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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

Respuesta :

Answer:

[tex]-0.5mv^2[/tex]

Explanation:

Given:

Mass of marble =[tex]m[/tex]

Initial velocity of marble = [tex]v[/tex]

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:

[tex]K.E.=\frac{1}{2}mv^2=0.5mv^2[/tex]

where [tex]m[/tex] represents mass of body and [tex]v[/tex] represents velocity of body.

Final kinetic energy:

[tex]K.E.=0.5m(0)^2=0[/tex]

Initial kinetic energy

[tex]K.E.=0.5m(v)^2=0.5mv^2[/tex]

Work done by friction on the marble [tex]=0-0.5mv^2=-0.5mv^2[/tex]

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