Question

the speed of the rollercoaster is 20.3 m/s at the position marked r1. the radius at this point is 14.2 m. calculate the size of the force required by the track for a coaster of mass 2,263 kg to negotiate this turn. report this value as a whole number.

Answer 1

The centripetal force required for a roller coaster of mass 2,263 kg to negotiate a turn of radius 14.2 m at a speed of 20.3 m/s is calculated using the centripetal force formula. After the calculation, the result is rounded to the nearest whole number.

Step-by-step explanation:

To solve the mathematical problem completely, we need to calculate the centripetal force that the roller coaster needs in order to negotiate a turn of radius 14.2 m at a speed of 20.3 m/s. The mass of the coaster is given as 2,263 kg. The centripetal force (Fc) required for an object moving in a circle of radius r at a constant speed v is given by the formula Fc = m*v2/r, where m is the mass of the object, v is the speed, and r is the radius of the circular path.

By plugging in the values, we get Fc = (2,263 kg)*(20.3 m/s)2/(14.2 m). Calculating this yields a centripetal force Fc. Since we need to report the value as a whole number, we will round it to the nearest whole number after calculation.