ball is released from a height of 12 m and weighs 35 N. What is the magnitude |AU| of the total change in potential ene en the ball falls to the ground? UT
ball is released from a height of 12 m and weighs 35 N. What is the magnitude |AU| of the total change in potential ene en the ball falls to the ground? UT
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![**Problem Statement:**
A ball is released from a height of 12 meters and weighs 35 newtons. What is the magnitude \(|\Delta U|\) of the total change in potential energy when the ball falls to the ground?
**Answer Box:**
\(|\Delta U|\) [J]
**Explanation:**
This question asks for the calculation of the change in potential energy as a ball is released from a certain height until it hits the ground. The following concepts will help in understanding:
- **Gravitational Potential Energy (\(U\))**: This is calculated using the formula \(U = m \cdot g \cdot h\), where \(m\) is the mass, \(g\) is the gravitational acceleration (\(9.81 \ \text{m/s}^2\) on Earth), and \(h\) is the height.
- **Change in Potential Energy (\(\Delta U\))**: This is the difference between the initial and final potential energies. Since the ball falls to the ground, the final potential energy is zero.
To find \(|\Delta U|\), the magnitude of the change in potential energy, use:
1. Initial potential energy \(U_i = m \cdot g \cdot h\).
2. Final potential energy \(U_f = 0\).
3. \(|\Delta U| = |U_f - U_i|\).
Since \(U_f = 0\), \(|\Delta U| = U_i\).
Given:
- Height (\(h\)) = 12 m
- Weight (force due to gravity, \(m \cdot g\)) = 35 N
Plug these into the equation to solve for \(|\Delta U|\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9081bc6b-9817-477c-9b8d-7c2dcc8c93d8%2F9942d78c-7064-4e3a-be76-b5ab4446a9e2%2Fgqzcwo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A ball is released from a height of 12 meters and weighs 35 newtons. What is the magnitude \(|\Delta U|\) of the total change in potential energy when the ball falls to the ground?
**Answer Box:**
\(|\Delta U|\) [J]
**Explanation:**
This question asks for the calculation of the change in potential energy as a ball is released from a certain height until it hits the ground. The following concepts will help in understanding:
- **Gravitational Potential Energy (\(U\))**: This is calculated using the formula \(U = m \cdot g \cdot h\), where \(m\) is the mass, \(g\) is the gravitational acceleration (\(9.81 \ \text{m/s}^2\) on Earth), and \(h\) is the height.
- **Change in Potential Energy (\(\Delta U\))**: This is the difference between the initial and final potential energies. Since the ball falls to the ground, the final potential energy is zero.
To find \(|\Delta U|\), the magnitude of the change in potential energy, use:
1. Initial potential energy \(U_i = m \cdot g \cdot h\).
2. Final potential energy \(U_f = 0\).
3. \(|\Delta U| = |U_f - U_i|\).
Since \(U_f = 0\), \(|\Delta U| = U_i\).
Given:
- Height (\(h\)) = 12 m
- Weight (force due to gravity, \(m \cdot g\)) = 35 N
Plug these into the equation to solve for \(|\Delta U|\).
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