A 60 kg bicyclist going 2 m/s increased his work output by 1,800 J. What was his final velocity? The final velocity of the bicyclist is 3 m/s.
When a 60 kg bicyclist going 2 m/s increased his work output by 1,800 J, the final velocity achieved was 3 m/s. This change in velocity can be understood through basic principles of physics. Let’s delve deeper into the concepts involved in this scenario.
Understanding Work and Energy
Work: In physics, work is defined as the amount of energy transferred by a force acting through a distance. Mathematically, work (W) is calculated as the product of the force (F) applied in the direction of motion and the distance (d) over which the force is applied.
Energy: Energy is a scalar quantity that is associated with motion, position, or the interactions of a system. In this case, we are dealing with mechanical energy and, more specifically, kinetic energy the energy an object possesses due to its motion.
WorkEnergy Theorem: The workenergy theorem states that the work done on an object is equal to the change in its kinetic energy. This theorem allows us to relate the amount of work done on an object to the resulting change in its velocity.
Applying Physics Principles to the Scenario
To determine the final velocity of the bicyclist after increasing his work output by 1,800 J, we can use the workenergy theorem to establish a relationship between the initial and final kinetic energies of the system.
Initial Kinetic Energy (KEi):
The initial kinetic energy of the bicyclist is given by the formula:
\[ KE_i = \frac{1}{2}mv_i^2 \]
Substituting the known values:
\[ KE_i = \frac{1}{2}(60 \, kg)(2 \, m/s)^2 = 120 \, J \]
Final Kinetic Energy (KEf):
The final kinetic energy of the bicyclist is calculated as:
\[ KE_f = KE_i + W \]
Given that the work done (W) is 1,800 J:
\[ KE_f = 120 \, J + 1800 \, J = 1920 \, J \]
Final Velocity Calculation:
The final velocity (vf) can be determined using the formula for kinetic energy:
\[ KE_f = \frac{1}{2}mv_f^2 \]
Rearranging the formula to solve for the final velocity:
\[ v_f = \sqrt{\frac{2KE_f}{m}} \]
Substituting the values:
\[ v_f = \sqrt{\frac{2(1920 \, J)}{60 \, kg}} = \sqrt{64} = 8 \, m/s \]
Conclusion
In conclusion, by applying the workenergy theorem and the principles of kinetic energy, we have determined that the final velocity of the 60 kg bicyclist who increased his work output by 1,800 J is 8 m/s. This increase in velocity showcases the direct relationship between work done on an object and its resulting kinetic energy and motion. Physics allows us to unravel the mysteries of motion and energy, providing insights into the fundamental laws governing our physical world.
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