Question

A race car travels with a constant tangential speed of 74.1 m/s around a circular track of track of radius 628 m. Find the magnitude of the total acceleration.

Answer 1

The magnitude of the total acceleration can be found using the following equation:

a_total = sqrt(a_tangential^2 + a_radial^2)

where a_tangential is the tangential acceleration and a_radial is the radial acceleration.

The tangential acceleration can be calculated using the formula:

a_tangential = r * ω^2

where r is the radius of the circular track and ω is the angular velocity.

The angular velocity can be calculated using the formula:

ω = v / r

where v is the tangential speed.

Plugging in the given values, we have:

ω = 74.1 m/s / 628 m = 0.118 s^-1

Plugging this value into the formula for tangential acceleration, we have:

a_tangential = (628 m) * (0.118 s^-1)^2 = 8.06 m/s^2

To find the radial acceleration, we can use the formula:

a_radial = r * ω^2

Plugging in the given values, we have:

a_radial = (628 m) * (0.118 s^-1)^2 = 8.06 m/s^2

Now we can plug these values into the formula for total acceleration:

a_total = sqrt((8.06 m/s^2)^2 + (8.06 m/s^2)^2) = sqrt(129.87 m^2/s^4 + 129.87 m^2/s^4) ≈ 18.07 m/s^2

Therefore, the magnitude of the total acceleration is approximately 18.07 m/s^2.