Physics Problem: Determining the Spring Constant
Question:
The woman pictured here is carrying a baby on her back and also carrying an additional 30 kg in the buckets on the pole. If she takes one step every second, what should the spring constant k of the pole be so that the buckets naturally rise up every time she takes a step, making it easier for her to walk?
Detailed Answer:
We are given the following values:
- Mass (m) = 30 kg
- Frequency (f) = 1 Hz (since she takes one step every second)
We use the formula that relates mass, frequency, and spring constant in oscillatory motion:
f = (1 / 2π) × √(k / m)
Rearranging this formula to solve for spring constant k:
k = (2πf)² × m
Now, substitute the known values into the equation:
k = (2 × π × 1)² × 30
k = (6.2832)² × 30 ≈ 39.478 × 30
k ≈ 1184.35 N/m
At this spring constant, the buckets will oscillate in sync with the woman’s steps, rising up every time she takes a step. This motion makes it a bit easier for her to walk, as the vertical oscillation assists her motion.