Question

Calculate A \(0.14-\mathrm{kg}\) pinecone is \(16 \mathrm{~m}\) above the ground. What is its gravitational potential energy?

Short answer

The gravitational potential energy is 21.95 J.

Step-by-step solution

Understanding the Problem

We need to find the gravitational potential energy (GPE) of a pinecone that is 16 meters above the ground and has a mass of 0.14 kg. Gravitational potential energy is given by the formula \[ GPE = m \cdot g \cdot h \]where \( m \) is mass, \( g \) is the acceleration due to gravity (approximated as \( 9.8 \ m/s^2 \)), and \( h \) is height.

Substituting the Values

Substitute the provided values into the formula. For the pinecone mass \( m = 0.14 \ kg \), \( g = 9.8 \ m/s^2 \), and \( h = 16 \ m \):\[ GPE = 0.14 \ kg \times 9.8 \ m/s^2 \times 16 \ m \]

Calculating the GPE

Perform the calculation by multiplying the values together:\( 0.14 \times 9.8 = 1.372 \).Then, multiply this result by the height:\( 1.372 \times 16 = 21.952 \).

Rounding the Result

Round the resulting gravitational potential energy value to two decimal places for precision. Thus, \[ GPE = 21.95 \ J \].

Key concepts

Physics Problem-Solving

When it comes to physics problem-solving, the key is to break down the question into manageable parts. In the case of calculating gravitational potential energy, start by identifying what is given: mass, height, and the constant of gravity. Follow these steps:

• Understand the question: Here, identify what needs to be calculated - the gravitational potential energy of a pinecone.
• Know the formula: The formula for gravitational potential energy is \( GPE = m \cdot g \cdot h \).
• Substitute the values: Place provided values into the formula. For example, here \( m = 0.14 \ kg \), \( h = 16 \ m \), and \( g = 9.8 \ m/s^2 \).
• Calculate step by step: Multiply the mass by gravitational acceleration, then by the height.
• Round your answer appropriately: This ensures that your answer is not only correct but also presented neatly.

By following these steps systematically, physics problems become less daunting and more approachable.

Acceleration Due to Gravity

Acceleration due to gravity, denoted as \( g \), is a fundamental concept in physics. It describes the rate at which objects accelerate towards the Earth due to gravitational pull.
This value is approximately \( 9.8 \ m/s^2 \) on Earth.

• Uniformity of g: Accelerations can vary slightly based on location due to Earth's shape and rotation, but \( 9.8 \ m/s^2 \) is standard for calculation purposes.
• Effect on objects: This constant affects all objects in free fall equally, regardless of their mass.
• In the formula: In the potential energy formula \( GPE = m \cdot g \cdot h \), \( g \) helps determine the energy associated with an object's position.

Understanding \( g \) helps students grasp why objects fall as they do, a foundational skill in physics.

Energy Calculation

Energy calculation involves understanding how energy is measured and converted. In our exercise, we find the potential energy a pinecone has based on its height above the ground.
Potential energy tells us how much work an object can potentially do due to its position.

• Gravitational Potential Energy: This form of energy increases with height and mass. It's calculated using \( GPE = m \cdot g \cdot h \).
• Unit of measurement: The result, in Joules, is a unit of energy. So, when the pinecone is dropped, it would eventually convert this energy into other forms like kinetic.
• Importance in calculations: Gravitational potential energy helps in understanding concepts like energy conservation and energy transition from potential to kinetic.

Energy calculations often provide insight into broader physics concepts such as systems in equilibrium, energy conservation, and physical work.

Physics Education

Physics education equips students with a framework to understand the natural world through principles and laws. It requires developing strong problem-solving skills and understanding of core concepts like energy and gravity.
Here's how these concepts are often taught:

• Conceptual understanding: Rather than relying solely on memorization, students are encouraged to understand the 'why' and 'how' behind formulas and phenomena.
• Hands-on learning: Experiments and real-life applications make learning engaging — like dropping objects to calculate potential energy.
• Mathematical skill development: Students improve their mathematical reasoning by working with formulas and solving physics problems.
• Interdisciplinary learning: Physics often combines knowledge from math, engineering, and technology, showing students the interconnectedness of scientific principles.

A strong foundation in physics education not only fosters curiosity and analytical skills but also empowers students to apply their knowledge in everyday situations.