A-roller-coaster-has-a-vertical-loop-with-radius-of-15m May 2026

To find the minimum speed required for a roller coaster to successfully complete a vertical loop with a radius of

) and the normal force from the track. For the "minimum" speed (the point where the car just stays on the track), the normal force is zero. We use: ≈is approximately equal to 2. Set up the equation a-roller-coaster-has-a-vertical-loop-with-radius-of-15m

At the top of the loop, two main forces are at play: gravity ( To find the minimum speed required for a

v2r=gthe fraction with numerator v squared and denominator r end-fraction equals g 3. Solve for velocity Rearrange the formula to solve for v=g⋅rv equals the square root of g center dot r end-root Set up the equation At the top of

The centripetal acceleration must equal the acceleration due to gravity to keep the car from falling:

The minimum speed required for the roller coaster to stay on the track at the top of a radius loop is .

, the car must maintain a speed where the centripetal force at the top of the loop is at least equal to the force of gravity. The minimum speed is approximately (or about 1. Identify physical constants