# Physics 22 Force and Mass

Newton’s Second Law of Motion is Force = Mass x Acceleration. He says the three are related. According to this Law, increasing the acceleration and leaving the mass the same should increase the force. Does it? How are force and mass related?

Question: How are acceleration, force and mass related?

Materials:

Spring scale

2 Small plastic cups (like those from apple sauce or fruit servings)

String

Stopwatch

Tape

Meter stick

Procedure:

Mark off a 1 m + 10 cm course on a smooth table (if the table is rough, use smooth cardboard or a smooth board)

Put two small holes directly opposite from each other in each plastic cup near the rim

Cut a length of string two times as wide as the cup

Put the ends through the holes in the cup and knot them to form a handle

Put the masses in the cups

Zero the spring scale

A regular scale is much more accurate for finding the mass of an object.

Use the scale to mass Cup 1 and Cup 2

Remove the mass from Cup 1

Pull one end of the string out of the hole it is in

Knot the string and pull it through the other hole until the knot holds the end

Put a loop in the loose end of the string

Put the cup 10 cm before the starting line

Put the mass in the cup

Hook the spring scale to the loop

Practice pulling the cup down the course using a constant force on the spring scale

Pulling a mass with a spring scale shows the force used. It is hard to read the force accurately especially when pulling the force quickly.

Time how long it takes to pull the cup down the meter course

Record the force needed

Try pulling the cup faster recording the time and force

Remove the mass from Cup 2

Change the string the same way for Cup 2 but attach it to Cup 1

Put the second mass in Cup 2

Time how long it takes to pull the two cups down the course

Record the force needed

Pull the cups faster recording the times and force needed

Observations:

Masses

Hanging a mass on a spring scale reads more force than pulling the same mass across a table. The mass is the same but the acceleration of gravity is much greater so the force is greater.

Cup 1:

Cup 2:

Times:

One mass:

Force needed:

Both masses:

Force needed:

Conclusions:

Should you start pulling the cup before the starting line? Why?

Compare the force needed for one mass and for two masses.

How are force and mass related?

Does the force needed seem to change if you pull the cup fast or slowly?.

Why do you think this is the case?

Did you expect to need more force to make the cups go faster? Why?

How could you use greater force to move the cups?

Newton’s Second Law of Motion says increasing the acceleration should increase the force. Did the force increase? Is a spring scale a really accurate way to measure this acceleration force?

Doubling the mass being pulled does double the force needed.

What I Found Out:

I used four smaller lead wheel weights used for balancing tires for masses. One cup of weights was a little heavier than the other one. I tried using smaller masses but found it too hard to read the forces on the scale. The ones I used were 68 g and 48 g.

As was the case in the last Project, it took more force to start the cup moving than it did to keep it moving. Starting to pull before the starting line let me measure the steady force only.

When I pulled Cup 1 the first time, I did it slowly in 5.15 sec and had a force of .1 N. I expected to use more force when I pulled the cup faster.

When I pulled Cup 1 in 3.34 sec, it still took .1 N. I tried it at several different speeds. As long as the cup moved steadily, the force remained the same.

When I tied Cup 2 to Cup 1, the force needed to pull the two increased to .2 N. Again this didn’t change if I pulled fast or slowly.

Force and mass are related as increased mass increases the amount of force needed to move the mass. Once the pulling force gets the mass moving, that is all the force needed to keep it moving regardless of how fast or slow the force is applied.

I think I could increase the force used to move the cups if I pushed on them. Possibly I could use a collision to apply the forces like with the projectiles but that would not be sustained over a distance.

The spring scale didn’t stay steady very well. It is difficult to read accurately. Trying to read the scale and time pulling the cup was difficult. I don’t think the force increased but it may have. Having a much heavier mass might have made the force easier to see too.