At the max speed the spring stops accelerating the mass and starts to slow it down. The max speed is at the equilibrium of the spring where the acceration is zero because it is where the transition from positive to negative acceleration occurs.
When the mass reaches its equilibrium position the acceleration reaches zero because the tip between negative and positive acceleration occurs here. That would mean that acceleration is at its minimum causing speed to be at a maximum due to the fact that all the potential energy has switched over to kinetic energy at that specific point. -Emily F
The equilibrium of the spring marks the maximum speed and also the minimum acceleration (which would actually be zero here). As the mass transitions above the equilibrium, the acceleration is a negative, and as the mass transitions below this point, the acceleration becomes positive. This is not only the changeover for acceleration, but it is also the conversion from kinetic to potential energy. Rachel R
When equilibrium is achieved, speed is a maximum and acceleration is a minimum. This is the point at which the forces acting on the mass (gravity and normal) are equal to zero. This means that there would be no unbalanced forces at this point to affect the object's speed. This means that the speed would be at its maximum. This being said, one can also observe that the acceleration is equal to zero. The forces are equal to zero. This makes F=ma into 0=(a constant mass)(a). Acceleration would have to be equal to zero, making it a minimum. It is also a property of equilibrium for acceleration to be 0 m/s/s.
I wasn't able to look at this on the 24th, so today when I used the link the site said it was a problem for the 26th. I don't think it is the same problem, what should I do?
The physics question was something along the lines of a spring has a mass on it, and the spring gets pulled so that it goes up to down vertically and repeatedly. There were no values, and then one had to say what Mr. Crane asked here, assuming the equilibrium is in the center of that motion. I'm not sure how they worded it, but that's the general idea...
I too was not able to get on the blog on the 24th, but from what I can gather from these comments the problem involves some sort of spring and an equilibrium. An equilibrium is a state in which all forces acting on an object, the mass in this case, are balanced. In a case where an mass is being swung in a circle, equilibrium occurs when the acceleration is at a minimum and the speed at a maximum. Sydnee V
I wasn't able to look at the blog on the 24th either so the question has now changed. But I read Brooke's synopsis of the problem and read all the comments and what i can put together is that when the the spring and mass are at an equilibrium, the maximum would be the speed and the minimum would be the acceleration. The acceleration would be equal to zero because if there is an equilibrium and the forces equal 0 then according to f=ma, acceleration would have to be 0. If acceleration is zero it has reached its minimum. At this point it seems that the acceleration also changes from positive to negative.
Being on vacation I too was not able to view this problem until now, but just as Nicole and Sydnee did I was able to gather information from previous comments made. When the speed of the spring is a maximum, the acceleration of the spring is a minimum, which is also when it is at its equilibrium. At this moment, all forces are equal, hence the word "equilibrium". Therefore, F=ma is zero in that moment. The reason the acceleration is zero is because it is shifting from positive to negative and no object can change direction without being zero for at least an instant.
The equilibrium of the spring, or the position when the forces are equal to zero is when the speed is at a maximum and the acceleration is at a minimum. This is also the middle of the motion, in which the spring is either retracting from the farthest point and decelerating into the compressed position and vice versa. The minimum speed(s) would occur at the furthest positive and negative positions from the point of equilibrium (when the spring is stretched the furthest and shrunk to being the most compact).
After answering the fourth day question and looking up the phrase "simple harmonic motion", I found that the phrase relates to this spring motion, as well. Therefore, I'd like to add to my answer the maximums and mins of kinetic and potential energy. The maximum kinetic energy occurs at equilibrium or the middle of the motion, and this is also where potential energy is at its minimum. In contrast, the minimum kinetic energy occurs at the points of maximum and minimum displacement, where the potential energy is at its maximum.
At the point of equilibrium the sum of the forces are equal to zero, F=ma=0, just as everyone else has said... At that point the acceleration is zero and when the object continues upwards gravity will start pulling it down, increasing the acceleration again. To me this means that at the point of equilibrium the acceleration must be at a minimum. The maximum would have to be the speed of the object because right before the object is in equilibrium it's speed is increasing and suddenly after the point of equilibrium the object starts to decrease meaning at the point of equilibrium the speed of the object must be at a maximum.
When the spring is in a state of equilibrium the forces are equal to zero. This is when the speed is a maximum but the acceleration is a minimum. This state of equilibrium occurs when the spring is neither compressed or stretched out. It occurs in the center. When the spring is completely stretched out and compressed the speed is at a minimum due to the acceleration being greater. Because the acceleration is at a maximum at these points it allows the spring to slow down to its minimum speed.
When the spring is at the equilibrium, the net force acting on it is zero. F=ma, and because the mass is a non-zero constant and F=0, then a=0. Also, the point of equilibrium is a point of inflection. This means that the acceleration changes from positive to negative. Therefore, the velocity is at its maximum. Then, when the spring as at its endpoints, the acceleration is a maximum, and the velocity is equal to 0.
From what i can gather about other's posts, the spring is in an equilibrium. Therefore the mass times the acceleration is zero. The point at which this occurs would be when the spring is in its natural shape, neither compressed or stretched. When it is stretched or compressed, the forces of gravity and acceleration are stronger. -Kelly Glenn
when the spring is in a state of equilibrium, the sum of the forces acting on it is zero. the acceleration is inversely proportional to speed, meaning when the speed is at its maximum, the acceleration is at a minimum and vice versa. this is also when the spring is in a state of equilibrium (F=ma=0). the acceleration is ) because it is shifting from positive to negative and has to be zero for an instant when changing direction.
At the max speed the spring stops accelerating the mass and starts to slow it down. The max speed is at the equilibrium of the spring where the acceration is zero because it is where the transition from positive to negative acceleration occurs.
ReplyDeleteWhen the mass reaches its equilibrium position the acceleration reaches zero because the tip between negative and positive acceleration occurs here. That would mean that acceleration is at its minimum causing speed to be at a maximum due to the fact that all the potential energy has switched over to kinetic energy at that specific point.
ReplyDelete-Emily F
The equilibrium of the spring marks the maximum speed and also the minimum acceleration (which would actually be zero here). As the mass transitions above the equilibrium, the acceleration is a negative, and as the mass transitions below this point, the acceleration becomes positive. This is not only the changeover for acceleration, but it is also the conversion from kinetic to potential energy.
ReplyDeleteRachel R
When equilibrium is achieved, speed is a maximum and acceleration is a minimum. This is the point at which the forces acting on the mass (gravity and normal) are equal to zero. This means that there would be no unbalanced forces at this point to affect the object's speed. This means that the speed would be at its maximum. This being said, one can also observe that the acceleration is equal to zero. The forces are equal to zero. This makes F=ma into 0=(a constant mass)(a). Acceleration would have to be equal to zero, making it a minimum. It is also a property of equilibrium for acceleration to be 0 m/s/s.
ReplyDeleteAre both the speed and acceleration changing?
DeleteI believe so. Someone correct me if I'm wrong.
DeleteI wasn't able to look at this on the 24th, so today when I used the link the site said it was a problem for the 26th. I don't think it is the same problem, what should I do?
ReplyDeleteThe physics question was something along the lines of a spring has a mass on it, and the spring gets pulled so that it goes up to down vertically and repeatedly. There were no values, and then one had to say what Mr. Crane asked here, assuming the equilibrium is in the center of that motion. I'm not sure how they worded it, but that's the general idea...
ReplyDeleteI too was not able to get on the blog on the 24th, but from what I can gather from these comments the problem involves some sort of spring and an equilibrium. An equilibrium is a state in which all forces acting on an object, the mass in this case, are balanced. In a case where an mass is being swung in a circle, equilibrium occurs when the acceleration is at a minimum and the speed at a maximum.
ReplyDeleteSydnee V
I wasn't able to look at the blog on the 24th either so the question has now changed. But I read Brooke's synopsis of the problem and read all the comments and what i can put together is that when the the spring and mass are at an equilibrium, the maximum would be the speed and the minimum would be the acceleration. The acceleration would be equal to zero because if there is an equilibrium and the forces equal 0 then according to f=ma, acceleration would have to be 0. If acceleration is zero it has reached its minimum. At this point it seems that the acceleration also changes from positive to negative.
ReplyDeleteBeing on vacation I too was not able to view this problem until now, but just as Nicole and Sydnee did I was able to gather information from previous comments made. When the speed of the spring is a maximum, the acceleration of the spring is a minimum, which is also when it is at its equilibrium. At this moment, all forces are equal, hence the word "equilibrium". Therefore, F=ma is zero in that moment. The reason the acceleration is zero is because it is shifting from positive to negative and no object can change direction without being zero for at least an instant.
ReplyDeleteThe equilibrium of the spring, or the position when the forces are equal to zero is when the speed is at a maximum and the acceleration is at a minimum. This is also the middle of the motion, in which the spring is either retracting from the farthest point and decelerating into the compressed position and vice versa. The minimum speed(s) would occur at the furthest positive and negative positions from the point of equilibrium (when the spring is stretched the furthest and shrunk to being the most compact).
ReplyDeleteAfter answering the fourth day question and looking up the phrase "simple harmonic motion", I found that the phrase relates to this spring motion, as well. Therefore, I'd like to add to my answer the maximums and mins of kinetic and potential energy. The maximum kinetic energy occurs at equilibrium or the middle of the motion, and this is also where potential energy is at its minimum. In contrast, the minimum kinetic energy occurs at the points of maximum and minimum displacement, where the potential energy is at its maximum.
DeleteAt the point of equilibrium the sum of the forces are equal to zero, F=ma=0, just as everyone else has said... At that point the acceleration is zero and when the object continues upwards gravity will start pulling it down, increasing the acceleration again. To me this means that at the point of equilibrium the acceleration must be at a minimum. The maximum would have to be the speed of the object because right before the object is in equilibrium it's speed is increasing and suddenly after the point of equilibrium the object starts to decrease meaning at the point of equilibrium the speed of the object must be at a maximum.
ReplyDeleteWhen the spring is in a state of equilibrium the forces are equal to zero. This is when the speed is a maximum but the acceleration is a minimum. This state of equilibrium occurs when the spring is neither compressed or stretched out. It occurs in the center. When the spring is completely stretched out and compressed the speed is at a minimum due to the acceleration being greater. Because the acceleration is at a maximum at these points it allows the spring to slow down to its minimum speed.
ReplyDeleteEmma H.
When the spring is at the equilibrium, the net force acting on it is zero. F=ma, and because the mass is a non-zero constant and F=0, then a=0. Also, the point of equilibrium is a point of inflection. This means that the acceleration changes from positive to negative. Therefore, the velocity is at its maximum. Then, when the spring as at its endpoints, the acceleration is a maximum, and the velocity is equal to 0.
ReplyDeleteFrom what i can gather about other's posts, the spring is in an equilibrium. Therefore the mass times the acceleration is zero. The point at which this occurs would be when the spring is in its natural shape, neither compressed or stretched. When it is stretched or compressed, the forces of gravity and acceleration are stronger. -Kelly Glenn
ReplyDeletewhen the spring is in a state of equilibrium, the sum of the forces acting on it is zero. the acceleration is inversely proportional to speed, meaning when the speed is at its maximum, the acceleration is at a minimum and vice versa. this is also when the spring is in a state of equilibrium (F=ma=0). the acceleration is ) because it is shifting from positive to negative and has to be zero for an instant when changing direction.
ReplyDelete