Mass-Spring Oscillations Lab

We predict that the Period Vs Mass graph should be a power 1/2 curve and Period Vs Spring constant should be a power -1/2 curve.

Period Vs Mass

Period Vs Spring Constant 

Find the period of swinging semi-cycle and triangle when they are hanging two ways.

compare the calculation value, T 1=0.627 s which is not quite close the measurement value 0.728 s 

T 2 =0.731 s is a good prediction because the measurement value is 0.737 s .

compare with calculation value T=0.771 s less than 1% mistake.

compare with calculation value T=0.737 s less than 1% mistake. 

Find the moment of inertia of a uniform triangle about its center.

Use the parallel axis theorem to find the moment of inertia of the triangle.

Conform the calculation by the experiment.

The calculated value is close to the actual value.

Conservation of linear and angular momentum

step 1. finding the velocity of the ball leave from the track.

using the conservation of energy to solve the velocity 

Depends on the experiment, using the kinetic equation to solve the velocity.

Step 2. Determent the moment of inertia of the system

the same method we used in the last few labs.

Step 3. Do the experiment as the ball release from the marked starting point, the ball will catch by the catcher.

 The calculation for the final angular velocity.

The actual value of the angular velocity is 1.64 rad/s.

Those values are pretty close therefore our experiment can conform the conservation of linear and angular momentum.

Use conservation of moment of inertia to calculate the mix height after the collision.

Set up the equipment as shown.

Measure the mass of the meter stick is 86.4 gram and the the mass of the clay is 36.7 gram.

Release the meter from horizontal and video capture the clay's motion after the collision.  

The calculation of the the maximun hieight of the clay.

The date analyzed from the video shows the actual height is 0.47 m-0.20 m =0.27 m. Those data is close to our calculation. 0.47 m is the highest point and 0.20 m is the distance from floor to the bottom of the meter stick.

A lab problem--- moment of inertia

The calculation for the moment of inertia of the system.

Use the video capture to collect the disk from spinning to rest. Track a certain point as we marked at the edge of the disk. Build two calculations columns (Vx= x^2 and the other  Vy= y^2).

Then the tangential velocity is square root of  Vx+Vy

Tthe slope of the line is the tangential acceleration.
Once we find the a, the angular acceleration is a/r.
Assume we have a track and a 500-gram dynamics cart connected to the wheel. Calculate the time need for the cart travel from rest to 1 meter. the angle between the track and horizontal is measured as 46.6 degree.

the time required should be 7.55 second.

Do the experiment and conform the value. The time spent is 11.5 s.

It may have something wrong during the calculation.

I think the reason is the radius we used to convert the tangential acceleration to angular acceleration is 1/2 of the diameter. Should be smaller because the point marked on the wheel is not really on the edge of the wheel. Then the fractional torque is bigger, the time required for this traveling is longer.

 The second way of calculating the angular acceleration effect by the fractional torque.
Pick the points when the marked points at the top, and bottom.
As the times passed, collect a list of the points.

Type the data in excel.
B2==(B4-B3)/((A4-A2)/2)
C3=(B4-B3)/((A4-A2)/2)
then fill down. find the average of the C column which is the angular acceleration effect by the fractional torque.
repeat the same calculation as shown above. the time require is 11.87 s. Closed to our measurement.

Determent the how does each factor affects the angular acceleration (Radius of the torque pulley, Mass of the hanging mass, mass of the disk)

Do the measurement as shown in step 1 .

Set up the equipment as below.

1. One hanging mass only, with a small torque pulley and top steel disk only.
 collect the data as the following picture.

2. Two hanging mass, with a small torque pulley and top steel disk only.
 collect the data as the following picture.

3. Three times of the hanging mass, with a small torque pulley and top steel disk only.
 collect the data as the following picture.

4.One hanging mass only, with a large torque pulley and top steel disk only.
 collect the data as the following picture.

5.One hanging mass only, with a large torque pulley and both top and bottom are steel disks .
 collect the data as the following picture.

After analyzed the data. We can tell the angular acceleration is doubled as the hanging mass doubled, Tirple by three times of the hanging mass.

The angular acceleration is doubled when the radius of the torque pulley is doubled.

The angular acceleration is decreased when the disk change from steel to aluminum.

The angular acceleration is decreased when the spinning disk change from only top to both top and bottom.