A-roller-coaster-has-a-vertical-loop-with-radius-of-15m <Must Watch>

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

To find the minimum speed required for a roller coaster to successfully complete a vertical loop with a radius of a-roller-coaster-has-a-vertical-loop-with-radius-of-15m

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 At the top of the loop, two main

) 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 Set up the equation v2r=gthe fraction with numerator

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

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