The record of the women's 200 m is 21.34 sec. If all racers at that speed, how much more force would be needed by the racer in lane 1 to stay in her lane than by racer in lane 8. Assume that all racers weigh 534 N. The track is a 400 m Olympic track.
You need more data to answer this. 200 m races are run around a curve. You need to know the radius of curvature R of lanes 1 and 8 as they go around the curve at one end of the track. Find that information, and then use the formula
F = M V^2/R
to get the lateral centripetal force required to stay in a lane. It will be higher for the inside lane.
According to
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each lane is 1.22 meters wide. Lane 1 has a radius of curvature of 36.8 meters
To find the amount of force needed by the racer in lane 1 compared to the racer in lane 8, we need to calculate the difference in the lateral centripetal force required to stay in their respective lanes.
First, let's calculate the velocity of the racers. We know that the record time for the women's 200m is 21.34 seconds. Since we want to find the force needed for a complete lap around the Olympic track (400 meters), we can divide the distance by the time to find the average velocity:
Velocity = Distance / Time
Velocity = 400 meters / 21.34 seconds
Now, let's calculate the velocity for both racers:
Velocity = 18.718 meters per second
Next, we need to calculate the lateral centripetal force required to stay in the lane. We can use the formula:
Force = (Mass x Velocity^2) / Radius
The mass of the racers is given as 534 N (Newtons), and we know the radius of curvature for lane 1 is 36.8 meters.
Now, let's calculate the force needed for the racer in lane 1:
Force_lane1 = (534 N x (18.718 m/s)^2) / 36.8 m
Similarly, let's calculate the force needed for the racer in lane 8:
Force_lane8 = (534 N x (18.718 m/s)^2) / Lane_radius
At this point, we need to know the radius of curvature for lane 8. Unfortunately, the provided information does not include the value for lane 8's radius of curvature. To solve this problem, we need additional data.
Once we have the radius of curvature for lane 8, we can substitute it into the equation and calculate the force needed for the racer in lane 8. The difference in force between lane 1 and lane 8 will represent the additional force needed by the racer in lane 1 to stay in her lane.