Why does work equals kinetic energy of friction?

[zzoo4]

Why does work equals kinetic energy of friction??

Homework Statement

After hitting a long fly ball that goes over the right fielder’s
head and lands in the outfield, the batter decides to keep going
past second base and try for third base. The 62.0-kg player begins sliding 3.40 m from the base with a speed of 4.35 m/s. If
the player comes to rest at third base, (a) how much work was
done on the player by friction?

Homework Equations

w=fd
ke=.5mv^2

The Attempt at a Solution

I already know how to do this but

KE= .5X6.2x4.35^2 = -587J

But Why do we use Kinetic energy equation to find the work of friction?

 

[aftershock]

Energy can't be created or destroyed. Friction basically produces heat energy. In order to get this heat energy we need to take it from somewhere else, like kinetic energy.

Energy is the ability to do work so in your problem the work done by friction is equal to the loss of kinetic energy of the baseball player.

 

[vela]

Homework Equations

w=fd
ke=.5mv^2

The Attempt at a Solution

I already know how to do this but

KE= .5X6.2x4.35^2 = -587J

How did you get a negative answer when multiplying a bunch of positive numbers?

But Why do we use Kinetic energy equation to find the work of friction?

The work-energy theorem says $\Delta KE=W$. What's ΔKE for the batter?

 

[zzoo4]

Tyyyy

 

[asteriatic]

I would explain that the work of friction is equal to the kinetic energy because friction is a force that acts in the opposite direction of motion. When the player is sliding towards third base, friction is acting against their motion, causing them to slow down and eventually come to a stop. This means that the force of friction is doing negative work on the player, taking away their kinetic energy and converting it into other forms of energy, such as heat. The amount of work done by friction is equal to the change in the player's kinetic energy, as given by the equation KE = 0.5mv^2. Therefore, we can use this equation to calculate the work of friction in this situation.