Motion and Force Relation Scans

Spring-Stretch Force Three-Row Scan

stretch makes restoring force

Three Hooke's-law rows hold spring stiffness fixed while stretch changes, so restoring force grows in direct proportion.

mechanics With stiffness 2 N/m, stretches 1 m, 2 m, and 3 m give restoring forces 2 N, 4 N, and 6 N.

Example

With spring stiffness fixed, restoring force scales with stretch. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Hold stiffness fixed and scan stretch

Hooke's law is a direct proportionality while the spring stays ideal. More stretch gives more restoring force.

F=kxF = k x

Small stretch

Stretch 1 m gives restoring force 2 N.

F=kx=2 N/m ⋅ 1 m=2 NF = k x = 2\ \text{N/m}\,\cdot\,1\ \text{m} = 2\ \text{N}
Spring relation rowA stretched spring pulls the block back toward the wall.F

Middle stretch

Stretch 2 m gives restoring force 4 N.

F=kx=2 N/m ⋅ 2 m=4 NF = k x = 2\ \text{N/m}\,\cdot\,2\ \text{m} = 4\ \text{N}
Spring relation rowA stretched spring pulls the block back toward the wall.F

Large stretch

Stretch 3 m gives restoring force 6 N.

F=kx=2 N/m ⋅ 3 m=6 NF = k x = 2\ \text{N/m}\,\cdot\,3\ \text{m} = 6\ \text{N}
Spring relation rowA stretched spring pulls the block back toward the wall.F

The restoring force follows stretch

The stiffness column stays fixed. The stretch column changes, and the force column follows the same scale.

kxF2 N/m1 m2 N2 N/m2 m4 N2 N/m3 m6 N\begin{array}{c|c|c}k & x & F \\ \hline 2\ \text{N/m} & 1\ \text{m} & 2\ \text{N} \\ 2\ \text{N/m} & 2\ \text{m} & 4\ \text{N} \\ 2\ \text{N/m} & 3\ \text{m} & 6\ \text{N}\end{array}