Question

free - body diagrams with task tracker
a sledder has reached the bottom of a hill and is coasting to the right while slowing down along the loosely - packed snow. ignore air resistance.
identify the type of forces and their relative magnitude.

Explanation:

Step1: Identify vertical forces

The sledder has a gravitational force $F_g = mg$ acting downwards (where $m$ is the mass of the sledder - sled system and $g$ is the acceleration due to gravity, $g\approx9.8\ m/s^2$) and a normal force $F_N$ acting upwards. Since there is no vertical acceleration ($a_y = 0$), according to Newton's second - law $\sum F_y=ma_y = 0$. So $F_N=F_g$.

Step2: Identify horizontal forces

The sledder is moving to the right and slowing down, so there is a frictional force $F_f$ acting to the left. According to Newton's second - law $\sum F_x=ma_x$, and since it is slowing down, $a_x<0$. The frictional force is given by $F_f=\mu_kF_N$ where $\mu_k$ is the coefficient of kinetic friction.

Answer:

Vertical forces: Gravitational force $F_g$ (downwards) and normal force $F_N$ (upwards) with $F_N = F_g$. Horizontal force: Kinetic frictional force $F_f$ (to the left) causing the sledder to slow down.