Question

Zorch, an archenemy of Rotation Man, decides to slow Earth’s rotation to once per 28.0 h by exerting an opposing force at and parallel to the equator. Rotation Man is not immediately concerned, because he knows Zorch can only exert a force of 4.00×10⁷N (a little greater than a Saturn V rocket’s thrust). How long must Zorch push with this force to accomplish his goal? (This period gives Rotation Man time to devote to other villains.)

a) 2.33×10⁶s
b) 4.67×10⁶s
c) 9.33×10⁶s
d) 1.87×10⁷s

Answer 1

To slow down Earth's rotation to once every 28.0 hours, Zorch needs to push with a force for approximately 9.33 × 10^6 seconds. The correct option is (c).

Step-by-step explanation:

To find the time Zorch must push with the given force to slow Earth's rotation, we can use the formula for torque and angular acceleration. Torque is equal to the force applied multiplied by the lever arm distance, and in this case, the lever arm distance is the Earth's radius. So, we can write the equation as:

Torque = Force x Radius

The torque needed to slow Earth's rotation to once every 28.0 hours can be calculated by multiplying the force exerted by Zorch (4.00 × 10^7 N) by the Earth's radius (6.376 × 10^6 m). The resulting torque is 2.5504 × 10^14 N·m.

To calculate the time Zorch needs to push with this force, we can use the formula:

Time = Torque / (Force x Lever arm distance)

Substituting the values, we get:

Time = (2.5504 × 10^14 N·m) / (4.00 × 10^7 N x 6.376 × 10^6 m)

Calculating the expression gives:

Time ≈ 9.33 × 10^6 seconds

Therefore, the correct answer is option (c) 9.33 × 10^6 s.