Part B The tomato is dropped. What is the velocity, v, of the tomato when it hits the ground? Assume 91.9 % of the work done in Part A is transferred to kinetic energy, E, by the time the tomato hits the ground. Express your answer with the appropriate units.
Part B The tomato is dropped. What is the velocity, v, of the tomato when it hits the ground? Assume 91.9 % of the work done in Part A is transferred to kinetic energy, E, by the time the tomato hits the ground. Express your answer with the appropriate units.
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Part B
![**Understanding Energy through a Practical Example**
An object can have two primary types of energy: **kinetic energy**, the energy of motion, and **potential energy**, the energy of position. Energy transfer can occur in various ways, one of which is through work. Work, represented as \( w \), is the energy transferred when an object moves over a distance, \( d \), due to a force, \( F \).
Mathematically,
\[ w = Fd \]
*Force* is determined by the product of an object's mass, \( m \), and its acceleration, \( \alpha \):
\[ F = ma \]
When acceleration is due to gravity, we use \( g \) instead of \( \alpha \), where \( g = 9.81 \, \text{m} \cdot \text{s}^{-2} \).
---
**Part A: Calculating Work Done**
**Question:** How much work is done when a 125 g tomato is lifted 13.0 m?
To determine the work done, express your answer with appropriate units.
- **Solution:** \( w = 15.9 \, \text{J} \)
This indicates that 15.9 joules of energy is transferred to the tomato, increasing its potential energy as it is elevated above the ground.
---
**Kinetic Energy**
*Kinetic energy*, \( E_k \), is calculated using the formula:
\[ E_k = \frac{1}{2} mv^2 \]
where \( m \) is the mass in kilograms and \( v \) is the velocity in meters per second.
---
**Part B: Determining Velocity upon Impact**
**Scenario:** If the tomato is dropped, what is its velocity when it reaches the ground? Assume 91.9% of the work calculated in Part A is converted to kinetic energy, \( E_k \).
Provide your answer with appropriate units.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4a2bd348-d826-4056-b9ee-5fd404bc60f1%2Febd6711d-855b-47c0-8383-1861b568bb6e%2Fa95u3zg_processed.png&w=3840&q=75)
Transcribed Image Text:**Understanding Energy through a Practical Example**
An object can have two primary types of energy: **kinetic energy**, the energy of motion, and **potential energy**, the energy of position. Energy transfer can occur in various ways, one of which is through work. Work, represented as \( w \), is the energy transferred when an object moves over a distance, \( d \), due to a force, \( F \).
Mathematically,
\[ w = Fd \]
*Force* is determined by the product of an object's mass, \( m \), and its acceleration, \( \alpha \):
\[ F = ma \]
When acceleration is due to gravity, we use \( g \) instead of \( \alpha \), where \( g = 9.81 \, \text{m} \cdot \text{s}^{-2} \).
---
**Part A: Calculating Work Done**
**Question:** How much work is done when a 125 g tomato is lifted 13.0 m?
To determine the work done, express your answer with appropriate units.
- **Solution:** \( w = 15.9 \, \text{J} \)
This indicates that 15.9 joules of energy is transferred to the tomato, increasing its potential energy as it is elevated above the ground.
---
**Kinetic Energy**
*Kinetic energy*, \( E_k \), is calculated using the formula:
\[ E_k = \frac{1}{2} mv^2 \]
where \( m \) is the mass in kilograms and \( v \) is the velocity in meters per second.
---
**Part B: Determining Velocity upon Impact**
**Scenario:** If the tomato is dropped, what is its velocity when it reaches the ground? Assume 91.9% of the work calculated in Part A is converted to kinetic energy, \( E_k \).
Provide your answer with appropriate units.
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