What is the potential energy of a soccer ball given it's mass and height from the Earth's surface as depicted on the figure below? Provide your answer to three (3) significant figures and correct SI unit symbol must be provided.

Question

BlackTom AI · Accepted Answer

To find the potential energy (PE) of an object near Earth's surface, use the formula PE = m g h, where m is mass, g is acceleration due to gravity, and h is height above the reference point.

First, convert the given mass to kilograms: 430 grams equals 0.430 kg (since 1,000 g = 1 kg).

Next, identify the height from the figure: h = 7 metres.

Use g ≈ 9.81 m/s^2 (standard gravitational acceleration).

Compute the expression step by step:
- Multiply mass and gravity: m × g = 0.430 kg × 9.81 m/s^2 ≈ 4.2183 kg·m/s^2 (which is newtons, N).
- Now multiply by height: (m × g) × h = 4.2183 N × 7 m ≈ 29.5281 J.

Rounding to three significant figures and keeping the SI unit, the result is approximately 29.5 J.

Notes on potential sources of error or variation:
- If a different value for g is used (e.g., 9.8 m/s^2), the result would be very close: 0.430 × 9.8 × 7 ≈ 29.542 J, which still rounds to 29.5 J.
- Ensure mass is converted correctly (grams to kilograms) since using 430 g directly would give a larger, incorrect value.

In summary, PE = m g h = 0.430 kg × 9.81 m/s^2 × 7 m ≈ 29.5 J, with the unit joule (J).

Dashboard Quiz 3

What is the potential energy of a soccer ball given it's mass and height from the Earth's surface as depicted on the figure below? Provide your answer to three (3) significant figures and correct SI unit symbol must be provided.

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