Question

At the 2004 Olympic Games in Athens, Greece, the Iranian athlete Hossein Rezazadeh won the super-heavyweight class gold medal in weightlifting. He lifted \(472.5 \mathrm{~kg}(1042 \mathrm{lb})\) combined in his two best lifts in the competition. Assuming that he lifted the weights a height of \(196.7 \mathrm{~cm}\), what work did he do?

Short answer

Answer: Hossein Rezazadeh did approximately \(9110.063125 \mathrm{J}\) of work to lift the weights.

Step-by-step solution

Convert the mass to weight

First, we need to find the weight of the 472.5 kg of lifted weights. Weight is given by the formula: \(W = mg\) where W is the weight, m is the mass, and g is the acceleration due to gravity, which is approximately \(9.81 \mathrm{m/s^2}\). Plug in the given mass: \(W = (472.5 \mathrm{kg})(9.81 \mathrm{m/s^2})\) \(W = 4631.075 \mathrm{N}\) The weight of the lifted weights is \(4631.075 \mathrm{N}\).

Calculate the work done

Now, we calculate the work done by the athlete using the formula: \(W = F × d × cos(\theta)\) Here, F is the force (weight of the lifted weights), d is the distance (height lifted), and \(\theta\) is the angle between the force and the distance. Since the weights were lifted straight up, the angle is 0 degrees, making \(cos(\theta) = 1\). Plug in the values for F, d, and \(cos(\theta)\): \(W =(4631.075 \mathrm{N})(1.967 \mathrm{m})(1)\) \(W = 9110.063125 \mathrm{J}\) Therefore, Hossein Rezazadeh did approximately \(9110.063125 \mathrm{J}\) of work to lift the weights during his winning lifts at the 2004 Olympic Games.

Key concepts

Work-Energy Principle

When we examine the physics behind Hossein Rezazadeh's Olympic weightlifting feat, we apply the work-energy principle, which is a fundamental concept connecting force, displacement, and energy. The work-energy principle states that the work done by all forces acting on an object is equal to the change in its kinetic energy. In our scenario, the kinetic energy of the weights starts at zero (since they are not moving before the lift), and when lifted off the ground, work is done against gravity.

Work is calculated by the equation:
\[ W = F \times d \times cos(\theta) \]
where W is the work done, F is the force applied, d is the displacement (how far the weights are lifted), and \( cos(\theta) \) accounts for the angle between the force and the direction of displacement. For weights lifted vertically, \( \theta = 0 \) degrees, and as in Rezazadeh's case, \( cos(0) = 1 \), meaning the force is applied in the same direction as the displacement. The work done to lift the weight, therefore, directly translates to gravitational potential energy.

In simpler terms, the work-energy principle helps us understand how Rezazadeh's effort, measured in joules (J), transformed into the potential energy of the weights in their raised position.

Force and Motion

The spectacle of an Olympian lifting weights is a prime example of force and motion in action. In physics, force is defined as an interaction that causes an object to change its velocity, its direction, or both. In the context of the exercise, the force applied by the athlete moves the weights from a stationary position on the ground to a certain height above it.

The weights are acted upon by two primary forces: the muscular force exerted by Rezazadeh's body and the opposing gravitational force exerted by Earth, which we commonly term as weight. The weight of an object is the product of its mass and the acceleration due to gravity \( (g) \), with a value of approximately \( 9.81 m/s^2 \) on Earth's surface. Upon exerting a force greater than the gravitational force, the athlete sets the weights into upward motion, evidencing Newton's second law of motion: \( F = ma \), where F is the force, m is the mass, and a is the acceleration.

Taken together, these concepts help students understand not just how Rezazadeh lifted the weights, but why he needed to apply a specific amount of force to achieve his gold-medal-winning lift.

Units of Measurement

Understanding units of measurement is crucial in physics as they provide the building blocks for quantifying and discussing different physical quantities. In our exercise, the key units are kilograms (kg) for mass, meters (m) for distance, and newtons (N) for weight (which, curiously, in physics is a force).

To calculate work (energy), which in the SI (International System of Units) is measured in joules (J), we need to understand how these units interact. One joule is equivalent to the work done by a force of one newton moving an object one meter in the direction of the force. The precise conversion helps us transform Hossein Rezazadeh's effort in the gym into a numerical value that we can analyze and appreciate.

These units are interconnected in physics equations. For example, when Rezazadeh's lifting performance is calculated, mass must first be converted into a weight (force) by multiplying by the acceleration due to gravity (g in m/s^2), yielding a force measured in newtons. When we speak of the weights moved by the athlete, we distinguish between their mass (kg) and their weight (N) due to Earth's gravity, before finally computing the work done as lifting that weight over a distance (J). Clear usage of each unit is imperative to avoid confusion, ensuring precise calculations and a better grasp of the physical phenomena being studied.