Catching a wave, a 77-kg surfer starts with a speed of 1.2 m/s , drops through a height of 1.60 m , and ends with a speed of 8.5 m/s .
How much nonconservative work was done on the surfer?
ok, I will do it all out
beginning Ke = (1/2)(77)(1.44)=
= 55.44 Joules
final Ke = (1/2)(77) (8.5)^2 = 2782 Joules
gain in Ke = 2782 - 55.4 = 2726 Joules
drop in Potential energy U = 77*9.8*1.6
1207 Joules
so 2726 -1207 = 1519 Joules came from something else non-conservative, like paddling
To calculate the nonconservative work done on the surfer, we need to use the work-energy principle. According to this principle, the total work done on an object is equal to the change in its kinetic energy.
The initial kinetic energy (K_i) of the surfer can be calculated using the formula:
K_i = (1/2) * mass * (velocity)^2
Substituting the given values:
K_i = (1/2) * 77 kg * (1.2 m/s)^2
= 55.32 J
The final kinetic energy (K_f) of the surfer can be calculated using the same formula:
K_f = (1/2) * mass * (velocity)^2
Substituting the given values:
K_f = (1/2) * 77 kg * (8.5 m/s)^2
= 2743.975 J
The change in kinetic energy (ΔK) is given by:
ΔK = K_f - K_i
Substituting the values:
ΔK = 2743.975 J - 55.32 J
= 2688.655 J
Therefore, the nonconservative work done on the surfer is equal to the change in kinetic energy, which is:
Nonconservative work = ΔK
= 2688.655 J