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9. The force of friction acts upon a baseball player as he slides into third base.

Ask by Ward Montgomery. in the United States
Mar 10,2025

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The force of friction slows down the baseball player as he slides into third base by doing negative work, reducing his kinetic energy.

Solución

1. We first note that friction opposes the motion of the player. When the player slides into third base, his velocity is directed along his motion, and the force of friction acts in the opposite direction. 2. The kinetic friction force is given by \[ f_k = \mu_k N \] where \(\mu_k\) is the coefficient of kinetic friction and \(N\) is the normal force. For a player on a horizontal field, the normal force is \[ N = mg, \] with \(m\) being the mass of the player and \(g\) the acceleration due to gravity. 3. Because friction acts opposite to the displacement, the work \(W\) done by friction over a displacement \(d\) is \[ W = f_k d \cos(180^\circ) = -f_k d. \] Substituting for \(f_k\) we obtain \[ W = -\mu_k mgd. \] The negative value indicates that friction removes energy from the system (i.e., it does negative work). 4. According to the work-energy theorem, the net work done on the player is equal to the change in his kinetic energy: \[ \Delta KE = W_{\text{net}}. \] Since the work done by friction is negative, it reduces the player’s kinetic energy, slowing him down as he slides. Thus, the key takeaway is that the force of friction does negative work, reducing the kinetic energy of the sliding baseball player as he comes to a stop at third base.

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Bonus Knowledge

Did you know that friction is actually what helps players maintain control during a slide? As a player slides into a base, the force of friction between their uniform and the ground creates resistance, allowing them to slow down and reduce the risk of injury. It's all about that perfect blend of speed and technique! When approaching a slide, it's crucial for players to lead with their body weight while keeping their feet up to avoid injury and friction burns. A common mistake is to slap the ground too hard, which can send them tumbling or losing momentum. Instead, a graceful, controlled slide ensures a vying chance for a safe arrival at the base!

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