1. Application of Vectors

2. Force The force due to gravity, 𝑭 𝑔 , pulls straight down on the box.
Part of the force, 𝑭 1 , pulls the box down the ramp.
The other part of the force, 𝑭 2 , pulls the box against the ramp.
The relationship can be expressed as 𝑭 𝑔 = 𝑭 1 + 𝑭 2
𝑭 𝟏
𝑭 2
𝑭 𝑔

3. hill/ breaking load scenario
These scenarios are about an object being parked on some sort of incline.
𝑭 𝑔 is force due to gravity. In these scenarios, it is just the weight of the object.
𝑭 1 is the force that needs to be cancelled to ensure the object doesn’t roll down the hill
𝑭 2 is your force perpendicular to your hill.
d is degree of incline
𝑭 1
𝑭 2 d
𝑭 𝑔

4. When looking for the force to cancel out 𝐹 1
𝑭 𝑔 ∙ sin 𝑑 = 𝑭 1
𝑭 1
𝑭 2
𝑭 𝑔

5. Example
An SUV weighing 5800 pounds is parked on a street that has an incline of 9°. Find the force required to keep the SUV from rolling down the hill. Round the force to the nearest hundredth.
𝑭 1
𝑭 2
𝑭 𝑔

6. When looking for force perpendicular to the hill/ 𝐹 2
𝑭 𝑔 ∙ cos 𝑑 = 𝑭 2
𝑭 1
𝑭 2
𝑭 𝑔

7. Example
An SUV weighing 5800 pounds is parked on a street that has an incline of 9°. Find the force of the SUV perpendicular to the hill. Round the force to the nearest hundredth.
𝑭 1
𝑭 2
𝑭 𝑔

8. Work
The work, W, done by a force ,F , moving an object from point A to point B is
𝑊=𝑭∙ 𝐴𝐵 = 𝑭 𝐴𝐵 cos 𝜃

9. Example:
A child pulls a sled along level ground by exerting a force of 30 pounds on a rope that makes an angle of 35° with the horizontal. How much work is done pulling the sled 200 feet? Round answer to the nearest hundredth.

10. Homework
Vector Application WS 1