How does tension work for a simple pendulum? What force is at play to keep a rigid body from stretching? Ask Question. Asked 2 years, 7 months ago. Active 2 years, 7 months ago. Viewed 4k times. Improve this question. Ayden Cook Ayden Cook 45 1 1 silver badge 4 4 bronze badges. Add a comment. Active Oldest Votes. Improve this answer.
BioPhysicist BioPhysicist So therefore, what force is the force that accelerates the bob upwards after reaching the equilibrium point?
The tension force is larger than the weight, which is what is causing the upward acceleration to change the direction of the velocity. The dot product is a scalar, and the tension force is a vector. I have been assuming a string of constant length. Were you assuming a string with elasticity? What you said helps though, so if the tension is larger than the weight when the angle is 0, is there an equation to determine the magnitude of the tension force during swinging?
I think you actually said that in your first response Show 1 more comment. Sign up or log in Sign up using Google.
Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown. Featured on Meta. You might think of the bob as being momentarily paused and ready to change its direction. Next the bob moves rightward along the arc from G to F to E to D.
As it does, the restoring force is directed to the right in the same direction as the bob is moving. This force will accelerate the bob, giving it a maximum speed at position D - the equilibrium position. As the bob moves past position D, it is moving rightward alo ng the arc towards C, then B and then A. As it does, there is a leftward restoring force opposing its motion and causing it to slow down.
So as the displacement increases from D to A, the speed decreases due to the opposing force. Once again, the bob's velocity is least when the displacement is greatest. The bob completes its cycle, moving leftward from A to B to C to D. Along this arc from A to D, the restoring force is in the direction of the motion, thus speeding the bob up.
So it would be logical to conclude that as the position decreases along the arc from A to D , the velocity increases. Once at position D, the bob will have a zero displacement and a maximum velocity. The velocity is greatest when the displacement is least. The animation at the right used with the permission of Wikimedia Commons ; special thanks to Hubert Christiaen provides a visual depiction of these principles.
The acceleration vector that is shown combines both the perpendicular and the tangential accelerations into a single vector. You will notice that this vector is entirely tangent to the arc when at maximum displacement; this is consistent with the force analysis discussed above. And the vector is vertical towards the center of the arc when at the equilibrium position. This also is consistent with the force analysis discussed above. In a previous chapter of The Physics Classroom Tutorial, the energy possessed by a pendulum bob was discussed.
We will expand on that discussion here as we make an effort to associate the motion characteristics described above with the concepts of kinetic energy , potential energy and total mechanical energy. The kinetic energy possessed by an object is the energy it possesses due to its motion. It is a quantity that depends upon both mass and speed. The equation that relates kinetic energy KE to mass m and speed v is.
The faster an object moves, the more kinetic energy that it will possess. We can combine this concept with the discussion above about how speed changes during the course of motion.
This blending of concepts would lead us to conclude that the kinetic energy of the pendulum bob increases as the bob approaches the equilibrium position.
And the kinetic energy decreases as the bob moves further away from the equilibrium position. The potential energy possessed by an object is the stored energy of position. Two types of potential energy are discussed in The Physics Classroom Tutorial - gravitational potential energy and elastic potential energy. Elastic potential energy is only present when a spring or other elastic medium is compressed or stretched.
A simple pendulum does not consist of a spring. The form of potential energy possessed by a pendulum bob is gravitational potential energy.
The amount of gravitational potential energy is dependent upon the mass m of the object and the height h of the object. The equation for gravitational potential energy PE is.
The height of an object is expressed relative to some arbitrarily assigned zero level. In other words, the height must be measured as a vertical distance above some reference position. For a pendulum bob, it is customary to call the lowest position the reference position or the zero level.
So when the bob is at the equilibrium position the lowest position , its height is zero and its potential energy is 0 J. As the pendulum bob does the back and forth , there are times during which the bob is moving away from the equilibrium position. As it does, its height is increasing as it moves further and further away. It reaches a maximum height as it reaches the position of maximum displacement from the equilibrium position.
As the bob moves towards its equilibrium position, it decreases its height and decreases its potential energy. Now let's put these two concepts of kinetic energy and potential energy together as we consider the motion of a pendulum bob moving along the arc shown in the diagram at the right. We will use an energy bar chart to represent the changes in the two forms of energy. The amount of each form of energy is represented by a bar. The height of the bar is proportional to the amount of that form of energy.
The TME bar represents the total amount of mechanical energy possessed by the pendulum bob. The total mechanical energy is simply the sum of the two forms of energy — kinetic plus potential energy. What do you notice? When you inspect the bar charts, it is evident that as the bob moves from A to D, the kinetic energy is increasing and the potential energy is decreasing.
However, the total amount of these two forms of energy is remaining constant. Whatever potential energy is lost in going from position A to position D appears as kinetic energy. There is a transformation of potential energy into kinetic energy as the bob moves from position A to position D. Yet the total mechanical energy remains constant. We would say that mechanical energy is conserved.
As the bob moves past position D towards position G, the opposite is observed. Kinetic energy decreases as the bob moves rightward and more importantly upward toward position G. There is an increase in potential energy to accompany this decrease in kinetic energy.
Energy is being transformed from kinetic form into potential form. Yet, as illustrated by the TME bar, the total amount of mechanical energy is conserved.
This very principle of energy conservation was explained in the Energy chapter of The Physics Classroom Tutorial. Our final discussion will pertain to the period of the pendulum. As discussed previously in this lesson , the period is the time it takes for a vibrating object to complete its cycle. In the case of pendulum, it is the time for the pendulum to start at one extreme , travel to the opposite extreme , and then return to the original location.
Here we will be interested in the question What variables affect the period of a pendulum? We will concern ourselves with possible variables. The variables are the mass of the pendulum bob, the length of the string on which it hangs, and the angular displacement. The angular displacement or arc angle is the angle that the string makes with the vertical when released from rest. These three variables and their effect on the period are easily studied and are often the focus of a physics lab in an introductory physics class.
The data table below provides representative data for such a study. In trials 1 through 5, the mass of the bob was systematically altered while keeping the other quantities constant.
By so doing, the experimenters were able to investigate the possible effect of the mass upon the period. As can be seen in these five trials, alterations in mass have little effect upon the period of the pendulum. In trials 4 and , the mass is held constant at 0. However, the length of the pendulum is varied. By so doing, the experimenters were able to investigate the possible effect of the length of the string upon the period.
As can be seen in these five trials, alterations in length definitely have an effect upon the period of the pendulum. As the string is lengthened, the period of the pendulum is increased. There is a direct relationship between the period and the length.
Finally, the experimenters investigated the possible effect of the arc angle upon the period in trials 4 and The mass is held constant at 0. As can be seen from these five trials, alterations in the arc angle have little to no effect upon the period of the pendulum.
So the conclusion from such an experiment is that the one variable that effects the period of the pendulum is the length of the string. Increases in the length lead to increases in the period. But the investigation doesn't have to stop there. The quantitative equation relating these variables can be determined if the data is plotted and linear regression analysis is performed. The two plots below represent such an analysis. In each plot, values of period the dependent variable are placed on the vertical axis.
In the plot on the left, the length of the pendulum is placed on the horizontal axis. The shape of the curve indicates some sort of power relationship between period and length.
The results of the regression analysis are shown. The analysis shows that there is a better fit of the data and the regression line for the graph on the right. As such, the plot on the right is the basis for the equation relating the period and the length. For this data, the equation is. Using T as the symbol for period and L as the symbol for length, the equation can be rewritten as.
The value of 2. A pendulum bob is pulled back to position A and released from rest. The bob swings through its usual circular arc and is caught at position C. Determine the position A, B, C or all the same where the …. The force of gravity is everywhere the same since it is not dependent upon the pendulum's position; it is always the product of mass and 9. The restoring force is greatest at A; the further that the bob is from the rest position, the greater the restoring force.
The speed is greatest at C. The restoring force accelerates the bob from position A to position C. By the time the bob reaches C, it has accelerated to its maximum speed. The potential energy is the greatest at A. The potential energy is the greatest at the highest position.
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