A car with a mass of 1000 kg travels along a circular path with a radius of 50 m at a speed of 20 m/s. The centripetal force acting on the car is to be determined. The centripetal force \( F_c \) is calculated using the formula:
\[ F_c = \frac{m \cdot v^2}{r} \]
Where:
- \( m = 1000 \, \text{kg} \) represents the car's mass.
- \( v = 20 \, \text{m/s} \) represents the car's speed.
- \( r = 50 \, \text{m} \) represents the radius of the circular path.
Substituting the given values into the formula results in:
\[ F_c = \frac{1000 \cdot (20)^2}{50} \]
Performing the calculations:
- \( 20^2 = 400 \)
- \( 1000 \cdot 400 = 400000 \)
- \( \frac{400000}{50} = 8000 \)
The computed centripetal force is:
\[ F_c = 4000 \, \text{N} \]
Therefore, the centripetal force exerted on the car is \( 4000 \, \text{N} \).