To determine the centripetal force acting on a car navigating 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. **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**: \[ F_c = \frac{320000 \, \text{kg} \cdot \text{m}^2/\text{s}^2}{50 \, \text{m}} = 6400 \, \text{N} \] ### Correct Answer The calculated centripetal force is **6400 N**. However, since the options provided do not include this value, it seems there may have been a misunderstanding in the options or the question itself. ### Explanation of Options - **Option A: 1600 N** - This is incorrect. It does not match our calculated value. - **Option B: 800 N** - This is incorrect. It is significantly lower than the calculated centripetal force. - **Option C: 3200 N** - This is incorrect. It is also lower than the calculated centripetal force. - **Option D: 400 N** - This is incorrect. It is much lower than the calculated centripetal force. ### Common Pitfalls - **Misunderstanding the formula**: Ensure you are using the correct formula for centripetal force. - **Forgetting to square the speed**: A common mistake is to forget to square the speed when substituting into the formula. - **Incorrect unit conversions**: Always check that the units are consistent (e.g., mass in kg, speed in m/s, radius in m). ### Revision Summary - The formula for centripetal force is \( F_c = \frac{mv^2}{r} \). - Always square the speed when calculating centripetal force. - Ensure all units are consistent to avoid calculation errors. - The centripetal force is necessary for an object to maintain circular motion at a constant speed. In this case, the correct centripetal force calculated is **6400 N**, which does not match any of the provided options.