To look deeper into the relationship between kinetic energy and velocity, we made and LOL diagram. It shown above that there was work in done on the cart's motion by the gravitational force of the hanging mass, which activated a greater force of tension. This directly speed up the cart. There was more work in done by the gravitational force pulling the cart down the ramp. However much of this was offset by the frictional force of the ramp on the cart creating work out.
ΔEkin = Win Fg hanging masses
Our LOL diagram tells us that kinetic energy was added to the system in the third section and if we look at the transfer diagram we see that it was the gravitational force of the hanging mass that caused it. This direct relationship is written on the whiteboard above.
I think I have something that will help us reach our answer!
Fg = m x gfs2.45N = 0.250kg x 9.81N/kg
The equation to solve for the amount of Win done by the hanging mass is written above. First we needed to solve for the gravitational force, as shown, and then we plugged this into our work formula. Since we already concluded that ΔEkin = Win Fg hanging masses, we now know that the system's kinetic energy was ΔEkin = 1.54J when the hook hit the ground.
W in hanging mass = Fg in hanging mass x D
2.45N x 0.63m = 1.54JWin hanging mass = 1.54J
Now we find the speed of the cart after the hook hits the ground. We just found the kinetic energy, but what is the velocity of the cart at this exact moment? Looking back at this section in our data we can see that it is an average of 1.304m/s, 1.307m/s, 1.308m/s, and 1.308m/s. When calculated the final average velocity is 1.306m/s.
Now that we know how to find the kinetic energy and the velocity data points, we can formulate a graph as shown above. However, we can see from the graph that although the points all follow the same line, they actually curve. This tells us that the graph cannot be a slope-intercept form (y=mx + b). After taking the slope of the graph we concluded that the slope was half of the mass (1/2 m). We also can see that the y - intercept cannot be 0, therfore we know that the variable b in y = mx + b doesn't make sense. Finally, we can piece together what we know o be true. Since variable b has been eliminated and we are solving for the y axis (Ekin), we can say that y = mx. Our x axis is v2 and the slope equals 1/2 of the mass so our formula is Ekin = 1/2mv2.
The relationship of Kinetic Energy and Velocity is Ekin = 1/2mv2