A 60 kg Bicyclist’s Final Velocity Calculation
A 60 kg bicyclist going 2 m/s increased his work output by 1,800 J. What was his final velocity? m/s
Understanding the Scenario
In this scenario, we are given the following information about the bicyclist: Initial mass (m₁): 60 kg Initial velocity (v₁): 2 m/s Added work output (ΔW): 1,800 J
The final velocity (v₂) of the bicyclist after the work output increase needs to be calculated.
Applying the WorkEnergy Principle
To determine the final velocity, we can utilize the workenergy principle, which states that the work done on an object is equal to the change in its kinetic energy.
The work done on the bicyclist can be expressed as: \[ W = ΔKE \]
Given that the kinetic energy (KE) of an object is given by: \[ KE = 0.5 \times m \times v^2 \]
Calculating the Change in Kinetic Energy
- Initial Kinetic Energy (KE₁):
\( KE₁ = 0.5 \times 60 kg \times (2 m/s)^2 \) \( KE₁ = 120 J \)
- Final Kinetic Energy (KE₂):
We can express the final kinetic energy in terms of the final velocity (v₂): \( KE₂ = 0.5 \times 60 kg \times v₂^2 \)
Determining the Work Done
Given that the work output increased by 1,800 J, we can equate this to the change in kinetic energy: \[ W = KE₂ KE₁ \] \[ 1,800 J = KE₂ 120 J \]
Solving for the Final Velocity
By substituting the expressions for kinetic energy into the work done equation: \[ 1,800 J = 0.5 \times 60 kg \times v₂^2 120 J \]
- Isolating the Final Velocity Term:
\( 1,800 J + 120 J = 0.5 \times 60 kg \times v₂^2 \) \( 1,920 J = 30 kg \times v₂^2 \)
- Calculating the Final Velocity:
\( v₂^2 = \frac{1,920 J}{30 kg} = 64 \) \( v₂ = \sqrt{64} = 8 m/s \)
Conclusion
Therefore, the final velocity of the 60 kg bicyclist after increasing his work output by 1,800 J is 8 m/s. This significant increase in velocity showcases the direct relationship between work done on an object and its resulting kinetic energy and speed.
