Question

Consider a tall, skinny pine tree, initially upright, that falls over in a forest. As it is falling, its base remains in contact with the ground and does not move from side to side. 1. As the tree falls, the vertical component of the force exerted on it by the ground is: zero, greater than the tree's weight, equal to the tree's weight, or less than the tree's weight?

Answer 1

less than the tree's weight

The tree isn't actually free-falling. We model it as a point mass on a massless stick planted at the location of the tree's base. As the tree falls, it's angle with the ground changes. Gravity acting on the tree's center of mass to pull it down will tend to drive the stick into the spot at the tree's base. The vertical component of the tree into the ground is mg* sin(theta) where theta is angle with the ground and the falling tree. When the tree is fairly vertical, the force acts into the ground and while lying on the ground horizontally, very less vertical force acts.