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mmh One ounce of a well-known breakfast cereal contains 110 Calories (1 food Calorie 4186 J). If 2.0% of this energy could be converted by a weight lifter’s body into work done in lifting a barbell, what is the heaviest barbell that could be lifted a distance of 2.1 m?

Short Answer

Expert verified
The heaviest barbell is approximately 449.5 kg.

Step by step solution

01

Calculate Energy in Joules

First, we need to convert the Calories in the cereal into Joules. We know that 1 Calorie equals 4186 Joules. Thus, \[ E = 110 \times 4186 = 460460 \text{ J} \].
02

Determine Usable Energy for Work

We are given that only 2.0% of this energy is converted into work. Therefore, the usable energy is \( 0.02 \times 460460 = 9209.2 \text{ J} \).
03

Calculate the Work Done

The work done lifting the barbell is given by the formula \( W = mgh \), where \( m \) is the mass, \( g \) is the acceleration due to gravity \( (9.8 \text{ m/s}^2) \), and \( h \) is the height lifted (2.1 m).
04

Set Usable Energy to Work Done Formula

Using the work done formula, set \( W = 9209.2 \text{ J} \). Therefore, \[ 9209.2 = m \times 9.8 \times 2.1 \].
05

Solve for Mass

Rearrange to find \( m \): \[ m = \frac{9209.2}{9.8 \times 2.1} \approx 449.5 \text{ kg} \].

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Calories to Joules
To understand the energy involved in lifting a barbell, we first need to convert Calories, a common food energy unit, into Joules, the standard metric unit for measuring energy.
One food Calorie is equivalent to 4186 Joules. When converting Calories to Joules, simply multiply the number of Calories by 4186.
For instance, if a breakfast cereal contains 110 Calories, the energy content is calculated as follows:
  • Energy in Joules: \( 110 \times 4186 = 460460 \text{ J} \)
Understanding this conversion is essential for calculating the potential energy transformations that occur within the body or during physical activities.
Work Done Formula
The concept of work in physics is tied to energy transfer. Specifically, it is the energy transferred to an object when a force moves it over a distance. The formula for work done is given by:
  • \( W = mgh \)
where:
  • \( W \) is the work done
  • \( m \) is the mass of the object
  • \( g \) is the acceleration due to gravity \( (9.8 \text{ m/s}^2) \)
  • \( h \) is the height the object is lifted
Essentially, this formula helps you calculate the amount of energy used (or work done) while lifting an object vertically. By understanding how work is calculated, you can determine energy expenditure in any activity involving vertical movement.
Acceleration Due to Gravity
A key component in the physics of lifting objects is gravity, which exerts a force on objects pulling them towards the earth’s center. This force is characterized by the acceleration due to gravity, typically denoted as \( g \), and approximated as \( 9.8 \text{ m/s}^2 \).
Gravity’s constancy means that for each kilogram of mass, an object experiences a force of approximately 9.8 Newtons downward.
This predictable force is crucial in calculating work done during lifting, allowing us to compute the exact force needed to overcome gravitational pull at a given height. Using \( g \) ensures our calculations for work or energy are accurate and consistent across different scenarios.
Energy Efficiency in Biomechanics
When discussing energy efficiency in physical activities, it is vital to understand how efficiently the human body converts consumed energy into work.
In biomechanics, energy efficiency refers to the percentage of energy intake that translates into actual physical work. Due to various physiological processes, the human body is not 100% efficient.
In the provided exercise, only 2% of the consumed energy is used effectively to lift a barbell, which is a typical reflection of energy conversion efficiency in human muscles during physical exertion.
Improving energy efficiency can enhance performance in sports and daily activities, making such calculations valuable for athletes and fitness enthusiasts alike.

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