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LAB 4: Work and Energy

OBJECTIVES

m  To understand the concept of work in physics as an extension of the intuitive understanding of effort.

m  To explore kinetic energy, gravitational potential energy, and conservation of mechanical energy.

INTRODUCTION

While Newton’s laws provide the basic framework for attacking any problem in physics, the calculations they use are sometimes more complicated than are necessary to find a solution. One of the first shortcuts which physics uses is the concept of work and energy.

We intuitively think of “work” being synonymous with “effort”. This, however, comes closer to merely meaning force than anything else. When a physicist says that work has been done, then, he means something else: namely, that force has been exerted, and that what it has been exerted on has moved in the direction of the force.

If gravity pulls on your textbook sitting on your desk, it does no work. If, however, you knock your book off the desk, gravity works as the object accelerates to the floor.

Interestingly enough, when an object is moving opposite to the force, the force does negative work. When you pick your textbook off the floor, you do work in lifting it, but gravity does negative work as it continues to pull down as the book goes up.

Energy is a trickier concept. We see energy in various forms all around: we turn on lights, hear sounds, burn fuel in fireplaces, and avoid getting run over by rapidly moving cars. However, quantifying energy is not nearly so intuitive. As it turns out, however, the work done on an object can be represented by the following equation:

This quantity is defined to be the kinetic energy (energy of motion) of the object or particle. The difference between initial and final kinetic energy is the work done on the object.

One consequence of this is that all energy – not merely kinetic, but also chemical, electromagnetic, nuclear, and even potential energy – is measured in Joules, just like work.

One of the most powerful ideas in all of physics is the law of conservation of energy. In this lab, you will be working with only one form of this law: the conservation of mechanical energy in situations where there is no friction. (Friction steals energy from systems and dissipates it in another form, usually heat.)

INVESTIGATION 1: THE CONCEPTS OF PHYSICAL WORK AND POWER

You will need the following materials for this investigation:

m  force probe

m  ruler

m  protractor

m  PASCO motion track and cart

m  materials to incline track

m  two ½ kg masses

m  motion sensor

Activity 1.1: Work and Power: Motion In Line and out of Line with Force

In this activity you will measure the force needed to pull a cart up an inclined plane using a force probe. You will examine two situations. First, you will exert a force parallel to the surface of the track, and then you will exert a force at an angle to the track. You will then be able to see how to calculate the work when the force and displacement are not in the same direction in such a way that the result makes physical sense.

Note: the hook on the force probe can be removed so that it can easily be inserted through the hole at one end of the cart. You can then screw the hook back on the force probe. The following experiment works best when you place the motion sensor at the bottom of the incline and record the velocity of the cart as you push it.

  1. Set up the cart and track as shown in the diagram below. Place the two weights in the top of the cart. Support one end of the track so that it is inclined to about 15°-20° or a little steeper.
  1. Open Data Studio. If the Force Probe data appears but says “Force, push positive,” click Setup and check the box next to “Force, pull positive” under the force sensor. Then, if there is not a graph already displayed, open a graph for force data. Make sure you also have a graph of velocity so you can watch it as you move the cart.
  2. Hook the force sensor onto the cart and take force data while pulling the cart up the track. The cart’s velocity should be as constant as you can make it.
  3. Use the Fit or Statistics tool to find the mean force exerted:

Mean force pulling parallel to track: ______N

Next you will pull the cart at an angle to the track surface.

Prediction 1-1: The force you will be exerting on the cart will be inclined 45° to the track. Predict what the force sensor will read as you pull the cart. (It may be helpful to draw a free-body diagram.)

Predicted force: ______N

  1. Test your prediction with the cart and inclined track, using the protractor to keep the force probe at the correct angle. Pull the cart slowly and steadily, and make sure that the wheels do not leave the track surface. Analyze the data as you did before, comparing a period of time when the average velocity was equal to that from the first trial.

Mean force pulling at 45° angle to track: ______N

Question 1-1: It is only the component of the total force which is parallel to the track which we use in calculating work. Find a formula for determining this component for any angle at which one might pull the cart. Express your answer in terms of q, the angle between the track and the force vector. Refer to Prediction 1-1, especially if you drew a free-body diagram.

Formula: Ftrack = ______

INVESTIGATION 2: WORK DONE BY CONSTANT AND NONCONSTANT FORCES

Few forces in nature are constant. Most vary according to the distance over which they are acting. In this investigation you will measure the work done by a constant force, namely gravity, and a spring force varying with the distance the spring is stretched from the spring’s point of equilibrium.

You will need the following equipment:

m  motion detector

m  force sensor

m  400 g mass

m  index card and masking tape

m  PASCO cart and track

m  spring

m  force accessory bracket (black S-shaped metal object)

Activity 2.1: Work done by a constant lifting force

In this activity you will measure the work done when you lift an object from the floor through a measured distance. You will use the force probe to measure the force and the motion detector to measure distance.

  1. The motion detector should be on the floor, pointing upward.
  2. Open the experiment file Work in Lifting 1 from the Physics 131 folder.
  3. Tape the index card to the bottom of the 400 g mass as shown. (This is so that the motion detector can see the system more easily. You will not be moving the mass fast enough for drag to build up and introduce error in this experiment.)
  4. Zero the force probe with the hook pointing vertically downward. (Push the “Zero” button on it.)
  5. Hang the 400 g mass from the probe’s hook. The index card must be very close to horizontal for the motion detector data to be accurate.

Prediction 2-1: You will be lifting the weight at constant velocity. Predict the upward force you will have to exert to obtain a constant upward velocity.

  1. Hold the force probe and hanging weight at least 20 cm above the detector. Begin graphing and lift the whole system at a slow, constant speed through a distance of about 1 m. Check the position vs. time graph to make sure you have clean data.
  2. When you get a graph in which the mass was moving at a reasonably constant velocity, print a graph of force and velocity vs. time to turn in at the end of lab.

Question 2-1: Did the force needed to move the mass depend on how high it was off the floor, or was it reasonably constant?

  1. There should be a force vs. position graph minimized behind the position-time graph you have been working with (if you cannot find it, Window > Force vs Position should bring it forward). Print out a copy of this graph also.
  1. Use the Statistics tool to find the average force during the period the mass was being lifted. Record this force and the distance below. (You can use the Smart Tool to find the distance.)

Average Force: ______N Distance lifted: ______m

Question 2-2: Did this average force agree with your prediction? If not, why not?

  1. Calculate the work done in lifting the mass. Show your calculation below:

Work: ______J

  1. Look at your second graph geometrically. Take any rectangle on it: its width is measured in meters, while its height has units of force. Therefore, the area of the rectangle has units of N•m, which simplifies to joules. Find the area of the region under your data between start and finish using Data Studio’s area function. To use the area function, select “area” in the pulldown menu for Statistics (S).

area: ______J

Does this equal your calculation of work from step 10? Should it?

Activity 2.2: Work Done by a Varying Spring Force

In this activity you will measure the work done when you stretch a string through a measured distance. First you will collect data on the force exerted by a spring as it moves from being stretched back to its equilibrium position. From the force vs. position graph you obtain you will be able to calculate the work done in the experiment as you did in the last activity.

  1. Set up the track, motion detector, force probe, and spring as shown in the diagram.

To mount the force probe, you will use the Force Accessory Bracket. It should be mounted to the metal track using the two bolts on the side. The nuts fit into the slot on the side of the metal track, as shown in the diagram below. Unscrew one of the accessory bolts on the bracket and put it through the hole on the Force Sensor. Use this screw to mount the Force Sensor to the bracket so that the hook on the Force Sensor sticks out towards the track.

(See diagram on the next page.)

  1. Continue to use the Work in Lifting activity file.
  2. When the spring is at equilibrium, record the position of the cart.
  3. Zero the force probe with the spring hanging loosely from its hook.
  4. Holding the cart with your hand (but letting the motion detector see only the cart!) begin graphing and slowly move the cart toward the motion detector, stretching the spring until you have displaced the cart at least one meter.

When you have a good force-position graph, print out a copy to turn in at the end of lab.

Question 2-1: Compare this graph to the force-position graph from Activity 2.1. Apply your fit tools to this graph to determine how the spring’s force varies with distance. Describe the relationship (e.g. linear, parabolic, etc.):

Question 2-2: Can you use the first definition you were given for work, , to calculate the work in this experiment? Why or why not?

As your last activity should have shown, the area under the graph is equal to the work in the experiment. Use the area function to measure the work done:

area = ______J

This technique of measuring work (and external energy) by taking the area under the force curve tells us something more general about the relation of work/energy to force:

As you can see from this formulation, is a special case of the above equation, namely when force is constant.

INVESTIGATION 3: KINETIC ENERGY AND THE WORK-ENERGY PRINCIPLE

In systems where only one force is acting on an object to accelerate it, it is easy to observe that the object’s energy is increasing as it accelerates. As you have learned, kinetic energy (that is, energy of motion) is defined as having a value of

The units energy is measured in () are the same as for work. This may be confusing at first; however, the matter is cleared up when we realize that doing work on a system is precisely the same as adding energy to it. This is called the “Work-Energy Principle”: a system’s total energy increases or decreases by the amount of external work done on the system.

You will need the following materials for this investigation:

m  motion detector

m  force probe

m  spring

m  track

m  PASCO cart

m  two 500 g masses to put on cart

Activity 3.1: Kinetic Energy from a Spring

  1. Set up the track, cart, motion detector, spring, and force probe as shown in the diagram that follows. Place both 500 g masses on the cart.
  1. Open the experiment file Work-Energy 1 in the Physics 131 folder.
  2. From the “Setup” menu, set the force probe and the motion sensor to take data at 50 Hz by pushing the (+) button. Otherwise, you will only get one or two data points.

The calculator should open when you open the experiment file; if it does not, you can open it with the “Calculate” button.

To enter an equation in the calculator, press “New”, enter the equation in the blank field, and press “Accept”. (We have entered a dummy equation for y in the following figure.)