Question

Question 1
For a "family" roller coaster the designer has a car moving 8 m/s. The designers want to keep the acceleration to 16 m/s/s. What do they need to make the radius of curvature of the element of the ride.
Use the centripetal acceleration equation ac=v2r
to put the numbers for the problem with the correct variable. Use "it" for the variable that is what you are looking for.

ac =
Choose...

v =
Choose...

r =
Choose...

Answer 1

To find the radius of curvature (r) using the centripetal acceleration equation \( a_c = \frac{v^2}{r} \), let's break down the variables according to the values given in the problem:

1. **Centripetal Acceleration (a_c)**: This is given as 16 m/s².
2. **Velocity (v)**: This is given as 8 m/s.
3. **Radius of Curvature (r)**: This is what we are looking for.

We can rearrange the centripetal acceleration formula to solve for r:

\[
r = \frac{v^2}{a_c}
\]

Now, we will substitute the values into the variables:

- **a_c = 16 m/s²**
- **v = 8 m/s**
- **r = ? (We will calculate this)**

Now we can substitute the known values into the rearranged equation:

\[
r = \frac{(8 \, \text{m/s})^2}{16 \, \text{m/s}^2}
\]

Calculating this gives:

\[
r = \frac{64 \, \text{m}^2/\text{s}^2}{16 \, \text{m/s}^2} = 4 \, \text{m}
\]

Therefore, the answers are:

- **a_c = 16 m/s²**
- **v = 8 m/s**
- **r = 4 m**