# Baseball vs Bowling Ball: Kinetic Energy, Speed, and Work Let's analyze the two scenarios using physics concepts. --- ## (i) Which Has Greater Speed? ### **Given:** - Both the baseball and bowling ball have the **same kinetic energy** (\( KE \)). ### **Kinetic Energy Formula:** \[ KE = \frac{1}{2}mv^2 \] where \( m \) = mass of object \( v \) = speed of object ### **Let:** - \( m_b \), \( v_b \): mass and speed of baseball - \( m_{bb} \), \( v_{bb} \): mass and speed of bowling ball - \( KE_b = KE_{bb} \) ### **Set Up Equation:** \[ \frac{1}{2}m_b v_b^2 = \frac{1}{2}m_{bb} v_{bb}^2 \] \[ m_b v_b^2 = m_{bb} v_{bb}^2 \] \[ \frac{v_b^2}{v_{bb}^2} = \frac{m_{bb}}{m_b} \] \[ \frac{v_b}{v_{bb}} = \sqrt{\frac{m_{bb}}{m_b}} \] ### **Analysis:** - **Bowling ball** has much greater mass (\( m_{bb} \gg m_b \)) than a baseball. - Therefore, \( v_b > v_{bb} \). - **Conclusion:** **The baseball must have a greater speed** to have the same kinetic energy as the much heavier bowling ball. --- ## (ii) Which Requires More Work to Stop? ### **Work-Energy Principle:** - The **work required to stop** an object is equal to the **kinetic energy it has**. \[ W = KE \] ### **Given:** - Both have the same kinetic energy. ### **Conclusion:** - **Both require the same work to stop**, because they both have the same kinetic energy. --- ## **Summary Table** | Object | Speed | Work to Stop | |----------------|-------------------|------------------| | Baseball | Greater | Same | | Bowling Ball | Smaller | Same | --- ## **Final Answers** 1. **The baseball has the greater speed.** 2. **Both require the same amount of work to stop.**