Question

A baseball player slides into third base with an initial speed of 4.0 m/s. If the coefficient of

kinetic friction between the player and the ground is 0.46, how far does the player slide
before coming to rest?

Answer 1

The frictional force is given by F = μmg

where μ is the coeficient of friction.

Work done by frictional force = Fd = μmgd

Kinetic energy "lost" = 1/2 mv²

Since we know that W = ΔK,

so, Fd = μmgd = 1/2 mv²

The m's cancel μgd = v² / 2

d = v² / 2μg

d = 4² / 2(0.46)(9.81)

d = 16 / 2(0.46)(9.81)

d = 1.77

Player slides 1.77 m .

Answer 2

The frictional force is given by F = μmg

where μ is the coeficient of friction.

Work done by frictional force = Fd = μmgd

Kinetic energy "lost" = 1/2 mv²


Fd = μmgd = 1/2 mv²

The m's cancel μgd = v² / 2



d = v² / 2μg

d = 8² / 2(0.41)(9.8)

d = 32 / (0.41)(9.8)

d = 7.96

Player slides 8 m .



Note. In your other example μ = 0.46 and v = 4 m/s



d = v² / 2μg




= 4² / 2(0.46)(9.8)

= 8 / (0.46)(9.8)

= 1.77 or 1.8 m.

Hope i Helped :D