How Far Will a Box Slide Before Stopping on a Frictional Surface?

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To determine how far a 25 kg box slides before stopping on a frictional surface, the force of friction and kinetic energy are calculated using the coefficient of friction (0.15) and the box's speed (12 m/s). The force of friction is derived from the coefficient and the normal force, while kinetic energy is calculated as 1/2 * mass * velocity squared. The distance the box travels before stopping is found by dividing the kinetic energy by the force of friction, confirming that the calculations are correct. The work done by friction equals the kinetic energy, validating the approach taken. This method effectively demonstrates the relationship between kinetic energy and frictional work in determining stopping distance.
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1. Determine the distance it takes for a 25 kg box to stop sliding if it has a speed of 12m/s on a surface with a coefficient of friction of 0.15.



2. W=F*d
Coefficient of friction = Force of friction/Normal Force
Kinetic energy = 1/2*m*v^2



3. With the mass and the coefficient of friction, I got the force of friction.
With the mass and velocity, I got the kinetic energy.
Then I divided the Kinetic energy by the force of friction because the Newton's would cancel out and I would be left with meters.

Is this the right solution? I checked the answer in the back and it is correct but I'm not sure if this was just a coincidence.
 
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The Kinetic Energy is equal to the work that the friction force must do to stop the box. Since W=Fd, the distance that box travels is d=W/F. So yes, you did it correctly.
 

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