Reflecting on Stunt Car Physics: Maximum Height and Normal Force
a. What is the maximum height (diameter) of the loop?
Calculate the minimum speed required at the top of the loop.
b. What normal force acts on the car at the bottom of the loop?
Calculate the normal force at the bottom of the loop.
a. Maximum Height (Diameter) of the Loop
The maximum height (diameter) of the loop is approximately 11.4 meters. To determine this, we need to consider the minimum speed required at the top of the loop to prevent the car from losing contact with the track. When the normal force becomes zero, the minimum speed occurs.
b. Normal Force at the Bottom of the Loop
The normal force acting on the car at the bottom of the loop is equal to three times the weight of the car, approximately 44,100 N. This normal force provides the necessary centripetal force to keep the car moving in a circular path.
Reflecting on the physics involved in a stunt car completing a vertical loop can be both intriguing and enlightening. The calculations for determining the maximum height (diameter) of the loop and the normal force at the bottom of the loop reveal the intricate balance between gravitational force, centripetal force, and velocity.
Calculating Maximum Height (Diameter) of the Loop
In the scenario provided, it's crucial to first calculate the minimum speed required at the top of the loop. By setting the normal force to zero, we can derive the minimum speed necessary to maintain contact with the loop. This speed is essential in determining the maximum height (diameter) of the loop.
Subsequently, calculating the radius of the loop allows us to understand the relationship between minimum speed and loop height. The maximum height is found to be equal to twice the radius, resulting in an approximate height of 11.4 meters. This calculation showcases the interplay between velocity, gravity, and loop dimensions in achieving a successful stunt car maneuver.
Determining Normal Force at the Bottom of the Loop
At the bottom of the loop, the normal force plays a critical role in providing the centripetal force needed for the car's circular motion. By analyzing the difference between the weight of the car and the normal force, we can calculate the normal force at the bottom of the loop, which is approximately 44,100 N.
Understanding the normal force at the bottom of the loop emphasizes the importance of balance and force distribution in stunt car physics. The car's ability to navigate the loop successfully relies on the precise calculation and application of these forces to maintain equilibrium throughout the maneuver.