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3D Spring Compression with Friction
This 3D simulation demonstrates a block compressing a spring while experiencing friction, based on Example 6.9 from the textbook.
Maximum Compression
0 m
Kinetic Energy
0 J
Spring Potential Energy
0 J
Work Done by Friction
0 J
Spring Force
Frictional Force
Velocity
Physics Explanation:
From the textbook example with a 1000 kg block moving at 5 m/s (18 km/h), spring constant 6.25 × 10³ N/m, and μ = 0.5:
Work-Energy Theorem with Friction:
Initial KE = Work done by spring + Work done by friction
½mv² = ½kxₘ² + μmgxₘ
Rearranged as quadratic equation:
kxₘ² + 2μmgxₘ - mv² = 0
Solution:
xₘ = [-μmg + √(μ²m²g² + mkv²)] / k
xₘ = 1.35 m (with friction) vs 2 m (without friction)
Initial KE = Work done by spring + Work done by friction
½mv² = ½kxₘ² + μmgxₘ
Rearranged as quadratic equation:
kxₘ² + 2μmgxₘ - mv² = 0
Solution:
xₘ = [-μmg + √(μ²m²g² + mkv²)] / k
xₘ = 1.35 m (with friction) vs 2 m (without friction)
The simulation shows how friction reduces the maximum spring compression by converting some kinetic energy into heat.