By Michelle Bradley
It seems like it’s about that time in the semester where everyone starts getting overwhelmed by the amount of work they have. I know that when I have too much work I love taking TV breaks, which mostly consist of my favorite show “Modern Family”. Recently, I was watching the Halloween and Thanksgiving episodes, and came across the scene where the entire family goes pumpkin chunkin’. I decided to take a look at these contests in real life, and saw that they nicely corresponded with our recent discussions about conservation of energy.
I thought it would be interesting to examine a scenario to find the velocity of the pumpkin right before it hits the ground. I made the assumption that the rope they use on the show works the same way as a bungee cord would (there is no friction between it and the pumpkin) and there is no air resistance. Additionally, I set the mass of the pumpkin to be about 6 kg and the initial launch height to be 5 m. Also, I added a Fapplied of about 2205 N because people pull back on the cord (distance= 2m) so that the pumpkin may gain potential energy. Before the pumpkin is launched, it only contains potential energy, and by the time it launches all of that energy turns into kinetic. Therefore:
ΔKE = -ΔPE + WNC
WNC= -Fappdcos180= Fappd
½ mvf2 =-(mghf – mgho) + Fappd
½(6 kg) vf2= -(6 kg)(9.8 m/s2)(- 5m) + (2205)(2)
vf = 39.60 m/s
The final velocity of the pumpkin in this scenario would be 39.60 m/s. If you wanted to increase the velocity, you could have a greater applied force when launching. When you have a great applied force it leads to a greater distance for the pumpkin to travel as well, which is after all what those judges are looking for!