A 2.2 kg rock is released from rest at the surface of a pond 1.8 m deep. As the rock falls, a constant upward force of 5.0 N is exerted on it by water resistance. Let y=0 be at the bottom of the pond. Calculate the nonconservative work, Wnc , done by water resistance on the rock, the gravitational potential energy of the system, U , the kinetic energy of the rock, K , and the total mechanical energy of the system, E , when the depth of the rock below the water's surface is 0 m.
When the depth of the rock below the surface is 0 m, it has not moved since it was released at the surface. No work has been done and there is zero kintic energy.
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There are 3 portions. The next one is at 0.50 m and the last one is when the rock is at 1.0 m.
To calculate the nonconservative work (Wnc) done by water resistance, you need to determine the distance the rock travels while the force is acting on it.
The work done by a force is given by the formula W = F * d * cos(theta), where F is the magnitude of the force, d is the distance over which the force is applied, and theta is the angle between the force and displacement vectors. In this case, the force is constant, so you can ignore the angle.
Since the rock is falling, the distance it travels is the depth of the pond, which is 1.8 m.
So, Wnc = F * d = 5.0 N * 1.8 m = 9 J.
Next, let's calculate the gravitational potential energy (U) of the system. The gravitational potential energy is given by U = m * g * h, where m is the mass of the rock, g is the acceleration due to gravity, and h is the height above the reference level (y = 0).
In this case, the height above the reference level is 0 m, so U = m * g * h = 2.2 kg * 9.8 m/s^2 * 0 m = 0 J.
Now, let's calculate the kinetic energy (K) of the rock. The kinetic energy is given by K = (1/2) * m * v^2, where m is the mass of the rock and v is its velocity.
Since the rock starts from rest, its initial velocity is 0. As the rock falls, it will gain speed. The relation between velocity and distance in a free-fall motion is v = sqrt(2 * g * h), where g is the acceleration due to gravity and h is the height fallen.
For the current situation, the height fallen is 1.8 m. So, v = sqrt(2 * 9.8 m/s^2 * 1.8 m) ≈ 7.14 m/s.
Now, we can calculate the kinetic energy: K = (1/2) * m * v^2 = (1/2) * 2.2 kg * (7.14 m/s)^2 ≈ 44.84 J.
Finally, the total mechanical energy (E) of the system is the sum of the gravitational potential energy and the kinetic energy, since there is no other form of energy involved: E = U + K = 0 J + 44.84 J ≈ 44.84 J.
To summarize:
- Nonconservative work done by water resistance (Wnc): 9 J
- Gravitational potential energy of the system (U): 0 J
- Kinetic energy of the rock (K): 44.84 J
- Total mechanical energy of the system (E): 44.84 J.