Question

station 5: equilibrium & collision safety design (5 min)
part a - quick equilibrium: a 10 kg object hangs motionless. what is the tension (f_g=f_tension) in the rope?
part b - collision design (hs-ps2-3):
scenario: an egg drops from 2 meters (v at impact ≈ 6.3 m/s)
without protection: stops in 0.01 s
with cushion: stops in 0.25 s
calculate the force in both cases using f = mδv/δt (assume egg mass = 0.05 kg)
design question: list 3 materials/design features that would increase collision time and reduce force.
prepare to teach the class: how increasing δt decreases f in collisions.

Explanation:

Step1: Calculate tension for Part A

Tension equals weight: \( F_{\text{tension}} = m \cdot g \), \( g = 9.8 \, \text{m/s}^2 \)
\( F_{\text{tension}} = 10 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 98 \, \text{N} \)

Step2: Calculate force without protection

Use \( F = \frac{m\Delta v}{\Delta t} \), \( m=0.05 \, \text{kg}, \Delta v=6.3 \, \text{m/s}, \Delta t=0.01 \, \text{s} \)
\( F = \frac{0.05 \times 6.3}{0.01} = 31.5 \, \text{N} \)

Step3: Calculate force with cushion

Same \( m\Delta v \), \( \Delta t=0.25 \, \text{s} \)
\( F = \frac{0.05 \times 6.3}{0.25} = 1.26 \, \text{N} \)

Answer:

Part A: 98 N
Part B without protection: 31.5 N
Part B with cushion: 1.26 N
Design Question examples: Foam padding, crumpled paper, inflated balloon
Prepare to teach: Increasing collision time (\( \Delta t \)) in \( F = \frac{m\Delta v}{\Delta t} \) decreases force (\( F \)) since they are inversely proportional.