Answer:
A) 1000 joules
Explanation:
In general work is given by the equation:
[tex]W=\intop_{a}^{b}\overrightarrow{F}\cdot d\overrightarrow{s} [/tex] (1)
A) With [tex] \overrightarrow{s} [/tex] the displacement and [tex] \overrightarrow{F} [/tex] the force applied, because the force and the displacement are parallel (the crate is pushed horizontally) [tex] \overrightarrow{F}\cdot d\overrightarrow{s}[/tex] is simply [tex] F\,ds[/tex], and because the path is a straight line and the force is constant work is:
[tex] W=FS [/tex] (2),
[tex] W=(100)(10)=1000\,J[/tex]
B) The work-energy theorem says that the total work on a body is equal to the change on kinetic energy:
[tex] W_{tot}=\varDelta K[/tex] (3)
The total work on the crate is the work done by the push and plus the work of the friction [tex]W_{tot}=W + W_{f} [/tex] (4) , as (A) because forces are parallel to the displacement [tex] W= FS [/tex] (5) and [tex] W_{f}=-fS[/tex] (6), the due friction always has negative sign because is opposite to the displacement, using (6), (5) and (4) on (3):
[tex]FS-fS=\varDelta K [/tex] (3)
[tex]1000-(70)(10)=300\,J [/tex]
C) The energy is lost by friction, so the amount of energy turned into heat is the work the friction does:
[tex]Q=fS=(70)(100)=700\,J [/tex] (3)
