# Leverage

Moving patients is a routine part of Jolene’s work as a MED floor RN, but in reality there is nothing routine about the biomechanics of lifting and transferring patients. In fact,  “disabling back injury and back pain affect 38% of nursing staff” and healthcare makes up the majority of positions in the top ten ranking for risk of back injury, primarily due to moving patients. Spinal load measurements indicated that all of the routine and familiar patient handling tasks tested placed the nurse in a high risk category, even when working with a patient that “[had a mass of] only 49.5 kg and was alert, oriented, and cooperative—not an average patient.” People are inherently awkward shapes to move, especially when the patient’s bed and other medical equipment cause the nurse to adopt awkward biomechanic positions. The forces required to move people are large to begin with, and the biomechanics of the body can amplify those forces by the effects of leverage, or lack thereof. To analyze forces in the body, including the effects of leverage, we must study the properties of levers.

# Lever Classes

The ability of the body to both apply and withstand forces is known as strength. One component of strength is the ability apply enough force to move,  lift or hold an object with weight, also known as a load. A is a rigid object used to make it easier to move a large load a short distance or a small load a large distance. There are three , and all three classes are present in the body.    For example, the forearm is a because the biceps pulls on the forearm between the joint (fulcrum) and the ball (load). To see these body levers in action check out this short video animation identifying levers in the body. The elbow joint flexed to form a 60° angle between the upper arm and forearm while the hand holds a 50 lb ball . Image Credit: Openstax University Physics



Using the  standard terminology of levers, the forearm is the , the biceps is the , the elbow joint is the ,  and the ball is the  . When the resistance is caused by the weight of an object we call it the . The   are identified by the relative location of the resistance, fulcrum and effort. have the fulcrum in the middle, between the load and resistance. have resistance in the middle.  have the effort in the middle. First (top), second(middle), and third(bottom) class levers and real-world examples of each. Image Credit: Pearson Scott Foresman



### Reinforcement Activity The foot acting as a lever arm with calf muscle supplying an upward effort, the weight of the body acting as downward load, and the ball of the foot acting as the fulcrum. Image adapted from OpenStax Anatomy and Physiology



# Static Equilibrium in Levers

For all levers the and () are actually just that are creating because they are trying to rotate the lever.  In order to move or hold a load the created by the effort must be large enough to balance the caused by the load. Remembering that torque depends on the distance that the force is applied from the , the effort needed to balance the resistance must depend on the distances of the effort and resistance from the pivot. These distances are known as the and (load arm). Increasing the reduces the size of the effort needed to balance the load torque. In fact, the ratio of the effort to the load is equal to the ratio of the effort arm to the load arm:

(1) ### Every Day Examples: Biceps Tension

Let’s calculate the biceps tension need in our initial body lever example of a holding a 50 lb ball in the hand. We are now ready to determine the bicep tension in our forearm problem. The effort arm was 1.5 in and the load arm was 13.0 in, so the load arm is 8.667 times longer than the effort arm. That means that the effort needs to be 8.667 times larger than the load, so for the 50 lb load the bicep tension would need to be 433 lbs! That may seem large, but we will find out that such forces  are common in the tissues of the body!

Finally, we should make sure our answer has the correct . The weight of the ball in the example is not written in , so it’s not really clear if the zeros are placeholders or if they are significant. Let’s assume the values were not measured, but were chosen hypothetically, in which case they are exact numbers like in a definition and don’t affect the significant figures. The forearm length measurement includes zeros behind the decimal that would be unnecessary for a definition, so they suggest a level of in a measurement. We used those values in multiplication and division so we should round the answer to only two significant figures, because 1.5 in only has two (13.0 in has three). In that case we round our bicep tension to 430 lbs, which we can also write in scientific notation: .

#### *Neglecting the Forearm Weight

Note: We ignored the weight of the forearm in our analysis. If we wanted to include the effect of the of the forearm in our example problem we could look up a typical forearm weight and also look up where the of the forearm is located and include that and .  Instead let’s take this opportunity to practice making justified . We know that forearms typically weigh only a few pounds, but the ball weight is 50 lbs, so the forearm weight is about an (10x) smaller than the ball weight.  Also, the of the forearm is located closer to the than the weight, so it would cause significantly less . Therefore, it was reasonable to assume the forearm weight was for our purposes.

The ratio of  to is known as the  (MA). For example if you used a (like a wheelbarrow) to move 200 lbs of dirt by lifting with only 50 lbs of effort, the mechanical advantage would be four. The  is equal to the ratio of the to .

(2) # Range of Motion

We normally think of as helping us to use less to hold or move large , so  our results for the forearm example might seem odd because we had to use a larger effort than the load. The bicep attaches close to the elbow so the is much shorter than the and the is less than one. That means the force provided by the bicep has to be much larger than the weight of the ball. That seems like a mechanical disadvantage, so how is that helpful? If we look at how far the weight moved compared to how far the bicep contracted when lifting the weight from a horizontal position we see that the purpose of the forearm lever is to increase rather than decrease required. Diagram showing the difference in distance covered by the contracting bicep and the weight in the hand when moving the forearm from horizontal.Image Adapted from Openstax University Physics

Looking at the similar triangles in a stick diagram of the forearm we can see that the ratio of the distances moved by the and must be the same as the ratio of to . That means increasing the effort arm in order to decrease the size of the effort required will also decrease the of the load by the same factor.  It’s interesting to note that while moving the attachment point of the bicep 20% closer to the hand would make you 20% stronger, you would then be able to move your hand over a 20% smaller range. Diagram of the forearm as a lever, showing the similar triangles formed by parts of the forearm as it moves from 90 degrees to 60 degrees from horizontal. The hypotenuse (long side) of the smaller blue triangle is the effort arm and the hypotenuse of the larger dashed red triangle is the load arm. The vertical sides of the triangles are the distances moved by the effort (blue) and the load (dashed red).

### Reinforcement Exercises

For the is always farther from the fulcrum than the , so they will always increase , but that means they will always increase the amount of effort required by the same factor. Even when the effort is larger than the load as for third class levers, we can still calculate a , but it will come out to be less than one.

always have the load farther from the pivot than the effort, so they will always allow a smaller effort to move a larger load, giving a greater than one.

can either provide or increase , depending on if the effort arm or load arm is longer, so they can have mechanical advantages of greater, or less, than one.

A lever cannot provide mechanical advantage and increase range of motion at the same time, so each type of lever has advantages and disadvantages: 