How much gravitational potential energy is gained by a cat of mass 1016 g when it climbs up a tree to a branch that is 6.8 m above the ground. Give your answer to the nearest whole number.

Question

BlackTom AI · Accepted Answer

Gravitational potential energy is given by ΔPE = m g h.

1. Relevant knowledge points and concepts
- Gravitational potential energy (GPE) change for raising an object vertically: ΔPE = mgh, where m is mass in kilograms, g is acceleration due to gravity (≈ 9.8 m/s^2), and h is height in meters.
- Units: mass must be in kg for standard SI units; energy will be in joules (J).

2. Step-by-step reasoning
- Convert the cat’s mass from grams to kilograms.
- Substitute m, g, and h into ΔPE = mgh.
- Compute the product and round to the nearest whole number.

3. Calculations with intermediate steps
- Mass conversion: 1016 g = 1016 / 1000 = 1.016 kg.
- Use g = 9.8 m/s^2 and h = 6.8 m.
- Compute g × h: 9.8 × 6.8 = 66.64.
- Multiply by mass: ΔPE = 1.016 × 66.64 = 67.70624 J.

4. Why this answer is correct
- The formula mgh applies directly because the cat is raised vertically against uniform gravity with no information about additional forces or energy losses. Using SI units yields energy in joules. The computed value 67.70624 J represents the increase in gravitational potential energy; rounding to the nearest whole number gives 68 J.

5. (Multiple-choice note) Why other numerical answers would be incorrect
- Any answer that fails to convert grams to kilograms (for example using 1016 as kg) would produce a value ~1000 times too large.
- Using an incorrect height or g value without justification would change the product and lead to an incorrect rounded result. Both g = 9.8 and g = 9.81 give nearly the same rounded result (≈68 J).

6. Conclusion
- The gravitational potential energy gained is approximately 67.70624 J, which rounds to 68 J. This confirms the provided answer: 68.

How much gravitational potential energy is gained by a cat of mass 1016 g when it climbs up a tree to a branch that is 6.8 m above the ground. Give your answer to the nearest whole number.Numerical

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