Question

the mass of the sled is 100lbs, and speed if 85 lbf at a 30 degree angle, find the normal force

Answer 1

To determine the normal force acting on the sled, we can break down the forces involved and apply some physics concepts.

1. **Identify the forces acting on the sled:**
- The weight of the sled, \( W = mg \), acts vertically downward.
- The applied force, \( F \), is 85 lbf at a 30-degree angle to the horizontal.

2. **Draw the force components:**
The applied force can be broken down into two components:
- Horizontal component: \( F_x = F \cos(\theta) \)
- Vertical component: \( F_y = F \sin(\theta) \)

Where:
- \( F = 85 \) lbf
- \( \theta = 30^\circ \)

3. **Calculating the weight of the sled:**
- The sled's weight is given as \( W = 100 \) lbs.

4. **Calculate the components of the applied force:**
\[
F_x = 85 \cos(30^\circ) = 85 \times \frac{\sqrt{3}}{2} \approx 73.6 \text{ lbf}
\]
\[
F_y = 85 \sin(30^\circ) = 85 \times \frac{1}{2} = 42.5 \text{ lbf}
\]

5. **Determine the normal force:**
The normal force \( N \) acts perpendicular to the surface and can be calculated using the force balance in the vertical direction. In equilibrium, the sum of the vertical forces must equal zero:

\[
N + F_y = W
\]

Therefore, we can express the normal force as:

\[
N = W - F_y
\]

Substituting the known values:

\[
N = 100 - 42.5 = 57.5 \text{ lbf}
\]

### Conclusion:
The normal force acting on the sled is approximately **57.5 lbf**.