Understanding the Concepts

* Centripetal Acceleration: When an object moves in a circular path, it experiences an acceleration towards the center of the circle. This is called centripetal acceleration.

* Acceleration due to Gravity (g): This is the acceleration experienced by objects near the surface of the Earth due to gravity, approximately 9.8 m/s².

Formula

The formula for centripetal acceleration (a_c) is:

a_c = v² / r

Where:

* v = velocity of the object

* r = radius of the circular path

Solving the Problem

1. Set up the equation: We want the centripetal acceleration (a_c) to be equal to the acceleration due to gravity (g):

a_c = g

2. Substitute the formula for centripetal acceleration:

v² / r = g

3. Solve for velocity (v):

* Multiply both sides by r: v² = g * r

* Take the square root of both sides: v = √(g * r)

4. Plug in the values:

* g = 9.8 m/s²

* r = 70 m

* v = √(9.8 m/s² * 70 m)

* v ≈ 26.2 m/s

Answer

The car would have to travel at approximately 26.2 m/s (about 58.6 mph) to have a centripetal acceleration equal to the acceleration due to gravity while rounding a 70 m radius turn.