Zorch, an archenemy of Superman, decides to slow Earth’s rotation to once per 29 h by exerting a force parallel to the equator, opposing the rotation. Superman is not immediately concerned, because he knows Zorch can only exert a force of 4.1 × 107 N. For the purposes calculations in this problem you should treat the Earth as a sphere of uniform density even though it isn't. Additionally, use 5.979 × 1024 kg for Earth's mass and 6.376 × 106 m for Earth's radius. How long, in seconds, must Zorch push with this force to accomplish his goal? (This period gives Superman time to devote to other villians.)
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
Zorch, an archenemy of Superman, decides to slow Earth’s rotation to once per 29 h by exerting a force parallel to the equator, opposing the rotation. Superman is not immediately concerned, because he knows Zorch can only exert a force of 4.1 × 107 N. For the purposes calculations in this problem you should treat the Earth as a sphere of uniform density even though it isn't. Additionally, use 5.979 × 1024 kg for Earth's mass and 6.376 × 106 m for Earth's radius.
How long, in seconds, must Zorch push with this force to accomplish his goal? (This period gives Superman time to devote to other villians.)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
