Introduction
In the world of physics, speed is a crucial concept that helps us understand the movement of objects in our universe. One key equation that ties together speed, work, and energy is the workenergy principle. This principle states that the work done on an object is equal to the change in its kinetic energy. In this article, we will explore this principle through a realworld scenario involving a bicyclist and his work output.
Understanding the Scenario
Imagine a 60 kg bicyclist cruising along at a speed of 2 m/s. Suddenly, he decides to pedal harder and increase his work output by 1,800 J. The question arises: what will be his final velocity after this increase in work?
Applying the WorkEnergy Principle
To solve this problem, we can utilize the workenergy principle, which states that the work done on an object is equal to the change in its kinetic energy. Mathematically, this can be represented as:
\[W = ΔKE\]
Where: W = Work done on the object (in Joules) ΔKE = Change in kinetic energy (in Joules)
Given that the work output has increased by 1,800 J, we can substitute this value into the equation:
\[1,800 J = ΔKE\]
Calculating the Change in Kinetic Energy
The change in kinetic energy can also be expressed as the difference between the final kinetic energy (KE_final) and the initial kinetic energy (KE_initial):
\[ΔKE = KE_final KE_initial\]
Given that kinetic energy is directly proportional to the square of velocity, we can represent KE as:
\[KE = 0.5 * m * v^2\]
Where: m = Mass of the object (in kg) v = Velocity of the object (in m/s)
Finding the Initial Kinetic Energy
Initially, the bicyclist was moving at a speed of 2 m/s. We can calculate his initial kinetic energy using the formula:
\[KE_initial = 0.5 * 60 kg * (2 m/s)^2 = 120 J\]
Determining the Final Velocity
Now that we know the initial kinetic energy and the change in kinetic energy, we can find the final kinetic energy using the equation:
\[1,800 J = KE_final 120 J\] \[KE_final = 1,920 J\]
To calculate the final velocity, we can rearrange the formula for kinetic energy and solve for velocity:
\[KE_final = 0.5 * 60 kg * v^2\] \[1,920 J = 0.5 * 60 kg * v^2\] \[v^2 = \frac{1,920 J}{30 kg}\] \[v^2 = 64\] \[v = \sqrt{64} = 8 m/s\]
Conclusion
In conclusion, by applying the workenergy principle and the concept of kinetic energy, we were able to determine that the 60 kg bicyclist’s final velocity after increasing his work output by 1,800 J would be 8 m/s. This calculation showcases the interplay between speed, work, and energy in a realworld scenario. Next time you see a cyclist speeding by, remember the physics behind their movement!
