MECHANICS · LAB 01The runaway wedge
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THE SETUP
A block. A wedge. No friction.
Release the block from rest. The ground exerts no horizontal force on the system; friction acts only at the block–wedge contact.
Px conserved · E conserved
INCLINATIONθ = 30°
FRICTIONLESS GROUND
M = 5.0 kgθ = 30°
m2.0 kgmg · 19.6 NN · 15.4 N
aw
01Make a prediction to unlock motionIntuition comes before calculation.
WEDGE · aₓ1.54 m/s²← left
BLOCK · aₓ (GROUND)3.86 m/s²→ right
BLOCK · aᵧ (GROUND)-3.12 m/s²↓ downward
BLOCK · |v| (GROUND)0.00 m/sat release
BLOCK · a RELATIVE6.24 m/s²down the plane
CENTRE OF MASS · Δx0.00000 mno horizontal drift
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THE ANCHOR IDEA
The centre of mass refuses to drift.
The block gains momentum to the right. Because the ground cannot provide a horizontal impulse, the wedge must gain exactly the opposite momentum. The two motions are not separate stories—they are one constraint.
pwedge+pblock,x= 0