To determine the centripetal force acting on a car traveling around a circular track, we can use the formula for centripetal force, which is given by: \[ F_c = \frac{mv^2}{r} \] where: - \( F_c \) is the centripetal force, - \( m \) is the mass of the object (in this case, the car), - \( v \) is the speed of the object, - \( r \) is the radius of the circular path. ### Step-by-Step Calculation 1. **Identify the given values**: - Mass of the car, \( m = 800 \, \text{kg} \) - Speed of the car, \( v = 20 \, \text{m/s} \) - Radius of the circular track, \( r = 50 \, \text{m} \) 2. **Substitute the values into the formula**: \[ F_c = \frac{800 \, \text{kg} \times (20 \, \text{m/s})^2}{50 \, \text{m}} \] 3. **Calculate \( v^2 \)**: \[ (20 \, \text{m/s})^2 = 400 \, \text{m}^2/\text{s}^2 \] 4. **Multiply \( m \) and \( v^2 \)**: \[ 800 \, \text{kg} \times 400 \, \text{m}^2/\text{s}^2 = 320000 \, \text{kg} \cdot \text{m}^2/\text{s}^2 \] 5. **Divide by \( r \)**: \[ F_c = \frac{320000 \, \text{kg} \cdot \text{m}^2/\text{s}^2}{50 \, \text{m}} = 6400 \, \text{N} \] ### Correct Answer The calculated centripetal force is **6400 N**, which does not match any of the provided options. However, if we consider the options given, it seems there might be a misunderstanding in the question or the options provided. ### Explanation of the Options - **A. 1600 N**: This value is too low. It does not account for the mass and speed of the car correctly. - **B. 3200 N**: This value is also incorrect based on our calculations. It seems to be a miscalculation or misinterpretation of the centripetal force formula. - **C. 400 N**: This is significantly lower than what we calculated and does not reflect the mass and speed of the car. - **D. 2000 N**: This is also incorrect as it does not match our calculations. ### Common Pitfalls - **Forgetting to square the speed**: A common mistake is to forget that the speed must be squared in the centripetal force formula. - **Misunderstanding the radius**: Ensure that the radius is in the same units as the other measurements (meters in this case). - **Confusing centripetal force with other forces**: Remember that centripetal force is not a separate force but rather the net force required to keep an object moving in a circular path. ### Revision Summary - The formula for centripetal force is \( F_c = \frac{mv^2}{r} \). - Always square the speed when using the formula. - Ensure all units are consistent (e.g., mass in kg, speed in m/s, radius in m). - Double-check calculations to avoid common errors. In conclusion, the correct centripetal force acting on the car, based on the provided values, is **6400 N**, which does not match the options given. This indicates a potential error in the options or the question itself.