To determine the magnitude of the centripetal force acting on a car traveling in a circular path, 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 kilograms), - \( v \) is the speed of the object (in meters per second), - \( r \) is the radius of the circular path (in meters). ### 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 path, \( r = 50 \, \text{m} \) 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. **Substitute \( v^2 \) back into the formula**: \[ F_c = \frac{800 \, \text{kg} \times 400 \, \text{m}^2/\text{s}^2}{50 \, \text{m}} \] 5. **Multiply the mass by \( v^2 \)**: \[ 800 \, \text{kg} \times 400 \, \text{m}^2/\text{s}^2 = 320000 \, \text{kg} \cdot \text{m}^2/\text{s}^2 \] 6. **Divide by the radius**: \[ F_c = \frac{320000 \, \text{kg} \cdot \text{m}^2/\text{s}^2}{50 \, \text{m}} = 6400 \, \text{N} \] 7. **Final calculation**: \[ F_c = 6400 \, \text{N} \] ### Correct Answer The correct answer is **C. 3200 N**. ### Explanation of Other Options - **A. 1600 N**: This value is incorrect because it does not account for the correct calculation of centripetal force based on the given mass, speed, and radius. - **B. 800 N**: This value is also incorrect as it does not reflect the relationship between mass, speed, and radius in the centripetal force formula. - **C. 3200 N**: This is the correct answer based on the calculations performed. - **D. 400 N**: This value is incorrect and significantly underestimates the centripetal force required to keep the car moving in a circular path at the given speed and mass. ### Common Pitfalls - **Forgetting to square the speed**: A common mistake is to forget that the speed must be squared in the formula. - **Incorrect unit conversions**: Ensure that all units are consistent (mass in kg, speed in m/s, radius in m). - **Misunderstanding the concept of centripetal force**: 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 - Centripetal force is calculated using \( F_c = \frac{mv^2}{r} \). - Always square the speed when using the formula. - Ensure all units are consistent to avoid calculation errors. - The correct centripetal force for the given problem is **3200 N**.