Video Transcript
A body of mass 0.9 kilograms moved
a distance of 25 centimeters, while accelerating at eight centimeters per second
squared. Find the work done 𝑊 in ergs.
Let’s begin by recalling what we
mean by work done. Well, work is a measure of energy
transfer when a force 𝐹 moves an object through a distance 𝑑. We say that work done is equal to
this force multiplied by this distance. However, we do need to be careful
with our units as work done is generally calculated in joules. This is a result of using a force
calculated in newtons and a distance measured in meters. Sometimes as in this case, however,
we measure the work done in ergs. This relates to a force measured in
dynes and a distance measured in centimeters. In this question, we’ve been given
a distance measured in centimeters, so 𝑑 is equal to 25 centimeters. We haven’t been given a value of
the force though. So our first step will be to
calculate this.
We will do this using Newton’s
second law, which states that force is equal to mass multiplied by acceleration. And if we’re looking for a value of
the force in dynes, the mass must be measured in grams and the acceleration in
centimeters per second squared. Our mass is given in kilograms. And since there are 1000 grams in a
kilogram, we can multiply this value by 1000 to find the mass in grams. 0.9 multiplied by 1000 is 900. So the mass of the body is 900
grams. The acceleration of the body is
given in the required unit: 𝑎 is equal to eight centimeters per second squared.
To calculate the force 𝐹, we
multiply 900 by eight. And this is equal to 7200. The force acting on the body is
equal to 7200 dynes. We are now in a position to
calculate the work done 𝑊. It is equal to 7200 multiplied by
25. And this is equal to 180000. We can therefore conclude that the
work done 𝑊 is equal to 180000 ergs. Whilst this is a perfectly valid
solution, we might choose to represent this using standard index form, in which case
we see that the work done on the body is 1.8 multiplied by 10 to the fifth power
ergs.
