Question

(A) how much work is done when you push a crate horizontally with 100 N across a 10-m factory floor?

Answer 1

Answer:

A) 1000 joules

Explanation:

In general work is given by the equation:

$W=\intop_{a}^{b}\overrightarrow{F}\cdot d\overrightarrow{s}$ (1)

A) With $\overrightarrow{s}$ the displacement and $\overrightarrow{F}$ the force applied, because the force and the displacement are parallel (the crate is pushed horizontally) $\overrightarrow{F}\cdot d\overrightarrow{s}$ is simply $F\,ds$, and because the path is a straight line and the force is constant work is:

$W=FS$ (2),

$W=(100)(10)=1000\,J$

B) The work-energy theorem says that the total work on a body is equal to the change on kinetic energy:

$W_{tot}=\varDelta K$ (3)

The total work on the crate is the work done by the push and plus the work of the friction $W_{tot}=W + W_{f}$ (4) , as (A) because forces are parallel to the displacement $W= FS$ (5) and $W_{f}=-fS$ (6), the due friction always has negative sign because is opposite to the displacement, using (6), (5) and (4) on (3):

$FS-fS=\varDelta K$ (3)

$1000-(70)(10)=300\,J$

C) The energy is lost by friction, so the amount of energy turned into heat is the work the friction does:

$Q=fS=(70)(100)=700\,J$ (3)