Energy, Work, and Simple Machines

Energy             Energy can be defined in terms of what it can do. If an object has energy, the energy it contains can cause a change in the object itself or in its surroundings. Say an object has some heat energy. The heat energy can cause the object or its surroundings to show a temperature rise. Perhaps if the material has enough heat energy, it might even catch on fire. Another example: if a material contains some light energy it may glow and then the glow may cause nearby plants to grow. Of course there are many examples of energy inside some material causing a change in the material and perhaps in surrounding materials. How might sound energy affect a material or its surroundings? Vibration?

             Two common forms of energy are kinetic and potential. The work done on an object to get it moving gives the object kinetic energy. If the moving object touches another object, the kinetic energy contained in the moving object will cause some change in the second object. (We know about this from our momentum studies.) Common sense tells us not to stand in the path of a charging rhino to avoid changes created in us by its kinetic energy.

             The work you do on an egg to lift it up in the air gives it potential energy. How do you know the egg has gained PE by you lifting it? Just let it drop. The changes you see and hear in the egg when it impacts the floor are possible because of its PE change. Just let the egg sit on a surface and nothing happens to it because it has not undergone a PE change. And, of course, the amount of change the egg undergoes is related to the amount of its PE change. Lift it just a tiny bit and drop it – it may not even crack. Use KE = ½ m v ² The kinetic energy is in Joules, the m in kg and the v in m/s. For PE use

PE = mgh The potential energy is in Joules, the m in kg, the g is 9.8 m/s² and the h is in m.

             Note: we always speak about an object’s PE compared to a reference condition, perhaps the floor if the investigation focuses on the PE changes involved in raising and then dropping an egg. What if we are investigating the PE changes involved in stretching and releasing an elastic band? The distortion causes it to gain PE. How do we know? Just let go of it and watch it fly. In this example, we compare the PE of the stretched elastic band with that of the slack elastic band – the reference condition is the length of the slack elastic.

Work   The simplest definition of work is the amount of energy transferred between bodies. Work can be + or – . Use W = Fd and, since d = v t, we can also write W = F v t So, work (in Joules) is done on an object if the force applied to it causes it to move a certain distance or if the applied force causes it to move at a certain speed for a certain length of time. Work has no direction and so is a scalar.

             Work is done on an object only when it moves in the direction of the applied force. In the following situations, consider the direction of the applied force and the object’s motion.

1. Pushing against a wall: This may be tiring but, in the strict sense, does no work on the wall because it

    does not move.

2. Holding a box: Arm muscles apply an upward force to the box but unless it moves up, no work is done

    on it. Note: raising the box does positive work on it while lowering the box does negative work on it.

    Negative work means the object does work on you, i.e., transfers energy to you.

3. Walking across the room holding the box: The motion is not in the direction of the force applied by the

    arm muscles and so no work is done on the box.

4. Climbing stairs while holding the box: Leg muscles apply an upward force to the box (through the

    body) and when the box ascends, positive work is done on it. Descending the stairs does negative work

    on it, i.e., energy is transferred from the box to you.

             How do we know work transfers energy? When you do work on a box by lifting it, you are giving it energy, potential energy. Just drop it to see what changes occur to the box or its surroundings. Or, say you do a lot of work on a bowling ball by moving your arm quickly. How do you know you have given it energy? Just look at its speed and hear the crash as the pins fly.

             The work done on an object can be expressed visually in a displacement – force graph. The under-curve area equals the work.

             When force is applied at an angle to the intended motion, use trigonometry to find the force component parallel to the intended direction. When you mow the lawn you must apply extra force to the lawnmower handle because some of your force is “wasted”; only the horizontal component can move the mower over the grass. Similarly when you are pulling a sled, you must pull on the rope with extra force because some of your force is “wasted”; only the horizontal component can move the sled over the snow.

Power  Power and work are related through time: power is the rate at which work is done. It is the rate at which energy is transferred between objects. Use P = W / t and, since t = d / v, P = W v / d The unit of power is the Watt, W.

Machine Definition      We use a machine to help us with a task when our muscle energy is less than required to do the job by hand. Machines make the job easier or more convenient by aiding the transfer of energy from you to the object you wish to move. Machines are used to:

a) transform energy: a turbine changes its kinetic (rotational) energy to electrical.

b) transfer energy: a car’s driveshaft transfers energy from the gearbox to the axle.

c) multiply force: a pulley allows huge masses to be lifted.

d) multiplies speed: one turn of a bicycle’s chainwheel causes the drive wheel to rotate several times.

e) change the direction of a force: a pulley can change the direction of a force by 180⁰.

Note: machines spread out the work over a greater distance but is do not reduce it. When we use a crowbar to pull out a nail, we move our end of the machine a big distance compared to how far the “pulling” end moves. Because the work is done over a greater distance, it is easier for our muscles.

Simple and Complex Machines            In spite of the thousands of designs of machines, there are only six simple machines. These are the: lever, pulley, wheel and axle, inclined plane, wedge and screw. See that the screw is actually an inclined plane wrapped into a spiral; just cut out a paper inclined plane (right triangle) and wrap it around a pencil to make a screw. The threads are just the spiraling upper edge of the inclined plane. All the complex machines we see around us are just groups of simple machines.

Energy Conservation and Mechanical Advantage

Actual Mechanical Advantage

A machine makes a job easier by magnifying our efforts through its mechanical advantage. The AMA takes into account the effect of friction on the behavior of the machine. It is based on the actual use of the machine, i.e., the amount of energy required for the job.

AMA = F_RESISTANCE / F_EFFORT or F_R /F_E

Ideal Mechanical Advantage

As the name implies, this value does not take into account the effect of friction. It is based just on the design of the machine, on the distances the various parts move. It relates how far the effort and resistance “ends” of the simple machine move.

IMA = d_E / d_R For the lever and the wheel and axle, the IMA also = r_E / r_R, where the r’s are the distances from the machine’s pivot point to the point where the effort and resistance contact the machine.

Efficiency         This value compares the intended and actual behavior of a simple machine. The IMA will always exceed the AMA because of energy loses due to friction, heat and sound. There are three ways of finding the efficiency.

Efficiency = (AMA / IMA) * 100% or (W_OUTPUT / W_INPUT) * 100% .

And, since W_OUTPUT = F_R * d_R and W_INPUT = F_E * d_E , the Efficiency = F_R * d_R / F_E * d_E

Complex Machines      A complex machine is a sequence of simple machines arranged so that the output of one becomes the input for the next, and so on. The complex machine’s overall MA’s are just the products of the individual MA’s. Mathematically and practically, the overall MA’s relate to only the very first input and the final output.

Skeletal Mechanical Advantage            Just about every body motion is created by levers, our weight as the resistance and our muscles supplying the effort to move the bones. Unfortunately, our skeletal levers are third class, the least advantageous type. In fact, a third class lever seems to be designed backwards – it has an IMA of less than 1, requiring more effort to operate than the resistance being moved! No wonder we get tired. The situation is worse for long limbed people because their r_EFFORT is about the same as for a shorter limbed person but their r_RESISTANCE is greater – the IMA is even less. This is why tall athletes are not often successful at long duration, continuous effort sports – they run out of gas sooner than a shorter person.