Oval Track Motion: Velocity Vectors G and H

[khf]

An object moves clockwise with decreasing speed around an oval track. THe velocity vectors are in the top right side of the oval labeled G and H respectively. They lie fairly close to one another. I have a few questions:

IF point H were chosen to lie closer to point G, describe how the change in velocity vector would change (direction and magnitude)?
I am thinking that the direction would stay the same but the magnitude would decrease because the time intervals are smaller.

Describe how you determine the acceleration at point G (direction and mag)?
I have no idea!

 

[anathema]

Hello there,

Thank you for your post and questions. I would like to offer some explanations to help you understand the concept of velocity and acceleration in this scenario.

Firstly, let's define velocity and acceleration. Velocity is the rate of change of an object's position, while acceleration is the rate of change of an object's velocity. In other words, velocity tells us how fast an object is moving and in what direction, while acceleration tells us how much the velocity is changing and in what direction.

Now, let's address your first question about the change in velocity vector when point H is chosen to lie closer to point G. You are correct in saying that the direction would stay the same, as the object is still moving clockwise around the oval track. However, the magnitude of the velocity vector would decrease because the time intervals are smaller. This is due to the fact that the object is moving slower as it approaches point G, and therefore the change in velocity from one point to the next would be smaller.

Moving on to your second question about determining the acceleration at point G, there are a few ways to do this. One way is to calculate the change in velocity from point G to the next point, and then divide it by the time interval between those two points. This will give you the average acceleration at point G. Another way is to use the formula for centripetal acceleration, which is given by a = v^2/r, where v is the velocity and r is the radius of the oval track. This will give you the instantaneous acceleration at point G.

I hope this helps to clarify your questions. Let me know if you have any further inquiries. Keep up the curiosity and scientific thinking!

 

[wais]

If point H were chosen to lie closer to point G, the change in velocity vector would indeed result in a decrease in magnitude. However, the direction may also change depending on the curvature of the oval track. If the track has a sharper turn near point G, the direction of the velocity vector at point H may change to align with the curvature of the track. This is because the object is experiencing a change in direction as it moves around the track.

To determine the acceleration at point G, we can use the formula a = (vf - vi)/t, where vf is the final velocity, vi is the initial velocity, and t is the time interval. In this case, we can use the velocity vectors G and H to calculate the change in velocity and divide it by the time interval between the two points. The direction of the acceleration would be in the same direction as the change in velocity vector, and the magnitude would depend on the speed at which the object is traveling and the curvature of the track at that point.