Paint scene

The Physics behind the Paint Can Scene: Home Alone 1

In case you've forgotten the scene....

 

So let's take a look at what's happening here....

 Kevin is releasing cans of paint from the top of the stairs in a way that they arc and hit Harry and Marv with an impact strong enough to send them flying. This may be humorous to watch, but how does this actually work? What are the physics behind this?

Let's break this down... 

When the paint cans are being held by Kevin at the top of the stairs they have gravitational energy and no kinetic energy. This is because there in no movement, so no kinetic energy. But there is stored energy due to it's position above the ground, so there is gravitational energy. To calculate the gravitational energy we can use the following equation: 

 Eg= mgh    (mgh stands for mass x force of gravity x height)

Assuming the paint can is full, it will have a mass of  11.3 lbs or 5.1 kg. The force of gravity will always be 9.8 m/s2. And the average height from the ground to the top of the stairs is 2.5 meters. So now that we have some numbers, let's plug it into the equation

Eg= mgh
     = (5.1)(9.8)(2.5)
     = 124.95 Joules

So what this means is that at the top of the stairs the paint can has 124.95 Joules of gravitational potential energy and 0 Joules of kinetic energy since it's not moving. But what about at the bottom of the arc when it hits Harry and Marv? 

Based on the Law of Conservation of Energy, we know that the energy will remain constant throughout the whole arc. So once it's dropped, the gravitational energy will decrease as the kinetic enerrgy increases. The energy isn't lost, it just changes form. So, based on our calculations of the paint can at the top of the stairs we can find the energy of the paint can at the bottom of the arc using this equation: 

Eg  top + Ek top = Eg bottom + Ek bottom

This shows the relationship between the two locations in the arch. We already know the values of energy at the top, so let's use the formula to solve for the bottom. Eg bottom won't be 0 because even the lowest point of the arc doesn't touch the ground. Instead, it's at the height or Marv and Harry's face a couple steps off the ground. So, let's say the bottom of the arc hits Harry's face at the third step. This would mean the height (h) would be Harry's height + the height of three steps. This is equal to 2.33 meters. So, lets plug this all into the equation.

Eg  top + Ek top = Eg bottom + Ek bottom
         124.95 + 0 =   mgh + 1/2 m (v bottom)2
               124.95 = (5.1)(9.8)(2.3) + 1/2 (5.1) (v bottom)2
               124.95= 115 + 2.55 (v bottom)2
     124.95 -115 =2.55 (v bottom)2
                 9.95 = 2.25 (v bottom) 2
                  3.9 = (v bottom)2
                  1.9 = v bottom

Eg top = 124.95 J
Ek top= 0 J
Eg bottom = 115 J
Ek bottom = 1/2 m (v)2
                  = 1/2 (5.1) (1.9)2
                   = 2.55 x 3.6
                   = 9.18 J 


This shows that as the gravitational energy decreases. the kinetic energy increases. So as the paint can travels in the arc, it loses gravitational energy and gains kinetic energy. It will have the most kinetic energy at the bottom of the arc.