Question

Ancilla applies a force of 200 N [E] horizontally to pull a 38 kg sled across the snow at a constant velocity for 200 m.

(a) Draw a FBD of the sled

Answer 1

To draw a Free Body Diagram (FBD) of the sled, we display the forces acting on it. Here's how the forces can be represented:

1. **Weight (\( W \))**: The force due to gravity acting downward. It can be calculated as:
\[
W = m \cdot g = 38 \, \text{kg} \cdot 9.81 \, \text{m/s}^2 \approx 373.8 \, \text{N} \, [\down]
\]

2. **Normal Force (\( N \))**: The force exerted by the surface upward. For a horizontal surface with constant velocity, the normal force will balance the weight of the sled:
\[
N \approx 373.8 \, \text{N} \, [\up]
\]

3. **Applied Force (\( F_a \))**: The force applied by Ancilla to pull the sled, which is given as 200 N [E].

4. **Frictional Force (\( F_f \))**: Since the sled is moving at a constant velocity, the frictional force will be equal in magnitude and opposite in direction to the applied force (acting to the west). Therefore, \( F_f = 200 \, \text{N} \, [W] \).

### Summary of Forces in FBD
- **Upward Force**: Normal Force \( N = 373.8 \, \text{N} \, [\up] \)
- **Downward Force**: Weight \( W = 373.8 \, \text{N} \, [\down] \)
- **Rightward Force (East)**: Applied Force \( F_a = 200 \, \text{N} \, [E] \)
- **Leftward Force (West)**: Frictional Force \( F_f = 200 \, \text{N} \, [W] \)

In your FBD:
- Draw a box to represent the sled.
- Draw an arrow pointing down labeled as \( W \) (373.8 N) for the weight.
- Draw an arrow pointing up labeled as \( N \) (373.8 N) for the normal force.
- Draw an arrow pointing right labeled as \( F_a \) (200 N) for the applied force.
- Draw an arrow pointing left labeled as \( F_f \) (200 N) for the frictional force.

This will illustrate that the sled is in equilibrium, with all forces balanced.