kinetic energy with collisions PBL

kinetic energy with collisions PBL

TEAM: Nomi, Dash, Yutong

research contents

Study whether different mass and collision energies are conserved and the degree of elasticity.

And there will be three different tests, each involving ten trials.

One track, two carts with sensors, and two cart masses. And an electronic scale.

Objectives

Free Body diagrams

Free body diagram for all three tests.

measurement and calculation

• In each test, we use two carts (red and blue) to record the speed at the moment before and after the collision.
• We mark it as Vi and Vf,And use an electronic scale to record the mass of the cart mass and carts.
• We pushed the cart in three different ways. Let them having collision. Then using formula to calculate the KE to check it is conversed or not.

Some unchanging data

red cart

MASS : 273.35g

blue cart

MASS: 271.2g

cart mass

MASS : 252.67g

TEST 1

The two carts have similar masses, and after the collision, the red cart comes to a complete stop while the blue cart gains kinetic energy and moves forward.

Table for test 1

SOME IMPORTANT GRAPH

CONCLUSION：test 1

The kinetic energy loss in the first set of experiments was 6.3%, and the linear fit R^2=0.9976, indicating a high degree of linear correlation in the experimental data. Considering these two points, I believe that in the absence of real-world factors, it should be an elastic collision, satisfying the conservation of kinetic energy.

TEST 2

Test 2 is similar to Test 1, except that the stationary blue car no longer has additional weight.However, precisely because of this, the difference in mass between the two cars will cause the red car to decelerate and continue moving in its original direction for a certain distance after the collision.

Table for test 2

SOME IMPORTANT GRAPH

CONCLUSION：test 2

With R² = 0.9978 and 7.23% energy loss, the collision is close to elastic but with minor inelastic effects, likely due to friction or slight deformation. The high R² suggests stable energy loss and reliable experimental data.

In Test 3, the two carts, with similar masses, collide head-on and bounce off each other after the collision.

TEST 3

Table for test 3

SOME IMPORTANT GRAPH

CONCLUSION：test 3

With R² = 0.9716 and 14% energy loss, the collision shows noticeable inelastic effects, likely due to deformation or friction. The lower R² suggests greater variation in energy loss, indicating a shift towards partially inelastic collision. However, due to the R² value being too high, it is unlikely to be very accurate.

TO sum up

• In the first test, our R² value is very close to 1, which means the data is accurate. Considering real-world factors, there is only a 6% loss, so we determine it to be an elastic collision.
• In the second test, our R² value is also very close to 1, indicating that the data is accurate. Considering factors such as friction and resistance, there is a 7% loss, so we determine it to be an elastic collision.

• In the final test, our R² value deviates significantly from 1, meaning the data is less accurate compared to the other two experiments. Additionally, the final energy loss rate reached 14%. Without considering the R² value, this is definitely not an elastic collision. However, due to the R² value, this experiment may not accurately reflect the real situation.

What if we can DO IT BETTER?

Improving Measurement Accuracy?

Enhancing Experimental Equipment?

Reducing External Interference?

Optimizing Data Collection Methods?

• Average
• Standard deviation

Red cart weight: 525.87 Blue cart weight: 271.27 Track angle 0*

Assumptions

Theoretical elastic collision

• Average
• Standard deviation

Red cart weight: 525.87 Blue cart weight: 273.87 Track angle 0*

Assumptions

Theoretical elastic collision

• Average
• Standard deviation

Red cart weight: 525.87 Blue cart weight: 523.87 Track angle 0*

Assumptions

Theoretical elastic collision

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