Unit 5 - Constant Force Particle Model

We began this unit by looking at the relationship between mass and weight.  We knew it was a direct relationship and when mass increases, weight increases.  We used different objects and spring scales to determine their weight in Newtons and triple beam balances to determine the mass of each object and then determined the relationship which was linear with a slope of 10 N/kg.  This led to a For every 1 kg, the force exerted by the Earth changes by 10 Newtons. 

At this point, we were asked for an operational definition for mass.  What is mass?  and we could not use the traditional answers for it.  We did not have a good definition; however, we did know that something that is more massive resists change in motion more than something with less mass.  Again, we reiterated the fact that An object in motion will stay in motion in a straight line at a constant speed as long as the forces are balanced. 

The model so far:

• Weight is a measure of gravitational field strength
• Schema tool leads to a Force diagram
• Forces at angles have components
• If the change in velocity is 0, then forces are balanced (in vertical and horizontal directions)
• Acceleration is in direction of unbalanced force
• 10 N/kg is the gravitational field strength on Earth

When drawing force diagrams,

1. Schema
2. Force Diagram
3. Shadow parts (components)
4. Change in velocity = 0 then there are balanced forces

Next, we drew a cart on a 30 degree ramp (we measured the 30 degree ramp on the whiteboard  with a protractor) and drew all the forces to scale.  We were drawing the force vectors to scale and then measured the corresponding angle for the components of the Force of Earth on the object with a protractor and measured the components as well.  It matched up rather nicely. 

Next, we pushed an air puck across two tables and we had to keep constant contact with it.  We ended up running at the end of the two tables (We had someone there at the end of the table to catch the air puck :) )  This was a good introduction to Newton's Second Law.  Now we had to determine this again with a lab.  Again we used the cart and the tracks.  We had to find the relationship between Force, acceleration and mass.  For one experiment, we kept mass constant.  We used a spring scale (push type) to apply a constant force of 0.5 N, then 1 N, up to 2.5 N and measured the acceleration by using the digital sonic ranger at the end of the track.  This was a tricky lab for two reasons.  One was trying to keep the force constant at the 5 different forces and the other reason was we had to stop the cart before it crashed into the digital sonic ranger.  We found a linear relationship, as force increased, acceleration also increased in a linear fashion.  Next experiment, we kept force constant while we increased the mass.  We noticed a linear relationship but as mass increased, the acceleration decreased.  In both of these labs, acceleration was the dependent variable.  This led us to the right causal effect where acceleration is caused by the force.  Newtons 2nd Law was established as acceleration = Force (unbalanced) / mass  

Mass (in kg) is a quantitative measurement of resistance to change in velocity.  1 N applied to 1 kg will accelerate 1 m/s/s, and 2 N applied to 1 kg will accelerate 2 m/s/s. 

We then looked at an elevator example.  We feel heavy when I am accelerating upward (This happens when the elevator starts going up and when it stops going down.)  The force of the floor on me is greater then the force of the entire Earth on me, then I feel heavy.  We feel light when we are accelerating downward (This happens when you stop going up or start going down.)  If the force of the floor on me is less than the force of the entire Earth on me, then I feel lighter.  We named 10 N/kg as the gravitational field strength on Earth.  On the moon, it is 1.6 N/kg.

After we did some more worksheet problems dealing with force diagrams, and really getting a good grasp of Newton's 3rd Law, we did some more whiteboarding along with a debate as to whether a pair of forces was actually a Newton's 3rd Law Force Pair.  (Even though forces are equal and opposite, does not mean they are necessarily a force pair.)

Then we did some lab experiments to determine the difference between static friction and kinetic friction and developed the coefficient of friction by using the force sensors and different surfaces dragged across a wood surface.  We determined that static friction was always greater then kinetic friction for the same situation and developed a mathematical model for force of friction.

Something else we discovered is that Earth pulls more on more massive objects.  It is due to Newton's 2nd law that everything falls at an acceleration of 10 m/s/s.

We then did some work with Modified Atwood machines and discussed two - body systems (two carts attached by a string and being pulled by a string, or a cart being pulled by a mass on a pulley).  We did some practice problems dealing with these type of problems and then had some practice facilitating whiteboard sessions.  This was an awesome experience and difficult as well.  It made me realize how difficult this can be and yet mentally stimulating at the same time.  According to research, students learn better this way.