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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

User Odd
by
7.2k points

1 Answer

3 votes

Answer:


-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

User Rahul Bansal
by
8.9k points