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

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

) 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

To find the minimum speed required for a roller coaster to successfully complete a vertical loop with a radius of At the top of the loop, two main

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 To find the minimum

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

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

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