Hands-on Activity: Tools and Equipment, Part I Contributed by: Integrated Teaching and Learning Program, College of Engineering, University of Colorado at Boulder

Ramps/Incline Plane

Summary Through a series of activities, students discover that the concept of mechanical advantage describes reality fairly well. They act as engineers creating a design for a ramp at a construction site by measuring four different inclined planes and calculating the ideal mechanical advantage versus the actual mechanical advantage of each. Then, they use their analysis to make recommendations for the construction site.

Keywords: inclined plane, simple machine, mechanical advantage, work inclined planesimple machinemechanical advantagework

Learning Objectives After this activity, students should be able to: Calculate the mechanical advantage of an inclined plane in two different ways. Explain why the concept of mechanical advantage is useful for engineers. Perform engineering design work in a group

Pre-Activity Assessment What are real life examples of incline planes? What does mechanical advantage describe? (Answer: A simple machine's mechanical advantage describes the decrease in force needed to do the same amount of work.)

Materials List Spring scale Meter stick Small car (Hot Wheels) with a string attached String Hot Glue Gun Hot Glue Weight (same size for each group) 4 copies of the Inclined Plane WorksheetInclined Plane Worksheet

Introduction Can you think of a situation when an inclined plane would be useful? Perhaps when you are moving a heavy piano onto a performance stage or furniture out of a truck?

What does mechanical advantage mean again? That's right: it's the factor by which the force is lessened or the degree to which a machine makes work easier. The mechanical advantage of all machines is defined by the general expression:

However, this expression is usually too general. The inclined plane gets its mechanical advantage by moving some object over a long gradual incline rather than moving it over a much shorter vertical path. Therefore, the input distance is equal to the slope length, and the output distance is the overall height of the inclined plane. In other words, by moving the load along the length of the slope, it is raised a vertical distance equal to the height of the inclined plane. Now, the mechanical advantage equation of the inclined plane is rewritten as:

Mechanical Advantage of Incline Plane

Is this calculation always right? Well, another way to find the mechanical advantage of an inclined planed is found by measuring the force used to move an object up an inclined plane. We call this the actual mechanical advantage. Looking back at our first equation, the output force is equal to the force needed to lift the object straight up the same distance (or the resistance force); the input force is equal to the amount of force needed to move the object up the ramp (or the effort force).

What is different about the actual mechanical advantage? Well, the actual mechanical advantage is quite different from the theoretical mechanical advantage since it accounts for friction, and there is no way to know it until after the work is already done.

Procedure Break into groups. Get incline plane worksheet. Gather supplies. Follow the directions on the worksheet. Measure the height and length of the plane, as shown in Figure 3, and calculate the mechanical advantage using this information.

Measure the force it takes to move the weight by attaching the spring scale to the weight and lifting it into the air without the ramp. Record this measurement as output force. Then, put the weight into the car and pull the car up the ramp with the spring scale, as shown in Figure 4. Record this from the spring scale in grams as input force. Calculate the actual mechanical advantage using this information.

Answer the following questions on the incline plane worksheet. Did you obtain different mechanical advantages for the different methods of measuring? If so, was the difference large or small? Which inclined plane had the greatest mechanical advantage? Does calculating mechanical advantage just with the dimensions of the inclined plane really work? That is, does the calculation describe what really happens? If you were the engineer designing a ramp for a construction site to move a wheelbarrow a height of 30 meters, which inclined plane would you use? Why? What are some possible sources of error in this experiment?

Turn in the incline plane worksheet when complete.