an object through a distance 𝑑. The formula we use is work done is equal to force multiplied by distance. We do need to be a little bit careful with the units we use though. Work done is often measured in joules. This corresponds to a force measured in newtons and a distance measured in meters. Sometimes though, we might choose to measure the work done in ergs. This corresponds to a force measured in dynes and a distance measured in centimeters.
Note, though, we’re looking to calculate the work in ergs and we have the force in dynes and the displacement or distance in centimeters. And so we can simply apply the formula 𝑤 equals 685 times 390. That gives us 267150 ergs or 267000 ergs, correct to three significant figures. We might then choose to write this in standard index form. Work done is 2.67 times 10 to the fifth power ergs.