) 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 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 a-roller-coaster-has-a-vertical-loop-with-radius-of-15m
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 ) and the normal force from the track
The minimum speed required for the roller coaster to stay on the track at the top of a radius loop is . Set up the equation , the car must
To find the minimum speed required for a roller coaster to successfully complete a vertical loop with a radius of
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
The centripetal acceleration must equal the acceleration due to gravity to keep the car from falling:
