An athlete running on curved track with 15 m radius and with speed of 6.7 m/s. If the athlete doesn't tilt to avoid falling down then calculate the torque on the athlete. Assume that the height of the athlete is 1.7 m and center of mass is at 57.1% of total height!
The torque calculation is impossible. Good luck on the take home test though! Never thought of posting the questions online...
i don't know answer
To calculate the torque on the athlete, we first need to determine the gravitational force acting on the athlete, and then find the force causing the centripetal acceleration as the athlete runs on the curved track.
1. Calculate the gravitational force:
The gravitational force acting on the athlete can be calculated using the formula: F_gravity = mass * g, where mass is the mass of the athlete and g is the acceleration due to gravity (approximately 9.8 m/s²).
To find the mass of the athlete, we'll use the average human density, which is approximately 1000 kg/m³. The volume of the athlete can be calculated using the formula: Volume = height * cross-sectional area.
The cross-sectional area of a human can be approximated as a rectangle with a width equivalent to the shoulder width and a height equal to the thickness of the athlete. Let's assume the average shoulder width is 0.4 meters and the thickness is 0.3 meters.
Cross-sectional area = shoulder width * thickness = 0.4 m * 0.3 m = 0.12 m²
Total volume = height * cross-sectional area = 1.7 m * 0.12 m² = 0.204 m³
Mass = density * volume = 1000 kg/m³ * 0.204 m³ = 204 kg
Now we can calculate the gravitational force: F_gravity = 204 kg * 9.8 m/s² = 2000.4 N
2. Calculate the centripetal force:
The centripetal force acting on the athlete is given by the formula: F_centripetal = (mass * velocity²) / radius, where mass is the mass of the athlete, velocity is the speed of the athlete, and radius is the radius of the curved track.
F_centripetal = (204 kg * (6.7 m/s)²) / 15 m = 422.9 N
3. Calculate the torque:
The torque on the athlete can be calculated by multiplying the centripetal force by the distance from the center of mass to the point where the force is applied.
The distance from the center of mass to the point of contact with the track can be calculated using the given information that the center of mass is at 57.1% of the total height.
Distance from center of mass to contact point = 1.7 m * 57.1% = 0.9717 m
Torque = F_centripetal * Distance from center of mass to contact point = 422.9 N * 0.9717 m = 410.8 Nm
Therefore, the torque on the athlete is approximately 410.8 Nm.