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

The minimum speed required for the roller coaster to stay on the track at the top of a radius loop is . a-roller-coaster-has-a-vertical-loop-with-radius-of-15m

At the top of the loop, two main forces are at play: gravity (

, 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 To find the minimum speed required for a

v=9.8⋅15v equals the square root of 9.8 center dot 15 end-root v=147v equals the square root of 147 end-root v≈12.12 m/sv is approximately equal to 12.12 m/s ✅ Final Result

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 The minimum speed required

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