A 54.0-kg skateboarder starts out with a speed of 1.70 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 6.00 m/s.
To find the change in kinetic energy of the skateboarder, we can use the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy.
The work done by the skateboarder on himself is +80.0 J, while the work done by friction is -265 J.
The total work done on the skateboarder is then given by the sum of these two values:
Total work = Work by skateboarder + Work by friction
Total work = +80.0 J - 265 J
Total work = -185 J (since work by friction is negative)
According to the work-energy theorem, the total work done on an object is equal to the change in its kinetic energy. Therefore, we can say that the change in kinetic energy of the skateboarder is -185 J.
We can now calculate the initial kinetic energy and the final kinetic energy of the skateboarder.
Initial kinetic energy (K_i) can be calculated using the formula:
K_i = 0.5 * mass * (initial velocity)^2
K_i = 0.5 * 54.0 kg * (1.70 m/s)^2
K_i = 80.715 J
Final kinetic energy (K_f) can be calculated using the same formula:
K_f = 0.5 * mass * (final velocity)^2
K_f = 0.5 * 54.0 kg * (6.00 m/s)^2
K_f = 972.0 J
Now, we can find the change in kinetic energy:
Change in kinetic energy = K_f - K_i
Change in kinetic energy = 972.0 J - 80.715 J
Change in kinetic energy = 891.285 J
Since we found earlier that the change in kinetic energy is -185 J, we can express this using the equation:
891.285 J = -185 J + Extra Work
Extra Work = 891.285 J - (-185 J)
Extra Work = 1076.285 J
Therefore, the total work done on the skateboarder by external forces (excluding the work done by the skateboarder and friction) is 1076.285 J.