Question

1. predict: which objects do you think will float in water? which do you think will sink? record your predictions below in the first column of the table.

object	prediction (sink or float?)	mass (g)	volume (cm³)	result (sink or float?)
golf ball	sink
apple	float
chess piece	float
penny	float
rock	sink

Explanation:

To solve this problem, we analyze the density of each object (density = mass/volume) and compare it with the density of water (1 g/cm³). Objects with density less than 1 g/cm³ float, and those with density greater than 1 g/cm³ sink.

Step 1: Ping pong ball

• Prediction: Sink (but actually, ping pong balls are hollow and have low density, so they float. Maybe the prediction here is initial guess).
• Mass: Typically around 2.7 g.
• Volume: Approx 33.5 cm³ (sphere volume formula \( V = \frac{4}{3}\pi r^3 \), radius ~2 cm).
• Density: \( \frac{2.7}{33.5} \approx 0.08 \) g/cm³ < 1 g/cm³ → Float (Result).

Step 2: Golf ball

• Prediction: Sink (golf balls are dense, solid core).
• Mass: Around 45 g.
• Volume: Approx 22 cm³ (sphere, radius ~1.7 cm).
• Density: \( \frac{45}{22} \approx 2.05 \) g/cm³ > 1 g/cm³ → Sink (Result).

Step 3: Apple

• Prediction: Float (apples have air pockets, density ~0.8 g/cm³).
• Mass: Around 100 g.
• Volume: Approx 100 cm³ (since density ~1, but apples are less dense).
• Density: \( \frac{100}{100} = 1 \) (but actual ~0.8) → Float (Result).

Step 4: Chess piece

• Prediction: Float (if wooden, density <1; if plastic, also low).
• Mass: Around 10 g.
• Volume: Approx 10 cm³ (if wooden, density 1, but chess pieces are often hollow or light).
• Density: \( \frac{10}{10} = 1 \) (but likely <1) → Float (Result).

Step 5: Penny

• Prediction: Float (initial guess, but pennies are dense).
• Mass: 2.5 g (US penny, zinc core, copper plating).
• Volume: Approx 0.36 cm³ (cylinder, radius ~0.95 cm, thickness ~0.15 cm, \( V = \pi r^2 h \)).
• Density: \( \frac{2.5}{0.36} \approx 6.94 \) g/cm³ > 1 g/cm³ → Sink (Result, correction from prediction).

Step 6: Rock

• Prediction: Sink (rocks are dense, density >1).
• Mass: Around 100 g.
• Volume: Approx 40 cm³ (density ~2.5 g/cm³, \( V = \frac{m}{

ho} = \frac{100}{2.5} = 40 \)).

• Density: \( \frac{100}{40} = 2.5 \) g/cm³ > 1 g/cm³ → Sink (Result).

Final Table (Filled with Typical Values)

Object	Prediction	Mass (g)	Volume (cm³)	Result
Golf ball	Sink	45	22	Sink
Apple	Float	100	100	Float
Chess piece	Float	10	10	Float
Penny	Float	2.5	0.36	Sink
Rock	Sink	100	40	Sink

Key Explanation:

Floating depends on density relative to water (1 g/cm³). Objects with density <1 float, >1 sink. Initial predictions may be wrong (e.g., penny), but results follow density.

Answer:

To solve this problem, we analyze the density of each object (density = mass/volume) and compare it with the density of water (1 g/cm³). Objects with density less than 1 g/cm³ float, and those with density greater than 1 g/cm³ sink.

Step 1: Ping pong ball

• Prediction: Sink (but actually, ping pong balls are hollow and have low density, so they float. Maybe the prediction here is initial guess).
• Mass: Typically around 2.7 g.
• Volume: Approx 33.5 cm³ (sphere volume formula \( V = \frac{4}{3}\pi r^3 \), radius ~2 cm).
• Density: \( \frac{2.7}{33.5} \approx 0.08 \) g/cm³ < 1 g/cm³ → Float (Result).

Step 2: Golf ball

• Prediction: Sink (golf balls are dense, solid core).
• Mass: Around 45 g.
• Volume: Approx 22 cm³ (sphere, radius ~1.7 cm).
• Density: \( \frac{45}{22} \approx 2.05 \) g/cm³ > 1 g/cm³ → Sink (Result).

Step 3: Apple

• Prediction: Float (apples have air pockets, density ~0.8 g/cm³).
• Mass: Around 100 g.
• Volume: Approx 100 cm³ (since density ~1, but apples are less dense).
• Density: \( \frac{100}{100} = 1 \) (but actual ~0.8) → Float (Result).

Step 4: Chess piece

• Prediction: Float (if wooden, density <1; if plastic, also low).
• Mass: Around 10 g.
• Volume: Approx 10 cm³ (if wooden, density 1, but chess pieces are often hollow or light).
• Density: \( \frac{10}{10} = 1 \) (but likely <1) → Float (Result).

Step 5: Penny

• Prediction: Float (initial guess, but pennies are dense).
• Mass: 2.5 g (US penny, zinc core, copper plating).
• Volume: Approx 0.36 cm³ (cylinder, radius ~0.95 cm, thickness ~0.15 cm, \( V = \pi r^2 h \)).
• Density: \( \frac{2.5}{0.36} \approx 6.94 \) g/cm³ > 1 g/cm³ → Sink (Result, correction from prediction).

Step 6: Rock

• Prediction: Sink (rocks are dense, density >1).
• Mass: Around 100 g.
• Volume: Approx 40 cm³ (density ~2.5 g/cm³, \( V = \frac{m}{

ho} = \frac{100}{2.5} = 40 \)).

• Density: \( \frac{100}{40} = 2.5 \) g/cm³ > 1 g/cm³ → Sink (Result).

Final Table (Filled with Typical Values)

Object	Prediction	Mass (g)	Volume (cm³)	Result
Golf ball	Sink	45	22	Sink
Apple	Float	100	100	Float
Chess piece	Float	10	10	Float
Penny	Float	2.5	0.36	Sink
Rock	Sink	100	40	Sink

Key Explanation:

Floating depends on density relative to water (1 g/cm³). Objects with density <1 float, >1 sink. Initial predictions may be wrong (e.g., penny), but results follow density.