Question

A marble of mass m rolls with initial speed v down a long, horizontal hallway. Eventually, the marble comes to a stop. How much work has friction performed on the marble?

-mv2

mv2

0.5mv2

-0.5mv2

Answer 1

Answer:

$-0.5mv^2$

Explanation:

Given:

Mass of marble =$m$

Initial velocity of marble = $v$

Final velocity of marble = 0 as it comes to rest.

By work energy theorem:

Work done by forces acting on marble is given by :

Work done = Final Kinetic energy - Initial Kinetic energy

Kinetic energy can be calculate using formula:

$K.E.=\frac{1}{2}mv^2=0.5mv^2$

where $m$ represents mass of body and $v$ represents velocity of body.

Final kinetic energy:

$K.E.=0.5m(0)^2=0$

Initial kinetic energy

$K.E.=0.5m(v)^2=0.5mv^2$

Work done by friction on the marble $=0-0.5mv^2=-0.5mv^2$