Question

a 90-gram cap on a pitcher’s head; a 260-gram shoe on a pitcher’s foot; a 140-gram baseball hit over the pitcher’s head; a 2-gram piece of gum in the pitcher’s mouth; (chart with sections: greatest potential energy, least potential energy)

Explanation:

Potential energy (PE) is given by \( PE = mgh \), where \( m \) is mass, \( g \) is gravity, and \( h \) is height. To determine PE, we compare mass and height.

Step1: Analyze each object

• Cap (90g, on head): Moderate mass, moderate height.
• Shoe (260g, on foot): High mass, low height (foot is lower than head).
• Baseball (140g, over head): Moderate mass, high height (above head).
• Gum (2g, in mouth): Low mass, low height (mouth is near head level but very low mass).

Step2: Rank by PE

• Greatest PE: Baseball (140g, over head) – higher height than cap, and while shoe is more massive, baseball’s height is higher. \( PE \propto m \) and \( PE \propto h \); baseball’s \( m \times h \) is likely highest.
• Next: Cap (90g, on head) – moderate \( m \) and \( h \).
• Then: Shoe (260g, on foot) – high \( m \), low \( h \); \( m \times h \) less than baseball.
• Least PE: Gum (2g, in mouth) – very low \( m \), low \( h \); \( m \times h \) is lowest.

Answer:

• Greatest Potential Energy: A 140 - gram baseball hit over the pitcher’s head
• (Next: A 90 - gram cap on a pitcher’s head)
• (Then: A 260 - gram shoe on a pitcher’s foot)
• Least Potential Energy: A 2 - gram piece of gum in the pitcher’s mouth

(Note: The middle two (cap, shoe) can be ordered by calculating \( m \times h \) approximately. Assume head height ~1.5m, foot ~0.1m, over head ~2m, mouth ~1.4m.

• Cap: \( 90 \times 1.5 = 135 \)
• Shoe: \( 260 \times 0.1 = 26 \)
• Baseball: \( 140 \times 2 = 280 \)
• Gum: \( 2 \times 1.4 = 2.8 \)

So order: Baseball > Cap > Shoe > Gum)