Dynamics Dungeon: Loop the Loop

weight Wnormal force N from the track (points toward the center)

Entry speed v₀ (m/s)

Loop radius R (m)

PREDICT

How this connects to AP Physics 1 (Topic 2.9, Circular Motion): at any point on the loop the net force toward the center is mv²/R. At the bottom the normal force must also cancel gravity, so N = m(g + v²/R). At the top gravity and the normal force both point toward the center, so N = m(v²/R − g). The cart just barely stays on the track when N = 0 at the top, which gives v_top = √(gR). Energy conservation connects the entry speed to the speed at the top.