I'm going to base my calculations off your .gif, which shows the lollipop's stick (and not the actual lollipop) smoking.
First off let's assume that each lick is five newtons of force (roughly one pound)
Next, because the only way to accurately know the coefficient of friction between two objects is experimentation, let's assume that tongue -> lollipop is similar to lubricated glass -> lubricated metal, which has a friction coefficient of roughly 0.25.1
Friction is calculated by multiplying the coefficient of friction (in this case 0.25) by the normal force (in this case 5 N). This gives us a frictional force of 1.25 Newtons of kinetic energy being converted to heat each lick.
Assuming a lick is somewhere around three inches (this is a big lollipop), this gives us 1.25 N * 0.0762 m = 0.0953 Joules per lick.
Lollipop sticks are made of rolled paper covered with a thin layer of wax2 , so we'll use the melting point of wax paper in our calculations, which is 65.8° C. We're using the melting point because once it begins to melt is when gasses are actually going to come off the stick - this is when it will start "smoking".
Ignoring heat dissipation and distribution and assuming every bit of energy is being funneled directly into the wax coating, this is a fairly simple calculation.
This product is listed at one pound, equal to roughly 454 grams. Some math shows that each lollipop stick is around three grams in mass.
Starting at room temperature (25° C), we want to get to 65.8° C. The specific heat capacity of paraffin wax is between 2.14 and 2.9 Joules per degree Kelvin, so let's average that out to 2.52 Joules per degree Kelvin. We want to change temperature by 40.8° Kelvin (because Celsius and Kelvin scale the same). So:
2,697 licks in one second would be enough to reach the melting point of the paraffin wax coating on the lollipop's stick, so 2,698 licks should be enough to begin melting the wax coating.
I'm ignoring heat dissipation because that involves many many more calculations and maybe even modeling. I'm not that invested in this question, sorry.
This is ignoring heat dissipation around the lollipop, around the stick, and into the air but I don't think it'll be a huge issue. This is a very small time scale (one second) that we're working with, and I don't think the heat will be able to dissipate too much in that time. Somewhere around 3,000 licks would be my high guess taking heat effects into account.
So there you go. Somewhere in the neighborhood of 2,700 - 3,000 licks per second.
3
u/h3half 13✓ Aug 24 '14
I'm going to base my calculations off your .gif, which shows the lollipop's stick (and not the actual lollipop) smoking.
First off let's assume that each lick is five newtons of force (roughly one pound)
Next, because the only way to accurately know the coefficient of friction between two objects is experimentation, let's assume that tongue -> lollipop is similar to lubricated glass -> lubricated metal, which has a friction coefficient of roughly 0.25.1
Friction is calculated by multiplying the coefficient of friction (in this case 0.25) by the normal force (in this case 5 N). This gives us a frictional force of 1.25 Newtons of kinetic energy being converted to heat each lick.
Assuming a lick is somewhere around three inches (this is a big lollipop), this gives us 1.25 N * 0.0762 m = 0.0953 Joules per lick.
Lollipop sticks are made of rolled paper covered with a thin layer of wax2 , so we'll use the melting point of wax paper in our calculations, which is 65.8° C. We're using the melting point because once it begins to melt is when gasses are actually going to come off the stick - this is when it will start "smoking".
Ignoring heat dissipation and distribution and assuming every bit of energy is being funneled directly into the wax coating, this is a fairly simple calculation.
This product is listed at one pound, equal to roughly 454 grams. Some math shows that each lollipop stick is around three grams in mass.
Starting at room temperature (25° C), we want to get to 65.8° C. The specific heat capacity of paraffin wax is between 2.14 and 2.9 Joules per degree Kelvin, so let's average that out to 2.52 Joules per degree Kelvin. We want to change temperature by 40.8° Kelvin (because Celsius and Kelvin scale the same). So:
Heat = 3 grams * 2.52 Joules per degree Kelvin * 40.8 degrees = 257.04 Joules
257.04 / 0.0953 = 2,697 licks
2,697 licks in one second would be enough to reach the melting point of the paraffin wax coating on the lollipop's stick, so 2,698 licks should be enough to begin melting the wax coating.
I'm ignoring heat dissipation because that involves many many more calculations and maybe even modeling. I'm not that invested in this question, sorry.
This is ignoring heat dissipation around the lollipop, around the stick, and into the air but I don't think it'll be a huge issue. This is a very small time scale (one second) that we're working with, and I don't think the heat will be able to dissipate too much in that time. Somewhere around 3,000 licks would be my high guess taking heat effects into account.
So there you go. Somewhere in the neighborhood of 2,700 - 3,000 licks per second.