47 Outcome 2: Simple Machines
Outcome/Competency: You will be able to solve physical problems using knowledge of simple machines
Rationale:
Why is it important for you to learn this skill?
Two thousand years ago, an old Greek man once said, “If you give me a lever and a place to stand, I can move the world.” Archimedes realized he could move very heavy object with a long stick, fulcrum, and comparatively little effort. Another simple machine that you will use often is a pulley because it will allow you to lift heavy loads with less effort. With a knowledge of simple machines, you will be able to predict how much effort you need to put into lifting very heavy objects.
Objectives:
To be competent in this area, the individual must be able to:
- Apply calculations and terms used in the study of mechanical work, power and energy
Learning Goals
- Calculate the mechanical advantage, velocity ratio and efficiency of a simple machine
- Apply a simple machine in order to solve a trade related problem.
Introduction:
In this module we will learn the concepts of work, power, and energy with respect to moving objects. Later in the course, we will apply these concepts to moving electrons (electricity.) You will complete practice and review activities throughout the module.
Topic 1: The Concept of Simple Machines
Prerequisite Skills:
- Manipulating equations- a review of algebra may be warranted.
Simply put, machines trade of velocity (distance per time) for force. If something takes too much force to do, a machine will allow you to spread the force over a larger distance, so it becomes manageable. This works both ways. Machines can:
- Reduce the force required by increasing the distance you apply the force
- Reduce the distance required by increasing the applied force
For our purposes, a machine takes energy and performs work. A simple machine has a single input force and a single output force. The input force is called effort and the force produced by the machine is called the load.
Remember, work is the product of force and displacement, so the input work is the product of effort and distance moved by the effort. The output work is the product of the load and the distance moved by the load.
Work
Input work (Nm) = Effort (N) X Distance Moved by Effort (m)
Output work (Nm) = load (N) X Distance Moved by Load (m)
Mechanical Advantage
Ideally, the effort you put into a machine is the same as the load you can lift. The ratio of effort to load, ideally, would be 1. This ideal machine would be 100% efficient. In reality, because of friction, slippage, or other factors, the effort put in is larger than the load that can be lifted. Actual mechanical advantage is less than 1, or less than 100%.
Mechanical Advantage (M.A.)
Example 1:
A simple machine moves a load of 2500 N when an effort of 165 N is applied to the machine. What is the mechanical advantage of the machine?
Solution
The actual load is 2500 N. The actual effort is 165 N.
The machine offers a mechanical advantage of 15.15. Notice that mechanical advantage is unitless.
Velocity Ratio (VR)
To achieve mechanical advantage, the effort must be applied over a greater distance than the load moves. The ratio of the distance the effort is applied to the distance the load travels is called the velocity ratio.
Velocity Ratio (V.R.)
Example 2:
An effort of 345 N is applied over a distance of 4.5 m to move a load 35 cm. What is the velocity ratio for this machine?
Solution
Firstly, all units must be expressed in m. 35 cm is 0.35 m. The effort distance is 4.5 m, and the load distance is 0.35 m.
The machine has a velocity ratio of 12.9. Like mechanical advantage, velocity ratio has no units.
Example 3:
A mass of 375 kg is moved a distance of 13 m using a simple machine with a velocity ratio of 12. How far must the effort move?
Solution
In this example, the load distance is 13 m and the effort distance is the unknown in this problem. The mass is irrelevant information.
Solve for effort distance
The velocity ratio is given as 12.
The effort distance is 156 m.
Efficiency
Efficiency is a comparison between the ideal or perfect velocity ratio, to the mechanical advantage. If the mechanical advantage equals the velocity ratio, the machine is 100% efficient. If the mechanical advantage is less than the velocity ratio (as in all cases in real life) the efficiency is less than 1, or less than 100%.
Efficiency
Example 4:
A simple machine lifts a load of 1700 N a distance of 6 m. If the actual effort applied is 125 N,
(a) What is the mechanical advantage (MA) of the machine?
Solution
In this example, the relevant information is the load of 1700 N and the effort is 125 N.
The mechanical advantage the machine offers is 13.6. It is 13.6 times easier to perform the lift.
(b) How far must the effort move if the machine is 75% efficient?
We are given efficiency of 75% and found the mechanical advantage to be 13.6 in the previous part. We can find the velocity ratio by solving for that unknown:
The question asks about effort distance not velocity ratio. We need the velocity ratio equation:
The velocity ratio was determined to be 18.1. The load distance is given in the problem as 6 m. We can use the above equation to determine the unknown effort distance.
The effort distance required is 108.6 m.
Example 5:
An object with mass 180 kg is raised through a height of 7 m by an applied effort of 170 N. The effort applied to the lifting machine moves a distance of 83 m. Find the velocity ratio, actual mechanical advantage, and the machines efficiency.
Velocity Ratio
The effort distance is 83 m, and the load distance is 7 m.
Actual Mechanical Advantage
It is given the object is 180 kg. The object is being lifted, so Newton’s equation applies.
F=mgwhereg=9.81ms2
To find the force required to lift the load:
The load force is 1766. It is given the effort is 170 N.
The mechanical advantage of the machine is 10.4.
Efficiency
We have found in the previous parts that the mechanical advantage is 10.4, and the velocity ratio, 11.9.
The machine is 87% efficient.
Topic 2: Pulley (45m)
Instructions
- Go through the content and examples, leaving time for questions.
- Review Exercises for this topic are at the end of the outcome.
A pulley is a way to multiply the force that is applied in lifting an object.
Figure 21 Single pulley with downward pull
When pulling a rope across a pulley, the tension in the string (the lifting force) is constant throughout the rope. If the rope is attached to the load twice, then each part of the rope applies the same lifting force. The total lifting force is doubled. The tradeoff is that the rope needs to be pulled a greater distance.
Figure 22: The force b is applied twice to the load, but the worker only pulls with the force b
In a compound pulley, the force is multiplied by each pulley in succession:
Figure 23: A compound pulley is a force multiplier.
A block and tackle is a series of pulleys connected in one block. The velocity ratio is the number of ropes attached to the load. In a block and tackle configuration with a downward pull, the number of ropes is the number of pulleys. In an upward pull configuration, the number of ropes is one plus the number of pulleys.
Figure 24: Block and Tackle
Figure 25: Various configuration of the block and tackle
Example 6:
A block and tackle system has 3 pulleys in each block. An effort of 120 N is required to raise a load of 500 N. Calculate the efficiency of the system (normal hook up with effort pulling down.)
Solution
It is given that there are 6 pulleys in total with a downward pull. This means the velocity ratio is 6.
In order to use this equation, we need the mechanical advantage. The effort is 120 N, and the load is 500 N, as given.
\text{Mechanical Advantage}=\frac{\text{Actual Load}}{\text{Actual Effort}}=\frac{500\ N}{120\ N}=4.2
Now, we can use the equation for efficiency
The machine is 70% efficient.
Review Exercises: Simple Machines (30m)
Instructions
1. Give the definition of actual mechanical advantage of a simple machine.
2. Give the definition of velocity ratio of a simple machine.
3. How is the velocity ratio in a pulley system determined?
4. How is efficiency of a simple machine determined?
5. What might cause a difference in velocity ratio and mechanical advantage in a pulley system?
6. The velocity ratio of a pulley system is 6. The machine lifts 2000 N a distance of 2 m with an effort of 400 N. Find the following:
a) Mechanical Advantage
b) Percent Efficiency
c) Distance Moved by the Effort
7. In the block and tackle system there are 4 pulleys with a downward pull. assume a system efficiency of 95%. Find the following:
a) mechanical advantage
b) Force it would take to lift a load weighing 500 lbs.
8. In a pulley simple machine, describe the trade off between force and distance.
Answer Key
1. Load (force) divided by the effort (force).
2. effort distance divided by the load distance.
3. In a downward pull, the velocity ratio is the number of pulleys. In an upward pull, the velocity ratio is the number of pulleys plus 1.
4. Efficiency is the mechanical advantage divided by the velocity ratio expressed as a percent.
5. Friction.
6. a) 5, b) 83%, c) 12 m
7. a) 3.8, 132 Lbs.
8. a) One has to pull more rope to lift an object a smaller distance. The force pulled on the rope is less than the force lifting the object
b) One needs to turn a wheel with a large radius to move an axle with a smaller radius. Less twisting force needs to be applied to the large wheel to create a greater twisting force on the axle.
c) An object needs to be pushed over a greater distance, but less force needs to be applied lifting the object.
d) A lever arm needs to be moved a great distance. The object moves a small amount, but the force applied to the object being lifted is greater.