Question

A runner weighing 55 kg, moving at a speed of 7.2 m/s rounds a bend with a radius of 10 m. What is the centripetal force needed to keep this runner on the curve?

Answer 1

To find the centripetal force needed to keep the runner on the curve, we can use the formula for centripetal force:

\[
F_c = \frac{mv^2}{r}
\]

where:
- \( F_c \) is the centripetal force,
- \( m \) is the mass of the runner (55 kg),
- \( v \) is the speed of the runner (7.2 m/s),
- \( r \) is the radius of the bend (10 m).

Now, let's plug in the values:

1. Mass, \( m = 55 \) kg
2. Speed, \( v = 7.2 \) m/s
3. Radius, \( r = 10 \) m

Now, substituting these values into the equation:

\[
F_c = \frac{55 \, \text{kg} \times (7.2 \, \text{m/s})^2}{10 \, \text{m}}
\]

Calculating \( (7.2 \, \text{m/s})^2 \):

\[
(7.2)^2 = 51.84 \, \text{m}^2/\text{s}^2
\]

Now substituting this back into the centripetal force equation:

\[
F_c = \frac{55 \, \text{kg} \times 51.84 \, \text{m}^2/\text{s}^2}{10 \, \text{m}}
\]

Calculating the numerator:

\[
55 \times 51.84 = 2851.2 \, \text{kg} \cdot \text{m}^2/\text{s}^2
\]

Now, dividing by 10 m:

\[
F_c = \frac{2851.2 \, \text{kg} \cdot \text{m}^2/\text{s}^2}{10 \, \text{m}} = 285.12 \, \text{N}
\]

Thus, the centripetal force needed to keep the runner on the curve is:

\[
\boxed{285.12 \, \text{N}}
\]