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

`-0.5mv^2`

Step-by-step 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.=(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`