Purpose of the experiment

Transcription

1 Work and Energy PES 1160 General Physics Lab I Purpose of the experiment What is Work and how is related to Force? To understand the work done by a constant force and a variable force. To see how gravitational potential energy is stored in a mass and how elastic potential energy is stored in a spring. To make an experimental verification of the Work-Energy Theorem. FYI FYI Celery has negative calories! It takes more calories to eat a piece of celery than the celery has in it. Work and Energy - 1

2 Background Information Conservation of Energy It is difficult to precisely define what energy is. A good definition is that energy is the stuff in the universe that is capable of doing work. (Energy really is some form of stuff, just like matter is stuff. In fact, Einstein s famous equation E = mc 2 tells us that mass is really just congealed energy.) Luckily, we do not have to worry about what energy is, but rather how it behaves. The way energy behaves is called conservation. Conservation has a specific meaning in physics. To a physicist, when something is conserved, it means that quantity does not change with time. One quantity that is conserved in physics is energy. In fact, the conservation of energy is a fundamental law of physics. Simply put, the conservation of energy states that: For any isolated system (i.e. a system that does not interact with its environment), the energy of the system will remain constant. Since the universe is an isolated system (as far as we know), the total amount of energy in the universe is constant. Another way of stating the conservation of energy is as follows: Energy cannot be created or destroyed. Instead, energy changes between forms. So, what causes energy to change form? The answer is force. Force is the agent that causes energy to change from one type (such as potential energy) to another (such as kinetic energy or heat). We can divide forces into two types: conservative forces that keep the energy with the object that the force is acting on (like gravity, tension, or a spring force), and non-conservative forces that cause energy to be exchanged between objects (such as friction or air resistance). The term non-conservative force is a little misleading, however. The energy is still conserved with a force like friction. However, it is usually converted to heat. Work and Energy - 2

3 Kinetic Energy Kinetic energy is the energy of motion. An object that has motion - whether it is vertical or horizontal motion - has kinetic energy. There are many forms of kinetic energy - vibrational (the energy due to vibrational motion), rotational (the energy due to rotational motion), and translational (the energy due to motion from one location to another). To keep matters simple, we will focus upon translational kinetic energy. The amount of translational kinetic energy that an object has depends upon two variables: the mass (m) of the object and the speed (v) of the object. The following equation is used to represent the kinetic energy (KE) of an object. K = 1 2 mv2 This equation reveals that the kinetic energy of an object is directly proportional to the square of its speed. That means that for a twofold increase in speed, the kinetic energy will increase by a factor of four. Like work and potential energy, the standard metric unit of measurement for kinetic energy is the Joule. 1 Joule = 1 kg m 2 /s 2 Potential Energy An object can store energy as the result of its position. For example, lifting a book above a table is storing energy when it is held at an elevated position. This stored energy of position is referred to as potential energy. Gravitational potential energy is the energy stored in an object as the result of its vertical position or height. The energy is stored as the result of the gravitational attraction of the Earth for the object. The gravitational potential energy of the massive ball of a demolition machine is dependent on two variables - the mass of the ball and the height to which it is raised. There is a direct relation between gravitational potential energy and the mass of an object. More massive objects have greater gravitational potential energy. There is also a direct relation between gravitational potential energy and the height of an object. The higher that an object is elevated, the greater the gravitational potential energy. Work and Energy - 3

4 These relationships are expressed by the following equation: U gravity = mgx Elastic potential energy is the energy stored in elastic materials as the result of their stretching or compressing. Elastic potential energy can be stored in rubber bands, bungee chords, etc. The amount of elastic potential energy stored in such a device is related to the amount of stretch of the device - the more stretch, the more stored energy. Springs are a special instance of a device that can store elastic potential energy due to either compression or stretching. A force is required to compress a spring; the more compression there is, the more force that is required to compress it further. The amount of force is directly proportional to the amount of stretch or compression (x); the constant of proportionality is known as the spring constant (k). Fspring = -k x Such springs are said to follow Hooke's Law. If a spring is not stretched or compressed, then there is no elastic potential energy stored in it. The spring is said to be at its equilibrium position. The equilibrium position is the position that the spring naturally assumes when there is no force applied to it. In terms of potential energy, the equilibrium position could be called the zero-potential energy position. There is a special equation for springs that relates the amount of elastic potential energy to the amount of stretch (or compression) and the spring constant. The equation is U elastic = 1 2 kx2 Work and Energy - 4

5 Displacement Work and Energy Applied Force Work is a measure of energy transfer. In the absence of friction, when positive work is done on an object, there will be an increase in its kinetic or potential energy. In order to do work on an object, it is necessary to apply a force along or against the direction of the object s motion. If the force is constant and parallel to the object s path, work can be calculated using: W = F x where F is the constant force and x the displacement of the object. If the force is not constant, we can still calculate the work using a graphical technique. If we divide the overall displacement into short segments, x, the force is nearly constant during each segment. The work done during that segment can be calculated using the previous expression. The total work for the overall displacement is the sum of the work done over each individual segment: W = F(x) x This sum can be determined graphically as the area under the plot of force vs. distance. Work and Energy - 5

6 If you ve had calculus, you should recognize this sum as leading to the integral: x f W = F(x)dx x o These equations for work can be easily evaluated using a Force Sensor and a Rotary Motion Sensor. In either case, the work-energy theorem relates the work done to the change in energy as: W = U + K where W is the work done, U is the change in potential energy, and K the change in kinetic energy, K = 1 2 mv2 1 2 mv O 2. Work is the measure of amount of energy transferred to an object via forces. Work and Energy - 6