Work= Force x Distance
Example: How much work is exerted to lift a 1.5 kg box from the floor onto a table that is 1.2 meters tall?
Using acceleration due to gravity 9.8 m/s2, find Force.
Force= mass x acceleration = 1.5x9.8= 14.7 N
Using the equation W=Force x Distance, find work.
Work= 14.7 x 1.2 = 17.64 Joules
Hooke's Law: f(x)= kx where k is the spring constant and x is the amount the spring is stretched beyond its length at rest
Example: A force of 35 N is exerted to keep a spring stretched 5 cm beyond its natural length. How much work is required to stretch the spring 3 cm more?
Solution: We know from Hooke's Law that the force needed to maintain a spring stretched x metres beyond the length at rest is f(x)= kx.
5cm=0.05m So 35=0.05k
Therefore k= 35/0.05= 700
Now we have f(x)=700x
The work required to stretch 3 cm more becomes:
W= ∫0.080.05700xdx= 700 (x2/2) from 0.05 to 0.08=
* Back to Integral Calculus