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In today's lab we will study motion on an incline.
Our main goals in this lab are to understand the relationship between
position velocity and acceleration,
interpret plots of these variables, and measure the acceleration of a cart down an
incline as a function of angle.
To learn about position velocity and acceleration we will take the motion
of a car as an example.
It starts from rest, accelerates to a constant speed,
moves at that speed for 5 seconds and then comes to a stop before the stop
sign.
First we will consider how the position of the car changes over time.
During acceleration the position has a quadratic form.
At constant velocity, or zero acceleration,
the position is linear. Next we look at how the velocity changes over the car's
motion.
During the acceleration the velocity increases at a constant rate
of three meters per second each second. When the acceleration is zero the
velocity is constant.
Next we consider how the acceleration changes over time.
It starts at a constant positive three meters per second squared,
goes to zero as the car moves at a constant velocity,
and then goes to -3 meters per second squared as the car stopped. Let's bring
all the plots together to look at the relationships between position velocity
and acceleration.
The instantaneous velocity at some time is the slope of the position graph
at that time while the instantaneous acceleration is the slope ofthe
velocity.
If we calculate the slope of the velocity curve during the initial
acceleration
we can see that the velocity increases three meters per second
each second. This gives us an acceleration of 3 meters per second
squared.
We can now watch the graphs evolve as the car moves
noting the differences between regions of constant acceleration and zero
acceleration.
Now we're ready to explore the equipment you're using this lab.
The cart and the track and each have magnets which repel each other.
Attach the metal reflecting vane to the end of the car. This provides a surface
for the motion sensor to measure.
Be sure to catch the cart before it hits the end of the track, as when released down
the incline it will have enough momentum to overcome the force of repulsion
from the magnet. You use the clamp and metal rod to elevate one end of the track.
Open the jaws of the clamp and then attach the clamp to the table.
Insert the metal rod in the hole in the clamp and tighten.
Check that both the metal rod and the clamp are secure.
There is a hole in a clamp attached to one end of the track. Slip this hole
over the metal rod
move the track to the desired position and tighten.
Your TA will give you three angles at which to measure the acceleration.
This angle is measured between the table and the track. Use trig to
determine the height needed for a given angle
and use a meter stick to verify you have set the track at this angle.
Once you have the track set up you can connect the motion sensor to the Pasco
interface.
Loosen the screw on the left side of the motion sensor to adjust the height.
You can also adjust the tilt of the motion sensor. The sensor should be
tilted at an angle parallel to the track so that you measure the distance the
cart moves along the track.
You are now ready to take data. let's release the cart from the top of the
incline.
Attach the reflecting vane to the cart and make sure someone is ready to catch
the cart at the bottom.
Let's watch that again at half the speed and take a look at what we will see in
data studio.
The top graph in the data studio window is the position
the middle graph is the velocity and the bottom graph is the
acceleration. Let's take a closer look at these graphs. As we saw with the car,
when moving under a constant acceleration, the position graph has
a quadratic form ane the velocity graph is linear.
To find the acceleration we just perform a linear fit of the velocity for the
time the court was rolling down the incline.
The acceleration for this period is just the slope of the velocity.
Once you measure the acceleration at three different angles,
make a plot of the accleration as a function of angle. What do you notice about
your data?
We will discuss the physical basis for your observations later in the semester
when we cover forces.