A 57.5-kg skateboarder starts out with a speed of 1.80 m/s. He does +80.0 J of work on himself by pushing with his feet against the ground. In addition, friction does -265 J of work on him. In both cases, the forces doing the work are nonconservative. The final speed of the skateboarder is 6.20 m/s.
To find the change in kinetic energy of the skateboarder, we can use the work-energy principle. The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. Mathematically, it can be represented as:
Work = Change in Kinetic Energy
We are given the work done by the skateboarder on himself (+80.0 J) and the work done by friction (-265 J). We can assume that positive work increases the kinetic energy, while negative work decreases it.
So, the total work done on the skateboarder is the sum of the work done by the skateboarder on himself and the work done by friction:
Total Work = Work by the skateboarder + Work by friction
Total Work = +80.0 J + (-265 J)
Total Work = -185 J
Now that we have the total work done, we can equate it to the change in kinetic energy:
-185 J = Change in Kinetic Energy
Since the initial speed is 1.80 m/s and the final speed is 6.20 m/s, we can calculate the initial kinetic energy (K₁) and the final kinetic energy (K₂) using the formula:
Kinetic Energy (K) = 0.5 * mass * velocity²
Initial Kinetic Energy (K₁) = 0.5 * 57.5 kg * (1.80 m/s)²
Final Kinetic Energy (K₂) = 0.5 * 57.5 kg * (6.20 m/s)²
Now, we can find the change in kinetic energy:
Change in Kinetic Energy = K₂ - K₁
Substituting the values:
Change in Kinetic Energy = (0.5 * 57.5 kg * (6.20 m/s)²) - (0.5 * 57.5 kg * (1.80 m/s)²)
Simplifying the expression, we get:
Change in Kinetic Energy = 418.46 J - 92.34 J
Change in Kinetic Energy = 326.12 J
Since the total work done (-185 J) is equal to the change in kinetic energy (326.12 J), we can state it as:
-185 J = 326.12 J
This result seems incorrect because the work done by the skateboarder and the work done by friction should not cancel out completely. Therefore, we need to re-evaluate the initial information or calculations.