Final answer:
The spring constant k for a pogo stick compressed by 0.120 m due to an 80.0-kg man standing on it is calculated using Hooke's Law, yielding a value of 6533.33 N/m, which does not match any provided answer choice. Additional information is required to determine if the spring will be compressed more when the man hops down the road.
Step-by-step explanation:
When an 80.0-kg man stands on a pogo stick, the spring is compressed by 0.120 m. Given that the force due to the man's weight is equal to the spring force (Fspring = kx), where k is the spring constant and x is the compression distance, we can calculate the spring constant k using the equation provided by Hooke's Law: F = kx. The force due to gravity on the man is Fgravity = mg, where m is the man's mass and g is the acceleration due to gravity (9.8 m/s2).
The force exerted by the weight of the man is Fgravity = 80.0 kg × 9.8 m/s2 = 784 N. Now, we can find the spring constant k as follows:
k = F/x = 784 N / 0.120 m = 6533.33 N/m
However, none of the answer choices match this calculated value, indicating a possible mistake in the question or the answer choices.
Regarding part (b) of the question, since it depends on dynamic conditions such as the man hopping, which introduces additional forces, it cannot be answered definitively with the information provided.