Final answer:
The tension in the string at the bottom of the vertical circle is determined by adding the centripetal force, which depends on the car's mass, speed, and the circle's radius, to the gravitational force acting on the car. Without knowing the car's speed, a numerical value for tension cannot be calculated.
Step-by-step explanation:
To calculate the tension in the string when the car is at the bottom of the circle, you can use the concepts of centripetal force and Newton's second law of motion. At the bottom of the circle, the centripetal force required to keep the car moving in a circular path is the sum of the tension in the string and the gravitational force acting on the car.
The formula for centripetal force is Fc = mv2/r, where m is mass, v is velocity, and r is the radius of the circle. The gravitational force is Fg = mg, where g is the acceleration due to gravity. The total force exerted by the track (or the tension in the string) at the bottom of the circle is therefore T + Fg = mv2/r. To find T, rearrange the formula to T = mv2/r - mg.
To solve for T, you need the speed of the car, which has not been given in the problem. This makes it impossible to provide a numerical answer. However, if you had the speed, you would plug in all the known values (mass, speed, radius, gravity) into the formula to find the tension T at the bottom of the vertical circle.