A roller coaster ride includes a circular loop with radius R = 13.1 m. What minimum speed must the car have at the top to stay in contact with the tracks?
Which equation is used here? I'm using a = v^2 / r and taking a = 9.8
AT the top
g=v^2/r
solve for v.
You are on the right track! To find the minimum speed required for the car to stay in contact with the tracks at the top of the loop, we can use the equation for centripetal acceleration:
a = v^2 / r
In this case, the given acceleration value is the acceleration due to gravity, a = 9.8 m/s^2. The radius of the loop is R = 13.1 m. We need to find the minimum speed, v, at the top of the loop.
First, substitute the known values into the equation:
9.8 = v^2 / 13.1
Next, rearrange the equation to solve for v:
v^2 = 9.8 * 13.1
v^2 = 128.38
Finally, take the square root of both sides to find the minimum speed, v:
v = √128.38
v ≈ 11.34 m/s
Therefore, the minimum speed the car must have at the top of the loop to stay in contact with the tracks is approximately 11.34 m/s.