Pumpkin with 259,764J of energy smashing a car
14.1 years ago pumpkin
For most people watching a pumpkin dropped on a car from a crane is good enough…though the scientist in me wants to know how much force did this pumpkin have on impact. If I have you curious as well I did the math below…
WARNING MATH/PHYSIC CONTENT!!!
UPDATE: It has been too long since I have thought about physics…thanks for the corrections to my incorrect memory of Weight/Mass in the comments…calculations have been updated.
The easiest way to calculate this is to simply calculate the kinetic energy of the pumpkin with the following formula:
KE=(mv2)/2
First to determine the mass…for a pumpkin that weighs 1169 pounds that converts to 530.2 kg.
Next we need to determine the velocity of the pumpkin. Since in the video they do not say the height I am going to do an estimate of 50 meters given the cars and people look pretty small when the pumpkin is released. By neglecting wind resistance (because I am too old and tired to think about differential equations again) this I can calculate the velocity of the pumpkin right before impact by taking the square root of 2*9.80665*50 to get 31.3 m/s or 112.7 KPH or 70 MPH.
Now I simply plug in these numbers to find the kinetic energy:
KE = (530.2 * 31.32) / 2
KE = 259,764 joules
Just to put this into perspective here are some other events to compare to:
| Event | Joules of Energy |
| Swinging of a baseball bat | 80 J |
| Shooting an elephant gun | 1200 J |
| Shooting an M16 gun | 1690 J |
| Exploding 1 gram of TNT | 4184 J |
| Dropping a 1169 lb pumpkin | 259,764 J |
Have a happy and safe Halloween
14.1 years ago
Very interesting and yet very weird! LOL.
14.1 years ago
As far as I am aware there is no need to divide the weight by gravity to get the mass, unless we are working on a body other than earth.
14.1 years ago
Follow up question:
Now remember that the energy was dissipated into the compression of the pumpkin along with the car, so how much of that energy was transfered into the car in the end?
14.1 years ago
David S, giving me flashbacks of my dynamics exam in my first year of college. If I remember right the formula (assuming you have the variables) was at least a page or two wide with pretty small font…I will let you guys figure that one out for extra credit.
KC, for this is is all about velocity and this is based on the accelleration caused my our gravitational pull 9.8 m/s/s. Weight as a measurement is basically when an object is a rest, in this example the object is moving thus we use mass with this velocity to determine the force of impact. For example if someone hits me in the head with a softball at 50 MPH it is the kinetic energy caused by mass and velocity that gives me a headache…the “weight” (gravity) simply makes the ball hit me slightly lower.
14.1 years ago
I’m pretty sure that’s wrong. Just calculate the potential energy and know it will all be converted to kinetic energy at the bottom of its fall.
Mass * Gravity * Height = 530 kg * 9.8 m/(s^2) * 50 m = 259700 kg*m^2/s^2
to find the velocity
mgh = 1/2 mv^2
gh = 1/2 v^2
2gh = v^2
sqrt(2gh) = v = 31.3 m/s
14.1 years ago
Steve, that is correct though I am thinking you should either leave out the 9.8 m/(s^2) since you used the weight number instead of mass which is why our numbers (with exception of rounding) are off by a factor of 10 (or really 9.8) I agree this formula is better to get energy…though I was also curious about the velocity of the falling pumpkin.
14.1 years ago
Steve,
His calculation isn’t wrong, he just did it another way. Using U=mgh is a lot easier, but instead using
U = mv^2/2
= m(sqrt(2gh))^2/2
= mgh
reduces to the same answer (within rounding errors).
That’s one cool thing about physics. It’s possible to do things using different approaches and still get the same answer. He’s not wrong, and neither are you.
14.1 years ago
No Düde, I mean our answers are off by a magnitude. And KC is correct that dividing 530 kg by 9.8 to get 54 kg is why CVG is wrong by a factor of 9.8. His energy equation is correct. I’m sorry I didn’t clarify. I mean really! I am more than 54kg how can you expect that pumpkin to be 54kg.
14.1 years ago
The mass of the pumpkin is 54kg its weight is 530kg. I am not a small guy with a weight of about 90kg, though my mass is only 9.2kg which is what is asked for in the equation…so I on the other hand would only have 4506 J of energy if dropped from a crane onto a car.
14.1 years ago
The mass of the pumpkin is 530kg. Weight is never given in kg. The misconception is that lbs is a unit of force AND mass, if it is assumed that the object is on the Earth’s surface. The metric unit of weight is the Newton. Once you know the weight in metric units, the mass is found by dividing by the acceleration due to gravity (9.8 m/s^2)
Fortunately, google knows units, so you can have it do the conversions:
Google the phrase:
1169 pounds in Newtons
Google will tell you that the weight in Newtons is about 5200 N.
Then google the phrase
5200 N / 9.8 m/s^2
And google will tell you the mass is about 530 kg.
To illustrate that we use lbs as a unit of mass AND weight google the phrase:
1169 pounds in kg
…and you’ll get the same answer.
So, I think the physics is all correct, but the unit conversion was off by a factor of 9.8.
14.1 years ago
You can roughly derive the height from the time it took to fall (http://en.wikipedia.org/wiki/Equations_for_a_falling_body) using d = 0.5g(t^2), which gives 44.1 meters for a fall of 3 seconds, and 60 meters for 3.5 seconds…
Using (http://en.wikipedia.org/wiki/Potential_energy#Gravitational_potential_energy), U=mgh, which would between 229297J and 311969J (roughly) depending on how long you think it took to fall.
With regards to the mass / weight issue, you are confusing mass (kg) with weight (N). The mass (m) of the pumpkin is 54kg in its weight (W=mg) is 530N (the force it would be exerting on the surface of the earth at rest).
Thanks for this! It’s always a good challenge to remember how to do these things…
14.1 years ago
Ok you guys are right…think I have a mental block on tricky physics teachers having the object in the story problem measured by weight in Newtons. Sorry for the confusion 🙂
13.9 years ago
Awesome video…even more awesome discussion..thanks everyone!