Lab#19: Conservation of Energy/Conservation of Angular Momentum

Conservation of Energy/Conservation of Angular Momentum

Samuel
Ellis
Mia
11-21-2016

Purpose:

To understand how momentum is conserve when energy is transferring.

Theory: 

Based on conservation of momentum, we know that we can transfer energy into momentum. Therefore, energy equal momentum. Since the stick swing down was cause by gravitational potential energy and inertia. In addition, when stick is vertically straight, that's when GPE equal 0. And at that moment, that's when stick collides with clay, and turn that into momentum.

Procedure:

1. Set up ring stand on the edge of the table

2. Insert ruler with hole (at the very end)into ring stand 

3. Make sure ruler swing without any external friction

4. Use tape taped around the ruler(inside out) and clay(inside out)

5. Place clay at the place that ruler can hit it

6. Use camera in your phone to videotape the whole movement

7. Upload video into computer

8. Dot every position of movement of the ruler and clay

9. And don't forget to set origin and distance ratio

Measurement:

Mass of clay: 36.7 grams

Mass of ruler: 92.3 grams

Graph:

(Above is the video capture software we used to capture the position of the whole movement. We set the intersection of the yellow line as our origin. And doted the position of ruler every second. And plot into the graph)

(Above is the graph of the center of the ruler verses end of the ruler. Since we set our origin at center of the ruler, therefore the blue dot(center of ruler) touch 0 when its vertically straight. And red dot(end of ruler) will go way under 0 because it is further than center of ruler)

Calculation:

Y-_center mass

y_cm = ((0.0923(0.9/2) + 0.0367(0.9))/(0.0923+0.0367)

          = 0.578

Energy = moment of inertia

mgh = 0.5*m*v^2 + 0.5*I*W^2

mgh = (0.5*m*r^2 * w^2) + (1/12 *m + 0.16 m)*w^2

0.9*g = 0.5 * 0.45^2 * w^2 + 0.5 (73/300)*w^2

17.64 = (0.45^2 + 73/30)*w^2

w = 6.29 rad/sec

Omega(w) after

I*w = (I_stick + I_clay)*w_after

(1/12 *M + 0.16*M)(6.29) = (1/12*M + 0.16*M + m*r^2)*w_after

0.14127 = 0.0521 * w_after

w_after = 2.7 rad/sec

Find Rising Distance

0.5*I*w^2 = m*g*Δh

0.5(1/12 *m + 0.16 * m +m*L^2)*w^2 = (0.0923 + 0.0367)*9.8*h

h = 0.15 m

Find angle

Δh = y_cm(1-cos𝛉)

0.0756 = 0.578(1-cos𝛉)

𝛉 = 30 degree

Conclusion:

In this experiment, we used conservation of momentum and inertia of the stick to determine how height and the angel of the stick after collides with clay on the floor. As usual, we make some assumptions to make this experiment easier. First, we assumed there's no frictional force acting between stick on the rod and clay on the floor. Also, we assume there's no human error when plotting dots on the video capture software. Lastly, we assume when we dropped the stick, we held it perfectly parallel respect to the horizontal floor. For our calculation, we make momentum equal to torque force. Since the momentum is based on gravitational force acting on the stick, we simply set it equal to torque force. In addition, since stick is rotating at 10 cm mark. We have to used axis parallel theorem to add the inertia to the total torque force. Therefore, we got the answer that is reasonable and close to our prediction.