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

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Chapter1: Units, Trigonometry. And Vectors
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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 \(|\Delta U|\).
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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