Determine whether the work done by the fisherman, normal force, gravitational force, and frictional force on the sled is positive, negative, or zero.

Steps to Solve

1. Identify the forces acting on the sled

   The forces acting on the sled include:

   • The force applied by the fisherman ($F_f$)
   • The gravitational force ($F_g = mg$)
   • The normal force ($F_n$)
   • The frictional force ($F_k$)

2. Determine the direction of each force

   • The force exerted by the fisherman is directed at an angle $\theta$ with respect to the horizontal.
   • The gravitational force acts vertically downwards.
   • The normal force acts vertically upwards.
   • The frictional force acts horizontally opposite to the direction of motion.

3. Analyze work done by the fisherman

   Work is calculated as $W = F \cdot d \cdot \cos(\phi)$, where $\phi$ is the angle between the force and the direction of motion. In this case, the fisherman’s force has a component in the direction of motion, so:

   • For the fisherman, the work done is positive since the force’s horizontal component and the displacement are in the same direction.

4. Analyze work done by the normal force

   The normal force acts perpendicular to the displacement of the sled. Since the angle between the normal force and the displacement is 90 degrees:

   • The work done by the normal force is zero ($W_n = F_n \cdot d \cdot \cos(90^\circ) = 0$).

5. Analyze work done by the gravitational force

   The gravitational force also acts perpendicular to the direction of displacement on the horizontal surface:

   • Thus, the work done by the gravitational force is also zero ($W_g = F_g \cdot d \cdot \cos(90^\circ) = 0$).

6. Analyze work done by the frictional force

   The frictional force acts opposite to the direction of motion. Therefore:

   • The work done by the frictional force is negative since it opposes the displacement ($W_k = F_k \cdot d \cdot \cos(180^\circ)$).