Acceleration around a running track

In summary, the person is running around a track with a speed of 5.11m/s and a radius of 31.8m. The question is asking to find the acceleration, which is 0.821ms-2, but the attempt at a solution uses incorrect equations. The correct equation to use is a=v^2/r, which is for centripetal acceleration. The tangential acceleration is not relevant in this case since the speed is constant. The person should have found the time by dividing the distance of 400m by the speed of 5.11m/s, which would give a time of 78.4s. Then, using the equation α=ω/t, the angular acceleration would be 0
  • #1
Ardinos
2
0

Homework Statement


He is running around a running track training for a 400m race. His velocity is 5.11m/s around the circular end of the track, which has a radius of 31.8m.
I'm trying to find his acceleration which I know is 0.821ms-2 but I can't find out how to get it.

Homework Equations


v=rω
d=rθ
a=rα
ω=θ/t
α=ω/t
ω=2πf
ƒ=1/T

The Attempt at a Solution


I first calculated his angular velocity of 0.160rad/s. Then re-arranged d=rθ to θ=d/r and got 12.57rad. Then I re-arranged ω=θ/t to get t=ω/θ and got 0.0127s which I know must be wrong... anyways I then used α=ω/t and got 12.59rads-2 and finally a=rα and I got 400ms-2 and the answer is 0.821ms-2.
 
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  • #2
The statement of the question is not quite right. The 5.11m/s is a speed, not a velocity. Velocity is a vector so also has a direction. The speed is just the magnitude of the velocity.
Since the speed is constant, the acceleration consists of its changes in direction. What kind of acceleration do you associate with an object going around in circles? What equations do you know that relate to that?
 
  • #3
If it is asking to find the acceleration then I assume I will be using a=rα to convert the angular acceleration from α=ω/t to 'linear' (not sure if that's that right word) acceleration. The problem is I can't find the time or if the displacement of 400m is relevant. And yes I think it is meant to say speed but it says velocity.
 
  • #4
Ardinos said:
If it is asking to find the acceleration then I assume I will be using a=rα to convert the angular acceleration from α=ω/t to 'linear' (not sure if that's that right word) acceleration.
No, that formula is for a as the tangential acceleration. Since speed is constant, there is no tangential acceleration, and so no angular acceleration.
When speed is constant, the only possible acceleration is at right angles to the direction of travel. Have you heard of centripetal acceleration?
 

1. What is acceleration around a running track?

Acceleration around a running track refers to the change in an athlete's speed as they run around a curved track. This change in speed is due to the athlete's constant change in direction as they run on the curved track.

2. How is acceleration calculated around a running track?

Acceleration around a running track can be calculated using the formula a = v^2/r, where a is the acceleration, v is the velocity, and r is the radius of the track. This formula takes into account the athlete's speed and the curvature of the track.

3. What factors can affect acceleration around a running track?

There are several factors that can affect acceleration around a running track, including the athlete's speed, the radius of the track, and the friction between the athlete's feet and the track surface. The athlete's body position and technique can also impact their acceleration.

4. How does acceleration around a running track differ from acceleration on a straight track?

Acceleration around a running track differs from acceleration on a straight track because of the athlete's constant change in direction on a curved track. On a straight track, an athlete's acceleration is typically measured in a straight line, while on a curved track, it is measured in a curved path.

5. Why is understanding acceleration around a running track important for athletes?

Understanding acceleration around a running track is important for athletes because it can help them improve their speed and efficiency while running. By understanding the factors that affect acceleration, athletes can adjust their technique and strategy to optimize their performance on a curved track.

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