Final answer:
To determine the time Zorch must push to slow Earth's rotation, we can use rotational dynamics. We calculate the change in Earth's rotational kinetic energy and relate this to work done by Zorch. However, this is an unrealistic scenario and serves as a learning exercise rather than a practical problem.
Step-by-step explanation:
To calculate the time Zorch would need to slow Earth's rotation to once per 28 hours, we need to apply the problem-solving strategy for rotational dynamics. We start by determining the change in Earth's rotational kinetic energy. Earth's current period of rotation is 24 hours, and Zorch wants to change it to 28 hours.
The moment of inertia of the Earth is I ≈ 8.04 × 1037 kg·m2. The initial angular velocity (ωi) and final angular velocity (ωf) are given by ω = 2π/T, with T being the period of rotation. We can then calculate the initial and final kinetic energies (KEi and KEf) using KE = 0.5 × I × ω2.
The work done by Zorch (W) is equal to the change in kinetic energy (ΔKE = KEf - KEi). Using the work-energy theorem, we equate W to the product of the force (F) applied and the distance (d) over which it is applied, where d can be calculated knowing that the force is applied tangentially to Earth's surface at the equator (d = r × θ, with r being Earth's radius and θ being the angular displacement).
The power (P) exerted by Zorch is equal to the force times the velocity at the equator, P = F × veq, and this equals the rate of work done, P = W / t, where t is the time. Solving for t gives us t = W / P. By substituting the appropriate values and solving for t, we can find the time Zorch needs to push with the given force.
However, this problem is actually not realistic and cannot have an exact answer since it ignores crucial factors such as the change in Earth's moment of inertia that would result from such a massive force application, conservation of angular momentum, and external torques. It is more of a hypothetical scenario used for pedagogical purposes.