The work done by friction is -560 J
Explanation:
According to the work-energy theorem, the work done by the force of friction on the runner is equal to his change in kinetic energy. Therefore:
[tex]W=\frac{1}{2}mv^2-\frac{1}{2}mu^2[/tex]
where
W is the work done by friction
m is the mass of the runner
v is his final velocity
u is the initial velocity
Here we have:
m = 70 kg is the mass
u = 4 m/s is the initial velocity
v = 0 is the final velocity
Solving for W,
[tex]W=0-\frac{1}{2}(70)(4)^2=-560 J[/tex]
And the sign is negative because the direction of the force of friction is opposite to the motion of the runner.
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