The reason for using a simple or complex machine to do work is to use less effort or force to do the same amount of work. How much force a machine will save is its mechanical advantage.

**Question:** What is the mechanical advantage of an inclined plane?

**Materials:**

2 boards, one twice as long as the other

stack of thick books, at least four 5 cm or more thick

spring scales

**Procedure:**

Set up the stack of four books

Measure the height of two, three and four book stacks

Lift your block using the spring scale to the top of the stack

Record the force needed

Measure the length of the two boards

Set up one board as an inclined plane to the top of the stack of four books

Pull the block up the ramp recording the force needed

Remove one book from the stack

Pull the block up the ramp recording the force needed

Remove another book from the stack

Pull the block up the ramp recording the force needed

Replace the ramp with the other board

Pull the block up this ramp recording the force needed

Add a book to the pile

Pull the block up the ramp recording the force needed

Add the last book to the pile

Pull the block up the ramp recording the force needed

**Analysis:**

Calculate the work done lifting the block up the height of two, three and four books using the formula W = Fd.

Calculate the mechanical advantage of the inclined planes using the formula M.A. = R/E where R is the force needed to lift the block up the pile of books and E is the effort or force needed to pull the block up the ramp.

Another way to calculate the M.A. of an inclined plane is to divide the length of the plane by the height it goes to. Use these measurements to calculate the M.A. of your ramps.

**Conclusions:**

The scale reading when you lifted the block up is the mass of the block, the force needed to lift it and the resistance for calculating mechanical advantage. How can it be all three?

How do the M.A. you calculated using R/E and using L/H compare? Should they be the same? If yours are not, why not?

Does a short or a long inclined plane have more mechanical advantage?

Does the height of the ramp end matter for the mechanical advantage?

The total amount of work done by each ramp for each pile of books was the same. What was not the same?

**What I Found Out:**

My scale read 200 g lifting the block up the pile of books. Two books were 14.5 cm high making the work done 2900 g-cm. Three books were 21.5 cm tall making the work done 4300 g-cm. The tallest pile of four books was 29 cm high making the work done 5800 g-cm.

The mass of the block is the pull of gravity on it. Lifting the block requires enough force to counter gravity, equal to the mass. Since gravity is pulling on the block, it is resisting being moved by the mass amount making the force needed to lift the block equal to the resistance from gravity which is the mass of the block.

The two boards I used were 74 cm and 105 cm long.

My long board was 1.5 cm thick so I added that to the height of the stacks. The short board was .5 cm thick.

For the short ramp the force needed was 100 g [2 books], 130 g [3 books] and 150 g [4 books]. For the long ramp the force needed was 80 g [2 books], 110 g [3 books] and 130 g [4 books].

Using the first formula the mechanical advantage for the long ramp was 2.5 [2 books], 1.8 [3 books] and 1.5 [4 books]. For the short ramp the mechanical advantage was 2 [2 books], 1.5 [3 books] and 1.3 [4 books].

Using the second formula the mechanical advantage for the long ramp was 6.6 [2 books], 4.6 [3 books] and 3.4 [4 books]. For the short ramp the values were 4.9 [2 books], 3.7 [3 books] and 2.5 [4 books].

My calculated mechanical advantages by the different formulas were very different. I had expected them to be similar. Perhaps my measurements were not as accurate as they should have been.

The special formula for calculating mechanical advantage for an inclined plane is the second one so I would prefer using those values. Another reason I would favor those is that my spring scales are not easy to read and inaccurate whereas my meter stick and rulers are easy to read and much more accurate.

Both ways indicate the longer ramp has a greater mechanical advantage. This value went down as the height the ramp went to became greater.

In all cases, the height of the book pile was the same for the 2, 3 and 4 books. The amount of work done was the same. What really changed was the distance the blocks had to be moved to get to the top of the book piles.