A hiker plans to traverse a snow-covered field while pulling a small supply sled. The combined mass of the hiker and the fully loaded sled is 85kg. The hiker can choose between wearing ordinary boots or attaching lightweight snowshoes. Each boot sole has a contact area of 220cm2, while each snowshoe provides an additional 1200cm2 of contact area per foot.
Snow-consistency tests made earlier that day indicate that the surface layer of the snow collapses whenever the pressure exerted on it exceeds 2.3×104Pa. Ignore any motion-related effects and assume the force on the snow is entirely due to the weight of the hiker–sled system distributed uniformly over the contact area with the snow.
(a) Calculate the total downward force exerted on the snow by the hiker–sled system while the hiker is standing still. Express your answer in newtons.
(b) When the hiker wears ordinary boots, determine the pressure applied to the snow surface. Show all work leading to your numerical result.
(c) Using the pressure threshold for snow collapse, evaluate whether the hiker can cross the field safely in ordinary boots. Clearly justify your conclusion with quantitative reasoning.
(d) If the hiker instead wears the snowshoes, calculate the new pressure exerted on the snow. Compare this value to the collapse threshold and discuss how increasing contact area changes the hiker’s mobility over soft snow.