A 66-kg base runner begins his slide into second base when he is moving at a speed of 3.4 m/s. The coefficient of friction between his clothes and Earth is 0.70. He slides so that his speed is zero just as he reaches the base (a) How much mechanical energy is lost due to friction acting on the runner. (b) How far does he slide?

a) = 381.48 J

b) = 84.25 cm

Explanation:

Kinetic energy of the runner

= 1/2 m v²

=.5 x 66 x 3.4²

= 381.48 J

The final kinetic energy of the runner is zero.

Loss of mechanical energy

= 381.48 J

This loss in mechanical energy is due to action of frictional force.

b)

Let s be the distance of slide

deceleration due to frictional force

= μmg/m

.7 x 66 x 9.8 / 66

a = - 6.86 m s⁻¹

v² = u² - 2 a s

0 = 3.4² - 2x6.86 s

s = 3.4² / 2x6.86

=.8425 m

84.25 cm