A roller coaster ride includes a circular loop with radius R = 11.6 m. What minimum speed must the car have at the top to stay in contact with the tracks?

How would I go around solving this, as in what formula would I need?

The centripetal acceleration is given by v²/r m/s².

Acceleration due to gravity is g=9.8 m/s²

If one is to offset the other, they must be equal. at the highest point of the loop.

So set
v²/r = g
to solve for v.
Note: at this speed, the normal force on the track is zero.

To solve this problem, we can use the concept of centripetal force.

The minimum speed required at the top of the loop occurs when the normal force is zero, meaning there is no contact between the coaster and the tracks. The only force acting on the car is gravity.

At the top of the loop, the gravitational force provides the centripetal force required to keep the car moving in a circular path.

The centripetal force (Fc) is given by the equation:

Fc = m * v^2 / R

Where:
- Fc is the centripetal force
- m is the mass of the car
- v is the velocity of the car
- R is the radius of the loop

In this case, we want to find the minimum speed required at the top of the loop, so we can set the normal force to zero.

The normal force can be expressed as:

Fn = m * g

Where:
- Fn is the normal force
- m is the mass of the car
- g is the acceleration due to gravity (approximately 9.8 m/s^2)

Since the normal force is zero at the top of the loop, we will ignore it in our calculations.

So, we can rewrite the centripetal force equation as:

m * g = m * v^2 / R

To find the minimum speed, we can rearrange the equation:

v^2 = g * R

v = √(g * R)

Plugging in the given values:

R = 11.6 m
g = 9.8 m/s^2

v = √(9.8 m/s^2 * 11.6 m)

Now, we can calculate the minimum speed required at the top of the loop.

To solve this problem, you can make use of the concept of centripetal force. In order for the car to stay in contact with the tracks at the top of the loop, the centrifugal force acting outward must be equal to or less than the gravitational force acting downward. This will prevent the car from losing contact with the tracks due to insufficient normal force.

The formula you need is the centripetal force formula:

F_c = m * a_c

where F_c is the centripetal force, m is the mass of the car, and a_c is the centripetal acceleration.

The centripetal force can also be expressed as:

F_c = m * v^2 / R

where v is the speed of the car at the top of the loop and R is the radius of the loop.

To find the minimum speed required, we can equate the centripetal force to the gravitational force at the top of the loop:

M * g = m * v^2 / R

where M is the mass of the car and g is the acceleration due to gravity.

To solve for the minimum speed, rearrange the equation to solve for v:

v^2 = R * g * M / m

v = sqrt(R * g * M / m)

Here, you would substitute the given values: R = 11.6 m, g = 9.8 m/s^2, and any other given masses or masses of the car that you may have in order to calculate the minimum speed required for the car to stay in contact with the tracks at the top of the loop.