a) False: the acceleration is a minimum when the displacement is at a MAX. The direction of the centripetal acceleration is always perpendicular to the ball's path. The magnitude of the centripetal acceleration depends on the ball's velocity. The larder the velocity, the larger the centripetal acceleration. At the top of the swing where the ball's velocity is momentarily zero, the centripetal acceleration is also zero. There is no tension in the string at that moment. b) False: The period of the motion for a pendulum is how long it takes to swing back-and-forth, measured in seconds. The reason lies in the nature of gravity: under the influence of gravity, all bodies, no matter what their mass is, accelerate at the same rate. This is also true for bodies attached to a rope, resulting in a pendulum. A good example of this is how an elephant, ant, human, dog, cat, and donkey all fall with the same reason c) False: At the top of its swing (the max displacement), its potential energy will be greatest, meaning there will be no kinetic energy. At the bottom of its swing, its potential energy will be the least, meaning there will be only kinetic energy. d) True? Process of elimination e) False: The period of a pendulum gets longer as the amplitude (width of swing) increases. - Rachel Rha
I believe a is the answer. When the displacement is a minimum, the mass is at the point at which it was released from. At this point, acceleration is zero, making it a minimum as well. B was incorrect because the mass would not changed the trend that occurs with the pendulum. C was incorrect because when displacement is a maximum, it is at the "turning point" of the motion. This means that the kinetic energy has become potential energy at this point. There is no kinetic energy here, so it cannot be a maximum. D is incorrect because frequency is the relationship between a trend and the time it takes to be completed. If theta was increased, the mass would experience a greater acceleration. A smaller theta would create a smaller acceleration. This relationship shows that the frequency would stay the same in any swing. E is incorrect because the length of the rope would change the course the mass takes. This was a tough question. I had trouble because I could imagine situations that made multiple answers true.
I believe d is the correct answer. The smaller the angle, the less distance the pendulum travels. Therefore it occurs more frequently. If you where to make the angle larger the distance traveled would be larger as well but have the same speed as the smaller angle. Therefore, the smaller the angle the more frequent
I also believe d to be the correct answer. If everything else in the problem remains constant including acceleration, m, and L then the mass will swing more frequently than a mass that has to travel a larger distance. I do feel that a pendulum with a larger displacement will pick up speed faster due to its momentum but I'm not sure. Out of all of the choices though, I feel this one is most fit
I believe that the answer is a). It is stated in the problem that the mass is negligible. Because the mass is negligible (someone correct me if I'm wrong) it won't effect the frequency as the angle changes, which means that d) is a false statement.
I agree that a is the correct answer, but in the problem it states that the mass of the string is negligible, not the mass of the object on the string. Although this is true, it really did not have any effect in my calculations to find a as the correct answer.
The correct answer is D. The angle affects the pendulum's frequency inversely. If the angle is increased, the frequency is decreased, and if the angle is decreased, the frequency is increased, assuming everything else remains the same in both scenarios. -John Mairone
I too believe believe that D is the correct answer. Just as John said, a change in the angle inversely affects the frequency of the swing. The higher up and object is pulled along its path of motion the longer it will take to complete one swing meaning the frequency is decreasing. However, the lower down you release the object the quicker it will complete one swing meaning the frequency is increased.
I was a little confused after first reading this problem, however, after going through the other posts, I began to understand the concept. It appears to me that D is the correct answer. By changing the angle, the time for the pendulum to complete a full swing is changed. A larger angle would mean the pendulum would have a larger distance to travel, and a smaller angle would mean a smaller distance. Larger distance would lead to a longer time, and a shorter distance would lead to a shorter time. So, a smaller angle would cause a full swing to occur much more frequently.
Because I was not familiar with the phrase "simple harmonic motion", I looked it up and was surprised that I was actually familiar with the phrase's motion. "Simple harmonic motion" or "harmonic motion" in general is also related to the action of the spring that was the first question in the 12 Days of Physics. So,
a) This answer is false because the motion is similar to that of the spring. The acceleration is actually at a max when it reaches displacement of a minimum, which is the equilibrium or the balance of all forces. b) This is false because regardless of the mass of the object attached, the motion will not change. c) After researching, this answer is also false. My research indicates that at a maximum displacement, the potential energy is actually at a maximum, and the kinetic energy is at a minimum- not a maximum. The maximum kinetic energy occurs at the equilibrium. d) This answer is true because even with the "When Pigs Fly" lab, the bigger the circle / the larger the diameter, the longer the period and the less times or the frequency of the rotations was lessened. The smaller the circle / the smaller the diameter, the smaller the period and the more frequent the rotations would occur (if any of this makes any sense). I think the same idea applies to this simple harmonic motion. e) This answer is false because again the longer the string, the longer the period.
I see there is a debate about whether it's a or d. At first I liked the answer that d had but it talks about frequency and I thought about that a bit. The pendulum isn't applying a force so frequency shouldn't be involved in this, if you graph the problem at differing angles the wavelength should be the only thing that changes. Due to process of elimination I concluded that it's a, but the way I would explain it to myself would be to look back at the First Day Of Christmas, at zero displacement the pendulum will be directly pointing down towards gravity, not moving, not accelerating, so the acceleration would have to be zero. If it was moving it would constantly be accelerating to a point of zero acceleration and it'll achieve it eventually due to air resistance.
I believe the answer is D. The angle affects the frequency of the pendulum. If m and L are constant, the angle will inversely affect it. The larger the angle, the frequency will decrease and vice versa. A larger angle means more distance and more time which would lessen frequency. This is why the larger angle will decrease frequency and a smaller one would increase it.
In my opinion, D is the correct answer to this problem. A is false because the acceleration is a max when displacement is min and acceleration is a min when displacement is a max. B is false because the acceleration of gravity, which affects the period of the pendulum, is the same for all objects regardless of mass. C is false because the kinetic energy is a max when the displacement is a min. However, the potential energy is a max when the displacement is a max. Lastly, E is false because if the string is longer, it will take more time for the object to swing back and forth. D is the correct answer because as the angel increases, frequency decreases, and as the angle decreases, frequency increases.
I believe the correct answer is answer D. D is correct because as the angle increases, the distance the pendulum will have to travel will increase and as the distance increases the frequency will decrease. As the angle decreases, the distance the pendulum will have to travel will decrease and as the distance decreases the frequency will increase. The angle and the frequency are inversely related. A is false because the acceleration and displacement are inversely related and when one is at a min the other will be at a max. B is false because the period is related to the acceleration of gravity and does not vary with the mass. C is false because the kinetic energy and dislacement are inversely related and when one is at a min the other will be at a max. Finally, E is false because the longer the string the more time it'll take to swing back and forth and the shorter the string the less time it'll take to swing back and forth.
A: false. acceleration is at a min when displacement is at a max. the two are inversely proportional. B: false. period is related to acceleration of gravity which is the same no matter what the mass of an object. C: false. potential energy will be at a max when displacement is at a max. kinetic energy is inversely related to displacement. D: true. distance and frequency are inversely proportional. as angle decreases, frequency increases and vice versa. E: false. I wasn't sure about this one, but after looking it up i learned that the distance the string has to travel will be greater, making the period greater, much like how spinning around with your arms out is much harder than spinning with your arms by your sides. what i don't understand is why this takes longer? if we were to increase the length of the string, wouldn't there still be a part of the string that would have to travel the same distance as the first string? am i missing something here or could someone explain this to me?
a) False: the acceleration is a minimum when the displacement is at a MAX. The direction of the centripetal acceleration is always perpendicular to the ball's path. The magnitude of the centripetal acceleration depends on the ball's velocity. The larder the velocity, the larger the centripetal acceleration. At the top of the swing where the ball's velocity is momentarily zero, the centripetal acceleration is also zero. There is no tension in the string at that moment.
ReplyDeleteb) False: The period of the motion for a pendulum is how long it takes to swing back-and-forth, measured in seconds. The reason lies in the nature of gravity: under the influence of gravity, all bodies, no matter what their mass is, accelerate at the same rate. This is also true for bodies attached to a rope, resulting in a pendulum. A good example of this is how an elephant, ant, human, dog, cat, and donkey all fall with the same reason
c) False: At the top of its swing (the max displacement), its potential energy will be greatest, meaning there will be no kinetic energy. At the bottom of its swing, its potential energy will be the least, meaning there will be only kinetic energy.
d) True? Process of elimination
e) False: The period of a pendulum gets longer as the amplitude (width of swing) increases.
- Rachel Rha
I believe a is the answer. When the displacement is a minimum, the mass is at the point at which it was released from. At this point, acceleration is zero, making it a minimum as well. B was incorrect because the mass would not changed the trend that occurs with the pendulum. C was incorrect because when displacement is a maximum, it is at the "turning point" of the motion. This means that the kinetic energy has become potential energy at this point. There is no kinetic energy here, so it cannot be a maximum. D is incorrect because frequency is the relationship between a trend and the time it takes to be completed. If theta was increased, the mass would experience a greater acceleration. A smaller theta would create a smaller acceleration. This relationship shows that the frequency would stay the same in any swing. E is incorrect because the length of the rope would change the course the mass takes. This was a tough question. I had trouble because I could imagine situations that made multiple answers true.
ReplyDeleteI believe d is the correct answer. The smaller the angle, the less distance the pendulum travels. Therefore it occurs more frequently. If you where to make the angle larger the distance traveled would be larger as well but have the same speed as the smaller angle. Therefore, the smaller the angle the more frequent
ReplyDeleteI also believe d to be the correct answer. If everything else in the problem remains constant including acceleration, m, and L then the mass will swing more frequently than a mass that has to travel a larger distance. I do feel that a pendulum with a larger displacement will pick up speed faster due to its momentum but I'm not sure. Out of all of the choices though, I feel this one is most fit
ReplyDeleteI believe that the answer is a). It is stated in the problem that the mass is negligible. Because the mass is negligible (someone correct me if I'm wrong) it won't effect the frequency as the angle changes, which means that d) is a false statement.
ReplyDeleteI agree that a is the correct answer, but in the problem it states that the mass of the string is negligible, not the mass of the object on the string. Although this is true, it really did not have any effect in my calculations to find a as the correct answer.
DeleteOoops, I misinterpreted what I said. Thanks for clearing it up for me.
DeleteThe correct answer is D. The angle affects the pendulum's frequency inversely. If the angle is increased, the frequency is decreased, and if the angle is decreased, the frequency is increased, assuming everything else remains the same in both scenarios.
ReplyDelete-John Mairone
I too believe believe that D is the correct answer. Just as John said, a change in the angle inversely affects the frequency of the swing. The higher up and object is pulled along its path of motion the longer it will take to complete one swing meaning the frequency is decreasing. However, the lower down you release the object the quicker it will complete one swing meaning the frequency is increased.
ReplyDeleteI was a little confused after first reading this problem, however, after going through the other posts, I began to understand the concept. It appears to me that D is the correct answer. By changing the angle, the time for the pendulum to complete a full swing is changed. A larger angle would mean the pendulum would have a larger distance to travel, and a smaller angle would mean a smaller distance. Larger distance would lead to a longer time, and a shorter distance would lead to a shorter time. So, a smaller angle would cause a full swing to occur much more frequently.
ReplyDeleteBecause I was not familiar with the phrase "simple harmonic motion", I looked it up and was surprised that I was actually familiar with the phrase's motion. "Simple harmonic motion" or "harmonic motion" in general is also related to the action of the spring that was the first question in the 12 Days of Physics. So,
ReplyDeletea) This answer is false because the motion is similar to that of the spring. The acceleration is actually at a max when it reaches displacement of a minimum, which is the equilibrium or the balance of all forces.
b) This is false because regardless of the mass of the object attached, the motion will not change.
c) After researching, this answer is also false. My research indicates that at a maximum displacement, the potential energy is actually at a maximum, and the kinetic energy is at a minimum- not a maximum. The maximum kinetic energy occurs at the equilibrium.
d) This answer is true because even with the "When Pigs Fly" lab, the bigger the circle / the larger the diameter, the longer the period and the less times or the frequency of the rotations was lessened. The smaller the circle / the smaller the diameter, the smaller the period and the more frequent the rotations would occur (if any of this makes any sense). I think the same idea applies to this simple harmonic motion.
e) This answer is false because again the longer the string, the longer the period.
I see there is a debate about whether it's a or d. At first I liked the answer that d had but it talks about frequency and I thought about that a bit. The pendulum isn't applying a force so frequency shouldn't be involved in this, if you graph the problem at differing angles the wavelength should be the only thing that changes. Due to process of elimination I concluded that it's a, but the way I would explain it to myself would be to look back at the First Day Of Christmas, at zero displacement the pendulum will be directly pointing down towards gravity, not moving, not accelerating, so the acceleration would have to be zero. If it was moving it would constantly be accelerating to a point of zero acceleration and it'll achieve it eventually due to air resistance.
ReplyDeleteI believe the answer is D. The angle affects the frequency of the pendulum. If m and L are constant, the angle will inversely affect it. The larger the angle, the frequency will decrease and vice versa. A larger angle means more distance and more time which would lessen frequency. This is why the larger angle will decrease frequency and a smaller one would increase it.
ReplyDeleteIn my opinion, D is the correct answer to this problem. A is false because the acceleration is a max when displacement is min and acceleration is a min when displacement is a max. B is false because the acceleration of gravity, which affects the period of the pendulum, is the same for all objects regardless of mass. C is false because the kinetic energy is a max when the displacement is a min. However, the potential energy is a max when the displacement is a max. Lastly, E is false because if the string is longer, it will take more time for the object to swing back and forth. D is the correct answer because as the angel increases, frequency decreases, and as the angle decreases, frequency increases.
ReplyDeleteI believe the correct answer is answer D. D is correct because as the angle increases, the distance the pendulum will have to travel will increase and as the distance increases the frequency will decrease. As the angle decreases, the distance the pendulum will have to travel will decrease and as the distance decreases the frequency will increase. The angle and the frequency are inversely related. A is false because the acceleration and displacement are inversely related and when one is at a min the other will be at a max. B is false because the period is related to the acceleration of gravity and does not vary with the mass. C is false because the kinetic energy and dislacement are inversely related and when one is at a min the other will be at a max. Finally, E is false because the longer the string the more time it'll take to swing back and forth and the shorter the string the less time it'll take to swing back and forth.
ReplyDeleteA: false. acceleration is at a min when displacement is at a max. the two are inversely proportional.
ReplyDeleteB: false. period is related to acceleration of gravity which is the same no matter what the mass of an object.
C: false. potential energy will be at a max when displacement is at a max. kinetic energy is inversely related to displacement.
D: true. distance and frequency are inversely proportional. as angle decreases, frequency increases and vice versa.
E: false. I wasn't sure about this one, but after looking it up i learned that the distance the string has to travel will be greater, making the period greater, much like how spinning around with your arms out is much harder than spinning with your arms by your sides. what i don't understand is why this takes longer? if we were to increase the length of the string, wouldn't there still be a part of the string that would have to travel the same distance as the first string? am i missing something here or could someone explain this to me?