10-April-2017: Work-Kinetic Theorem Activity

When we are running, during the accelerate part, we could tell we are accelerated by the friction from the ground. However, are we ever noticed that how much of work done by friction is converted into kinectic energy? Today, we did a lab on the relationship between work and kinetic energy. 

Purpose

Verify the work done by force is equal to the kinetic energy that object are gained. (by energy conservation)

Plan

Experiment 1:

1. Set up an apparatus as the following diagram. 
   
2. If the theory works, then the kinetic energy should be equal to the work done by the tension. 
3. Detect the distance and velocity by motion sense. 
4. Use a force sense to measure the tension force. 
5. Then, calculate the integral of force, to get work. 
6. Compare the work done and the kinetic energy. Find out whether it is equal or not. 
7. Repeat the experiment to find out whether the results come out the same conclusion. 

Experiment 2:

1. Set up an apparatus as the following diagram. 
   
2. This time, we use a changing force (spring) to check whether the work done by force is still equal to kinetic energy. 
3. To calculate the work, let us calculate the spring constant first. 
4. Detect the distance by motion sense. 
5. Use a force sense to measure the spring force. 
6. Calculate the spring constant by pulling the cart to different position. 

Experiment 3:

1. Using the appartus in the last experiment. 
2. Weight the cart. 
3. Detect the distance and velocity by motion sense. 
4. Use a force sense to measure the tension force. 
5. Calculate the integral of force to get the work, and compare it with the kinetic energy. 

Set up

Experiment 1:

Set up the apparatus as following and connect everything to Logger Pro. 

Then, calibrate the force sense with hanging no mass and hanging 500g (4.9N) mass. 

Next, weight the car. (We got 1183 gram in total)

Add a new column in Logger Pro, which is kinetic energy. (KE = 0.5 * "mass" * "velocity" ^ 2)

After we push the car, we get the data. 

Then, redo the experiment to get more data. 

Experiment 2:

Set up the apparatus as following and connect everything to Logger Pro (make sure that the motion detector can see the cart, and it is set to "Reverse Direction"). 

Then, pull out the cart to get the data. 

Experiment 3:

Using the apparatus in the last experiment. 

Measure the weight of cart. (The weight is 0.531 kg)

Pull the cart for a distance. After the cart get rest, let it go. 

Add a new column in Logger Pro, which is kinetic energy. (KE = 0.5 * "mass" * "velocity" ^ 2)

Integral the Force - Distance graph to get the work. 

Analyze

In the first experiment. We did it twice. 

In the first one, the integral of force - distance (work) is 0.196 J. The kinetic energy is 0.196 J. 

In the second one, the work is 0.244 J. The kinetic energy is 0.234 J. 

The result came out that they are very close; in other word, the work done is almost converted into kinetic energy. 

In the second experiment, we could find out the spring constant by the function

It means the slope of Force - Distance function is the spring constant. Then, it came out that the constant is 3.271 N/m. 

In the third experiment, even though there are some mistakes in the end part, we can use the beginning part to continue our experiment. 

In the first one, we got the work is 0.230 J, and the kinetic energy is 0.227 J. 

In the second one, we got the work is 0.397 J, and the kinetic energy is 0.377 J. 

The result almost came out that the work done on the cart is equal to the kinetic energy. 

The reason why there is some error is mainly because the spring also has mass. When the cart is accelerated, the spring are also accerlated, which will take a part of kinetic energy. 

Overall, the work done by force is close to the energy it has gained. 

Conclusion

From the experience above, we can say that the work done by force is equal to kinetic energy the cart gained (if there is no other source to convert the energy).