6-April-2015: Work-Kinetic Energy Theorem Lab

Lab 10: Work-Kinetic Energy Theorem Activity

Purpose: To understand and apply the Work-KE Theorem and to determine the work done on an object from a Force vs. Position graph.

Experiment 1: Work Done by a Non-constant Spring Force

Setup:

Above, you can see a track on a horizontal surface. On one end of the track, there is a motion sensor. On the other end, we positioned a force sensor and it is held up by a rod and a C-clamp. A spring is attached to the force sensor and to the end of the cart.

In this portion of the lab, we measured the work done on a stretched spring through a measured distance. First, we collected data for the force applied by a stretched spring vs. the distance the spring is stretched and plotted the results.

Procedure:
First, we calibrated the force sensor with an applied force of 4.9 N. Then, we did a test run to see if the motion sensor recorded the cart's position. Once this was achieved, we zeroed the force sensor and motion detector. We also reversed the direction of the motion detector, so that toward the sensor is the positive direction.
Now, for the experiment. We began graphing force vs. position, as the cart was moved slowly towards the motion detector. Logger Pro then recorded the force applied and the cart's position.

Data:
The data was plotted on a Force vs. Position graph.

• x-axis: Force Applied (N)
• y-axis: Position (m)

 

The picture above shows two Force graphs because we mistakenly collected data for 2 runs. For the purpose of the lab, only one graph was analyzed.

 

We then found the work done in stretching the spring by taking an integral of the graph.

• Work Done (Area under graph) = 0.1520 Joules

We were also able to determine the spring constant from the graph. This was achieved by finding the slope of the graph.

• Slope of Force vs. Position graph: Spring Constant = 6.969 N/m  

 

 

Experiment 2: KE and the Work-KE Principle

 

Setup: Same as in Experiment 1.

 

In part 2 of the lab, we will examine the work done by the spring and the change in KE of the cart.

 

Procedure: 

Procedure is basically the same as in Part 1, but a few changes were made. First, we added a Kinetic Energy graph by creating a new calculated column that would calculate the KE of the cart at any point.

• Measured mass of cart = .504 kg
• KE=1/2(m*v^2)

 The second, data was now taken after releasing the cart. We pulled the cart back and began graphing after we released the cart.

Data:

 

Red Graph: Position vs. Time
Green Graph: KE vs. Time

Like in Part 1, we found the work done by the spring by finding the area of the graph between two positions . We also noted the change in KE at this point. Next, we found the change in KE at different positions and compared it to the work done at that point.

• At x = .195 m : KE=.453 J and W=.432 J
• At x = .259 m : KE=.365 J and W=.344 J
• At x = .364 m : KE=.165 J and W=.152 J

Conclusions:
The work done on the cart by the spring and the change in kinetic energy are essentially the same. Our values do not match because the force sensor was not set to zero. As you can see, our Force graph does not start at zero. In conclusion, the work done on an object is conserved into Kinetic Energy. This can be seen in the experiment. As the work done on the spring system was conserved and then interpreted as the change in Kinetic Energy of the cart.

Experiment 3: Work-KE Theorem
This portion of the lab involved watching a video clip. In the clip, a professor uses a machine to pull back on a large rubber band. The force being exerted on the rubber is recorded by an analog force transducer onto a graph. The stretched rubber band is then attached to a cart of known mass. The cart, once released passes through two photogates a given distance apart. By knowing the distance and the time interval between the front of the cart passing through the first photogate and then the second photogate, you can calculate the cart's final speed and the final KE of the cart.

Essentially, we are finding the area under the Force vs. Position of the rubber band and the KE of the cart. Based on the Work-KE Theorem, the answers should match.

In order to find the area under, we broke it down into 4 different shapes: triangle, rectangle, and two trapezoids.

• Area of Triangle: (1/2)b*h = 9.18
• Area of Rectangle: b*h = 7.48
• Area of Trapezoid: (1/2)(b1+b2)*h = 2
• Area of Trapezoid: (1/2)(b1+b2)*h = 7.935
• Total Area under graph = 26.595 J

Then, we were given the following information:

• m cart= 4.3 kg
• t= .045 sec
• change in position (x)= 15 cm
• v= x/t
• KE=(1/2)m*v^2

Velocity = .15/.045 = 3.33 m/s
KE = (1/2)(4.3)(3.33)^2 = 23.9 J

As you can see the result for Work and KE are off. KE = 23.9 J and Work = 26.595 J. This can be the result of the uncertainties of the experiment. Essentially, the uncertainties of this experiment come from the precision of the instruments used. The experiment depends upon the accuracy of the analog force transducer and the photogate. The concept of how we solved for work and KE is correct, but due to imprecise readings our answers are off.