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.数值题

类似问题

Consider the following function: def PE(m, h): g = 9.81 E = m * g * h return E What is the value of d to the nearest integer after running the following commands? d = PE(5,5)

What is the gravitational potential energy of an object located 32 000m above the Earth’s Surface?

What is the gravitational potential energy of an object located 32 000m above the Earth’s Surface?

A 430 g soccer ball is 8.7 m above the ground. How much gravitational energy does it have? Give your answer to the nearest whole number.

Where is the potential energy the greatest?

What is gravitational potential energy?

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.

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单