April-06-2015 Lab 10:Work-Kinetic Energy Theorem Activity

Lab 10

Purpose of this lab is to test Work-Kinetic Energy Theorem by using 3 experiments.

Experiment 1:Work Done by a Nonconstant Spring Force.

For this first experiments we want to find out the spring constant and the work done by the spring.

Set up:

(Be sure that the motion detector sees the cart over the whole distance)

Open LogPro and then display force vs position axes.

set the motion detector to "Reverse Direction", so that toward the detector is the positive direction. Then, start the cart with slowly moving towards the motion direction from the unstretched to spring is stretched about 0.2M(Depend on the spring, if it's a big spring; we can stretch it longer).

Here is the photo of the force vs position.

If we liner fit this line we got the slope of line.

For a spring we know the function f = kx, so the slope of the force vs positon is the k spring constant, so k = 1.836 N/M.

Because we know force F is change with constant. F = kx, we can calculate the work by using intergral.(We should suppose to integral from the 0 to 0.2m, so there is some loophole for this experiments, but I just want to show how to get the work.)

(This is the formula we need to calculate the work, it will start form 0 to x.)

That's also the area under the line. Therefore, we integral the line we got the Work we done by spring is 0.03243 m*N from 0.045 to 0.192M.

Experiment 2:Kinetic Energy And The Work-Kinetic Energy Principle.

For experiment 2 we want o find out the area such that we did at first one is same as the kinetic energy.

we use the same set up as experiments 1.

We get the mass of this cart is 0.573 kg.

For this experiment, we also need to use this same set up, but the different is that we need to start the cart from a stretched place and then let the cart go back the calculate the work done by the spring.

To do this experiment we need to set up a new column is that Kinetic energy which will get by 1/2 m * v^2.

We can the v by using the LogPro, and we have mass so we can get the Kinetic energy vs position graph.

Also we can get the force vs position graph either, and we can do the same experiment as 1, get the area of the graph and compare to the Kinetic energy at that point(unstretched point) to see if there are same or not.

Then we use the set up to do this experiment. 

From a stretched position and release the cart.

We choose the part where it reach to the unstretched point. rest of them just not.

So, we integral the line, we got the area is 0.07395M*N is very close to the kinetic energy 0.074 which is calculated by using 1/2 m *v^2.
uncertainty = absolute (0.074-0.07395)/0.074 *100% = 0.0675%.
so this is very close, good result.

Conclusion:

The work done by the spring is the changing kinetic energy of this spring.

Experiment 3:Work-KE Theorem.

On the above is the approximate picture of the ball.
We can calculate the work done by the ball for the whole time.

We compare our result by Work and KE, they are very close to each other but all. So the whole experiment has uncertain such that the line is not all straight ,but we ideal it, also the velocity we got is not changing of distance and time, they may have errors.

Conclusions

We have done three experiments today, First one is about the how to test the spring constant and work by a Nonconstant pull. Second one is about check the changing of kinetic energy of spring is or not the work done by the spring. Last one is about calculation.

Uncertainty of this three experiment are friction on the surface which will made the kinetic energy small.