Problem 2 - Physics for Scientists and Engineers with Modern Physics

Question

(I) A 6.0-kg monkey swings from one branch to another \(1.3 \mathrm{~m}\) higher. What is the change in gravitational potential energy?

Step-by-Step Solution

Answer

The change in gravitational potential energy is \( 76.44 \mathrm{~J} \).

Step 1: Identify the Known Values

We are given that the mass of the monkey, \( m = 6.0 \) kg, and the height difference, \( h = 1.3 \) m. The acceleration due to gravity, \( g \), is \( 9.8 \mathrm{~m/s^2} \).

Step 2: Understand Gravitational Potential Energy Formula

The change in gravitational potential energy (GPE) can be determined using the formula: \( \Delta U = mgh \).

Step 3: Substitute the Known Values

Replace \( m \), \( g \), and \( h \) with the known values in the formula: \( \Delta U = 6.0 \times 9.8 \times 1.3 \).

Step 4: Calculate the Change in Gravitational Potential Energy

Perform the multiplication: \( \Delta U = 6.0 \times 9.8 \times 1.3 = 76.44 \mathrm{~J} \). The change in gravitational potential energy is \( 76.44 \mathrm{~J} \).

Key Concepts

Physics Problem Solving

Physics problem solving involves understanding the concepts and principles that govern physical phenomena. It requires analyzing given problems and applying relevant formulas to find solutions. When faced with a physics problem like finding the change in gravitational potential energy, follow these steps:

• First, identify what is known and what needs to be calculated. This helps in organizing information and targeting the required outcomes.
• Next, recall and apply the appropriate physics formulas. Double-check if these formulas are suitable for the given problem scenario.
• Plug in the known values into the formula and perform the necessary calculations.
• Lastly, always check your units and make sure your solutions make sense in the context of the problem.

Being methodical in solving a physics problem ensures systematic and accurate results. You can practice these skills with a variety of problems to improve your proficiency.

Potential Energy Formula

Gravitational Potential Energy (GPE) is a form of energy related to the position of an object in a gravitational field. To find the change in potential energy, you can use the formula:\[ \Delta U = mgh \]Where:

• \( m \) is the mass of the object, measured in kilograms (kg).
• \( g \) is the acceleration due to gravity. On the surface of the Earth, this is approximately \( 9.8 \, \mathrm{m/s^2} \).
• \( h \) is the change in height in meters (m).

This formula calculates the energy change resulting from a change in height of an object. For example, when a monkey swings to a higher branch, it gains potential energy owing to its elevated position relative to the ground. The product of the object's mass, gravity, and height gives a quantitative measure of this energy change. This concept is crucial not only for understanding energy changes in physics but also in practical applications, such as engineering and architecture.

Educational Physics

Educational physics aims to make learning physics intuitive and engaging for students. It involves breaking down complex concepts, like gravitational potential energy, into simpler, digestible parts. The use of practical examples, such as calculating the energy change of a swinging monkey, helps in creating relatable scenarios that aid learning. Here are some tips to enhance understanding in educational physics:

• Connect physics theories to real-world experiences. This bridges the gap between abstract concepts and tangible understanding.
• Use visual aids, such as diagrams or animations, to illustrate how forces and energy work in different situations.
• Encourage interactive activities that allow students to experiment with physics principles, providing a hands-on learning experience.
• Apply repetitive practice sessions with varied examples, which reinforce learning and recall.

The goal of educational physics is to create a foundation of knowledge that students can build upon. By engaging with topics creatively and contextually, students can develop a stronger grasp of physics principles.