# Ice Fishing Day: Pushing Coolers to the Limit

## What can be said about the distances the two coolers are pushed?

My friend and I plan a day of ice fishing out on a frozen lake. We each pack our own cooler full of supplies to be pushed out to our fishing spot. Initially both coolers are at rest and one has four times the mass of the other. In parts A and B we each exert the same horizontal force F on our coolers and move them the same distance d, from the shore towards the fishing hole. Friction may be ignored.

O The heavy cooler must be pushed 16 times farther than the light cooler.

O The heavy cooler must be pushed 4 times farther than the light cooler.

O The heavy cooler must be pushed 2 times farther than the light cooler.

O The heavy cooler must be pushed the same distance as the light cooler.

O The heavy cooler must be pushed half as far as the light cooler.

## Answer:

As per the given information, the force applied is the same on both coolers. Hence, the acceleration produced in both coolers is the same.

Let's break down the scenario. The mass of the 1st cooler is represented as m and the mass of the 2nd cooler is 4m. The horizontal force applied to both coolers is denoted as F.

According to Newton's second law of motion, the force acting on a body is equal to the product of its mass and acceleration. Therefore, the force applied on the lighter cooler (of mass m) is F, which can be expressed as F = ma.

Using the same equation, we can determine that the force applied on the heavier cooler (of mass 4m) is also F, with an acceleration produced in it of a/4.

Considering the relationship between force, mass, and acceleration, we can conclude that the heavy cooler must be pushed 4 times farther than the light cooler.