A 55 kg softball player slides into second base, generating 950 J of thermal energy in her legs and the ground. How fast was she running?

Verified step by step guidance

1. Identify the type of energy conversion involved. In this case, the kinetic energy of the player is converted into thermal energy due to friction as she slides into the base.
2. Use the formula for kinetic energy, which is given by \( KE = \frac{1}{2}mv^2 \), where \( m \) is the mass of the player and \( v \) is the velocity.
3. Set the kinetic energy equal to the thermal energy generated, since the kinetic energy is converted entirely into thermal energy. Thus, \( \frac{1}{2}mv^2 = 950 \, \text{J} \).
4. Substitute the mass of the player into the equation. Here, \( m = 55 \, \text{kg} \).
5. Solve the equation \( \frac{1}{2} \times 55 \times v^2 = 950 \) for \( v \), the velocity of the player. This will give you the speed at which she was running before sliding.

Key Concepts

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion, calculated using the formula KE = 1/2 mv², where m is mass and v is velocity. In this scenario, the softball player's kinetic energy is converted into thermal energy during the slide, which is essential for determining her speed before the slide.

Conservation of Energy

The principle of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. In this case, the kinetic energy of the player is transformed into thermal energy as she slides, allowing us to relate the thermal energy generated to her initial speed.

Work-Energy Principle

The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. When the player slides into second base, the work done by friction between her legs and the ground results in the generation of thermal energy, which can be quantified to find her initial running speed.