Problem 7-62 Energy cons. with friction - Part 5 - C

A pen of mass \(0.057 \;kg\) is sliding across a horizontal desk. In sliding \(25 \;cm\), its speed decreases to \(5.7 \;cm/s\). What was its initial speed if the force of kinetic friction exerted on the pen by the desk is \(0.15\; N\) in magnitude? Use conservation of energy.

FBD with all forces and directions indicated.

Accumulated Solution

\(E_K = (1/2)mv^2 \\ \text{Work against friction} = F_K \Delta x\)

Correct.

\(\text {Work against friction} = F_K \Delta x\)

Which statement is correct?

(A)   \((1/2)mv_0{^2}  = (1/2)mv^2 +  F_K \Delta x\)

(B)   \((1/2)mv_0{^2}  = (1/2)m^2 -  F_K \Delta x\)

(C)   \((1/2)mv_0{^2}  = (1/2)mv^2\)