Question

You flew from Pomona,California, and went ice fishing with Grandpa on a lake in rural Minnesota. You were concerned the ice would crack and you would fall with Grandpa onto the lake. The temperature right above the lake was 5 C. Your Grandpa said the lake won't crack, it is 65 ft deep and the temperature at the bottom of the lake is 20 C and he wanted to walk on the lake and start ice fishing. You didn't know if you should listen to Grandpa so you needed to calculate the thickness of the ice to see if it can hold. Your mass is 80 kg and your grandpa's mass is 54 kg. Was grandpa right?

Answer 1

For this first of all we have to calculate the temperature gradient
Top temperature is 5 C and the bottom temperature is 20 C and the depth is 65 ft therefore
15 C temp is change in 65 ft therefore 1 C will change in 65/15
Ice would be available up to 0 C therefore the thickness will be 5*(65/15) = 21.667 ft.
Now from Gold formula we know tha
P = Ah² where P is load, h is thickness of ice and A is constant
assuming standard value of constant the formula gets modified as h = 4(P)^0.5 where h is in inches and P is tons.
Now if we apply the value of load i.e.= (80+54)*9.8 =1313.2 = 1.31 ton
so require h will be 4.81 inches but the thickness of ice is more than this therefore grandpaa was right and they were safe.

Answer 2

yes, grandpa was right.