Draw the variation of kinetic energy and potential energy of a freely falling body with height

Let a body of mass m is at rest at a height h from the earth’s surface, when it starts falling, after a distance x (point B) its velocity becomes v and at earth’s surface its velocity is v’. Mechanical energy of the body : At point A : E A= Kinetic energy + Potential energy From third equation of motion at points A and C. Hence, the mechanical energy of a freely body will be constant. i.e. Total energy of the body during free fall, remains constant at all positions. The form of energy, however keeps on changing. At point A, energy is entirely potential energy and at point C, it is entirely kinetic energy In between A and C, energy is partially potential and partially kinetic. This variation of energy is shown in figure . Total mechanical energy stays constant ( mgh ) throughout. Thus is an isolated system, where only conservative forces cause energy changes, the kinetic energy and potential energy can change, but the mechanical energy of the system (which is sum of kinetic energy and potential energy) cannot change. We can, therefore, equate the sum of kinetic energy and potential energy at one instant to the sum of kinetic energy and potential energy at another instant without considering intermediate states. This law has been found to be valid in every situation. No violation, whatsoever, of this law has ever been observed.

\( \newcommand\) • • • • • • • Learning Objectives • Create and interpret graphs of potential energy • Explain the connection between stability and potential energy Often, you can get a good deal of useful information about the dynamical behavior of a mechanical system just by interpreting a graph of its potential energy as a function of position, called a potential energy diagram. This is most easily accomplished for a one-dimensional system, whose potential energy can be plotted in one two-dimensional graph—for example, U(x) versus x—on a piece of paper or a computer program. For systems whose motion is in more than one dimension, the motion needs to be studied in three-dimensional space. We will simplify our procedure for one-dimensional motion only. First, let’s look at an object, freely falling vertically, near the surface of Earth, in the absence of air resistance. The mechanical energy of the object is conserved, E = K + U, and the potential energy, with respect to zero at ground level, is U(y) = mgy, which is a straight line through the origin with slope mg . In the graph shown in Figure \(\PageIndex\). However, from the slope of this potential energy curve, you can also deduce information about the force on the glider and its acceleration. We saw earlier that the negative of the slope of the potential energy is the spring force, which in this case is also the net force, and thus is proportional to the acceleration. When x = 0, the slope, the force, and the acceler...

This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. See Answer See Answer See Answer done loading Question:POTENTIAL AND KINETIC ENERGY OBJECTIVES: To determine the potential and kinetic energy of a freely falling body To determine the loss in kinetic energy of an POTENTIAL AND KINETIC ENERGY OBJECTIVES: • To determine the potential and kinetic energy of a freely falling body • To determine the loss in kinetic energy of an inelastic collision • To calculate the percentage error of the experimental error of the velocity of a freely falling body using the conservation of mechanical energy of a body MATERIALS: • Tennis balls • Digital Timer • Meter stick THEORY: • Conservation of Mechanical Energy • A body raised to a certain height possesses potential energy due to its position. Since work was done to lift the body to a certain height, the body gains potential energy. When the body is released from its position, the potential energy is transformed into kinetic energy on its way down. Upon reaching the ground, the potential energy is converted into kinetic energy. Ideally, if there is no loss in kinetic energy, the body should bounce back to its original height. This only happens for a perfectly elastic collision • Inelastic Collision • In most situations however, once the body reaches the ground, some of its kinetic energy is lost (e.g., the body undergoes slight deformation upon collision with the gro...

This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. See Answer See Answer See Answer done loading Question:2. Potential and Kinetic energy OBJECTIVES: 1. To determine the potential and kinetic energy of a freely falling body 2. To determine the loss in kinetic energy of an inelastic collision 3. To calculate the percentage error of the experimental error of the velocity of a freely falling body using the conservation of mechanical energy of a body MATERIALS: 1. 2. Potential and Kinetic energy OBJECTIVES: 1. To determine the potential and kinetic energy of a freely falling body 2. To determine the loss in kinetic energy of an inelastic collision 3. To calculate the percentage error of the experimental error of the velocity of a freely falling body using the conservation of mechanical energy of a body MATERIALS: 1. Tennis balls (or any ball) 2. Digital Timer 3. Meter stick Procedural Instructions: 1. Decide as the original height from which the ball will be dropped. Record this in your data table. After the ball bounces up twice, record also the maximum height reached by the ball for each bounce. Note these two maximum heights. 2. Record the time for the ball to reach the ground from its original height, first maximum height, and second maximum height. Note you would be needed to measure these different times. Record these in your data table. 3. Complete your data table to find for the velocity of the ...

Energy of falling object Energy as a tool for mechanics problem solving The application of the The R Nave Object Falling from Rest As an object falls from rest, its If an object is dropped from height h = m, then the velocity just before impact is v = m/s. If the mass is m = kg, then the kinetic energy just before impact is equal to K.E. = J, which is of course equal to its initial potential energy. The accuracy of this calculation depends upon the assumption that R Nave

This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. See Answer See Answer See Answer done loading Question:POTENTIAL AND KINETIC ENERGY OBJECTIVES 1. To determine the potential and kinetic energy of a freely falling body 2. To determine the loss in kinetic energy of an inelastic collision 3. To calculate the percentage error of the experimental error of the velocity of a freely fulling body using the conservation of mechanical energy of a body MATERIALS 1. Tennis POTENTIAL AND KINETIC ENERGY OBJECTIVES 1. To determine the potential and kinetic energy of a freely falling body 2. To determine the loss in kinetic energy of an inelastic collision 3. To calculate the percentage error of the experimental error of the velocity of a freely fulling body using the conservation of mechanical energy of a body MATERIALS 1. Tennis balls 2. Digital Timer 3. Meter stick THEORY 1. Conservation of Mechanical Energy • A body raised to a certain height possesses potential energy due to its position Since work was done to lift the body to a certain height, the body gains potential energy. When the body is released from its position, the potential energy is transformed into Kinetic energy on its way down Upon reaching the ground, the potential energy is converted into Kinetic energy. Ideally, if there is no loss in kinetic energy, the body should bence back to its original height This only happens for a perfectly elastic ...

Energy of falling object Energy as a tool for mechanics problem solving The application of the The R Nave Object Falling from Rest As an object falls from rest, its If an object is dropped from height h = m, then the velocity just before impact is v = m/s. If the mass is m = kg, then the kinetic energy just before impact is equal to K.E. = J, which is of course equal to its initial potential energy. The accuracy of this calculation depends upon the assumption that R Nave

Let a body of mass m is at rest at a height h from the earth’s surface, when it starts falling, after a distance x (point B) its velocity becomes v and at earth’s surface its velocity is v’. Mechanical energy of the body : At point A : E A= Kinetic energy + Potential energy From third equation of motion at points A and C. Hence, the mechanical energy of a freely body will be constant. i.e. Total energy of the body during free fall, remains constant at all positions. The form of energy, however keeps on changing. At point A, energy is entirely potential energy and at point C, it is entirely kinetic energy In between A and C, energy is partially potential and partially kinetic. This variation of energy is shown in figure . Total mechanical energy stays constant ( mgh ) throughout. Thus is an isolated system, where only conservative forces cause energy changes, the kinetic energy and potential energy can change, but the mechanical energy of the system (which is sum of kinetic energy and potential energy) cannot change. We can, therefore, equate the sum of kinetic energy and potential energy at one instant to the sum of kinetic energy and potential energy at another instant without considering intermediate states. This law has been found to be valid in every situation. No violation, whatsoever, of this law has ever been observed.

\( \newcommand\) • • • • • • • Learning Objectives • Create and interpret graphs of potential energy • Explain the connection between stability and potential energy Often, you can get a good deal of useful information about the dynamical behavior of a mechanical system just by interpreting a graph of its potential energy as a function of position, called a potential energy diagram. This is most easily accomplished for a one-dimensional system, whose potential energy can be plotted in one two-dimensional graph—for example, U(x) versus x—on a piece of paper or a computer program. For systems whose motion is in more than one dimension, the motion needs to be studied in three-dimensional space. We will simplify our procedure for one-dimensional motion only. First, let’s look at an object, freely falling vertically, near the surface of Earth, in the absence of air resistance. The mechanical energy of the object is conserved, E = K + U, and the potential energy, with respect to zero at ground level, is U(y) = mgy, which is a straight line through the origin with slope mg . In the graph shown in Figure \(\PageIndex\). However, from the slope of this potential energy curve, you can also deduce information about the force on the glider and its acceleration. We saw earlier that the negative of the slope of the potential energy is the spring force, which in this case is also the net force, and thus is proportional to the acceleration. When x = 0, the slope, the force, and the acceler...

This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. See Answer See Answer See Answer done loading Question:2. Potential and Kinetic energy OBJECTIVES: 1. To determine the potential and kinetic energy of a freely falling body 2. To determine the loss in kinetic energy of an inelastic collision 3. To calculate the percentage error of the experimental error of the velocity of a freely falling body using the conservation of mechanical energy of a body MATERIALS: 1. 2. Potential and Kinetic energy OBJECTIVES: 1. To determine the potential and kinetic energy of a freely falling body 2. To determine the loss in kinetic energy of an inelastic collision 3. To calculate the percentage error of the experimental error of the velocity of a freely falling body using the conservation of mechanical energy of a body MATERIALS: 1. Tennis balls (or any ball) 2. Digital Timer 3. Meter stick Procedural Instructions: 1. Decide as the original height from which the ball will be dropped. Record this in your data table. After the ball bounces up twice, record also the maximum height reached by the ball for each bounce. Note these two maximum heights. 2. Record the time for the ball to reach the ground from its original height, first maximum height, and second maximum height. Note you would be needed to measure these different times. Record these in your data table. 3. Complete your data table to find for the velocity of the ...