Tag Archives: work

Physics 7 Mechanical Advantage

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.

materials for physics 7

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

finding work being done

The blocks are being lifted to the top of the book pile. No matter how the blocks get there, this is the work being done. Lifting a heavy weight is easier using a ramp. Mechanical advantage determines how well the ramp works.

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

mechanical advantage is efficiency

Pulling a weight up a ramp takes less effort than lifting the weight straight up. How efficient is the ramp?

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.

mechanical advantage of a short ramp

The short ramp is much steeper and takes more effort. It is also shorter. Is it more efficient? Is its mechanical advantage greater?

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?

mechanical advantage decreases with height

The shorter the height and/or the longer the ramp, the less effort is needed to get the blocks up onto the books. Do these increase mechanical advantage of the ramp?

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?

mechanical advantage is ramp length divided by height it goes to

The work done is the same so, why use a ramp? How do you get the most mechanical advantage out of a ramp?

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.

Physics 6 Meet the Inclined Plane

You are going to visit a friend and run up to the porch. How are you going to get onto the porch? You can jump up or you can walk up the steps.

Jumping up may be more fun. Walking up takes less effort. Those stairs are one kind of inclined plane.

Hailyann workman pulling blocks up ramp

Hailyann Workman’s help was greatly appreciated on this project. She seemed to think this was fun to do.

Question: How does an inclined plane work?

Materials:

3 Boards or pieces of stiff cardboard 10 cm wide and 0.5 m, 1 m and 1.5 m long

3 Bricks or 3 books about 5 cm thick

Spring scales

Meter stick

Block with loop

Procedure:

Set up the pile of books

Measure the height of the pile of books

Stand the block next to the pile of books

Use a spring scale to lift the block onto the books recording the force in grams

Remove the block

Measure the length of the boards

short inclined plane

A short ramp is steep. Since work is force times distance, the longer distance makes the amount of work much higher.

Lean the short board on the pile of books to form an inclined plane or ramp

Set the block just on the edge of the board

Use the spring scale to pull the block up onto the books recording the force needed

Repeat this for each of the other boards

Observations:

Height of book pile:

Length of short board:

Length of medium board:

Length of long board:

Force needed:

To lift the block

Short board

Medium board

Long board

Analysis:

Calculate the work needed to get the blocks onto the books by multiplying the force on the scale times the height of the books. This is W = Fd or Work = Force times distance.

Using a simple machine is supposed to reduce the force needed to get the same amount of work done. Now that we know how much total work is needed, we can calculate the force needed for each of the inclined planes by rearranging the formula so W/d = F or work divided by distance equals force.

Calculate the force needed for each inclined plane.

Go back to the Procedure to complete the Project

Conclusions:

Compare the force you measured for each inclined plane with the force you calculated.

Compare the force needed for each ramp with the force needed for the others and to the force needed to lift the blocks.

medium length inclined plane

A longer ramp has less of a slope making it easier to pull the blocks up.

What happens to the distance you must pull the block to use less force?

Would it be better to lift or use a ramp for a lightweight object? Why do you think so?

Would it be better to lift or use a ramp for a heavyweight object? Why do you think so?

What is the advantage of using a ramp?

 

What I Found Out:

This week I found Hailyann Workman to help me do this project. She is five and in kindergarten. She thought pulling the blocks up a ramp fun to do.

My stack of books was 15 cm tall. The scale registered 200 g lifting the blocks up. The work done was 3000 g-cm.

The short ramp was 44.5 cm long. The scale showed 150 g needed to pull the blocks up the ramp. I calculated 67.4 g-cm.

Next the blocks went up a 74 cm ramp using 100 g of force. I calculated needing 40.5 g-cm.

long inclined plane

Remember finding out about friction last week? My long ramp was rough making lots of friction. Covering the ramp with paper made it smooth.

The long ramp was 109 cm and rough. It was hard to pull the blocks up so I taped paper onto the ramp to make it smooth. The blocks pulled up easily with 70 g of force needed. My calculated amount was 27.5 g-cm.

My measured forces were much higher than my calculated forces. Perhaps I misread the scale. My block was smooth but not slick. My ramps were not slick so there was friction.

The needed force did decrease as the ramp got longer. The medium ramp took half the force of lifting the blocks.

The distance increases as the force needed decreases.

A lightweight object can be lifted up to move it the shortest distance. A heavyweight object should be moved up a ramp. This takes more distance but requires less force and is easier on you than lifting something heavy.

A ramp is a way to decrease the force needed to move an object even though it increases the distance needed to move it.

Physics 4 Exploring Work in Physics

Picture yourself helping to push a car. You shove. You turn around and push with your back. The car doesn’t move. Did you do any work?

According to your muscles you did a lot. According to the physics definition you did none.

In physics work is defined as moving something over a distance. Since the car did not move, you did no work. In physics this is written as: W = FD or work equals force times distance.

work project supplies

Question: How much work do you do?

Materials:

Spring scales [My set of 3 has a sensitive scale, a medium scale and a harder scale.]

Several blocks of different masses

Note: Another solution is to have stackable blocks.

Ruler

Procedure:

Each block will need a small loop to hook the spring scale to. An easy way to make such a loop for lighter blocks is to take a length of masking tape, attach one end to the block, crimp a length of the tape and attach the other end beside or over the other end on the block.

tape loop on block

The masking tape loop will only work for pulling light objects. It does a good job for that and is easy to make.

Place a block on a smooth table top

Set the ruler so you can see how far you will move the block

Hook a spring scale to the block

pulling a block with the scale

It is important to pull steadily on the spring scale but reading the force can be difficult. Be sure to read it when the blocks are moving along.

Pull the block steadily for 30 cm

Observe the amount of force on the scale in grams

Note: If the scale barely moves, try a scale with a more sensitive scale on it.

Repeat this for each block or additional block

Observations:

Record the distance and force for each block

work requires going a distance

My wood scrap blocks were mostly flat pieces making them easy to stack for pulling.

Analysis:

Multiply the grams times the distance in centimeters for each block to get the work done for each block.

Conclusions:

Which block has the most mass? Why do you think so? [You can check this by massing the blocks.]

Do you do more work moving a block with less mass or more mass?

work requires force

Each block added to the stack increased the amount of force needed to pull the stack.

If you pulled a block 15 cm, would you do more or less work? Why do you think this?

 

What I Found Out:

I used some scrap wood pieces for blocks so they came in various sizes and shapes. The biggest one was the one I chose to put the loop on. the others were piled on top of it one by one to increase the mass pulled by the spring scale.

The first block took 6 g to pull it the 30 cm. This made the work done 180 g-cm.

Two blocks took 40 g to pull the same distance. Now the work done was 1200 g-cm.

Three blocks took 49 g to pull. Now the work done was 1470 g-cm.

Four blocks took 52 g of effort making the work done 1560 g-cm.

Five blocks took 75 g of force making the work done 2250 g-cm.

Six blocks took 85 g of force making the work done 2550 g-cm.

Seven blocks took 90 g of force making the work done 2700 g-cm.

work done pulling 7 blocks

The last block was added to the stack. The pile was pulled for the 30 cm so work was done.

The more blocks on the pile, the more force it took to pull the pile across the table. That makes me think a heavier block will take more force than a lighter one.

Looking at the increases in effort, the first block took 6 g but the second took an additional 34 g so the second block must have more mass than the first one.

The third block increased the force 9 g and the fourth a mere 3 g. These are lighter than the second block.

The fifth block increased the force needed 23 g. The sixth added 10 g and the last one 5 g. The second block was the biggest block with the fifth block next.

Pulling the first block 30 cm required work of 180 g-cm. If I had pulled the block only 15 cm, it would be 6 g times 15 cm or 90 g-cm. It takes less work to move half the distance.