Starting at rest at the edge of a swimming pool, a 72.0-kg athlete swims along the surface of the water and reaches a speed of 1.15 m/s by doing the work Wnc1 = +170 J. Find the nonconservative work, Wnc2 done by the water on the athlete.
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Well, it seems like this athlete is really swimming against the current! Let me calculate the nonconservative work done by the water on the athlete.
Given that the initial speed is 0 m/s and the final speed is 1.15 m/s, we can use the work-energy principle to find the nonconservative work:
Wnc2 = ΔKE - Wnc1
Since the initial speed is 0, the initial kinetic energy (KE) is zero. The final kinetic energy can be calculated using the formula:
KE = (1/2)mv^2
Plugging in the values, we get:
KE = (1/2) * 72.0 kg * (1.15 m/s)^2
= 0.5 * 72.0 kg * 1.3225 m^2/s^2
= 47.43 J
Now we can calculate the nonconservative work:
Wnc2 = ΔKE - Wnc1
= 47.43 J - 170 J
= -122.57 J
So, the nonconservative work done by the water on the athlete is approximately -122.57 J. It looks like the water is putting in more effort than the athlete!
To find the nonconservative work done by the water on the athlete, we need to consider the change in kinetic energy of the athlete.
The work done by a force is given by the equation:
Work = Force * Distance * cos(theta)
Here, the distance is the displacement of the athlete in the direction of the force, and theta is the angle between the force and the displacement vectors.
Since the athlete starts from rest, their initial kinetic energy is zero. Therefore, the work done by the nonconservative forces on the athlete must equal the change in kinetic energy:
Wnc2 = ΔKE
We are given the athlete's mass (m = 72.0 kg) and the initial and final speeds. The change in kinetic energy can be calculated using the equation:
ΔKE = 0.5 * m * (vf^2 - vi^2)
Let's substitute the given values into this equation:
ΔKE = 0.5 * 72.0 kg * (1.15 m/s)^2
Solving this equation gives us:
ΔKE ≈ 47.25 J
Therefore, the nonconservative work, Wnc2, done by the water on the athlete is approximately 47.25 J.
To find the nonconservative work, Wnc2, done by the water on the athlete, we need to use the work-energy principle. The principle states that the work done on an object is equal to its change in kinetic energy.
The work done by the athlete (Wnc1) is given as +170 J. This means that the athlete did positive work, so the athlete gained energy through work.
Since the athlete starts at rest, the initial kinetic energy (K1) is zero. The final kinetic energy (K2) is given by:
K2 = (1/2) * m * v^2
Where:
m = mass of the athlete (72.0 kg)
v = final velocity of the athlete (1.15 m/s)
Plugging in the values:
K2 = (1/2) * 72.0 kg * (1.15 m/s)^2
= 0.5 * 72.0 kg * 1.3225 m^2/s^2
= 47.79 J
Now, we can use the work-energy principle:
Wnc2 = K2 - K1
Wnc2 = 47.79 J - 0 J
Wnc2 = 47.79 J
Therefore, the nonconservative work done by the water on the athlete (Wnc2) is 47.79 J.