Application of Vectors

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

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

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

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

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

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

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

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.

Homework Vector Application WS 1