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In this lesson, we will learn how to resolve a force to its components that act in two perpendicular directions using the rules of right triangles.

Q1:

A force of magnitude 190 N acts at the origin making an angle of 3 0 ∘ above the 𝑥 -axis. Find 𝐹 𝑥 and 𝐹 𝑦 , its components in the 𝑥 and 𝑦 directions.

Q2:

Resolve a force of 81 N into two perpendicular components 𝐹 1 and 𝐹 2 as shown in the figure. Give your answer correct to two decimal places.

Q3:

A body weighing 72 N is placed on a plane that is inclined at 4 5 ∘ to the horizontal. Resolve its weight into two components 𝐹 1 and 𝐹 2 , where 𝐹 1 is the component in the direction of the plane and 𝐹 2 is the component normal to the plane.

Q4:

Resolve a force of magnitude 48 N acting northwest into two components, 𝐹 1 and 𝐹 2 , acting north and west respectively.

Q5:

A particle weighing 69 N is placed on a plane inclined at an angle 𝜃 to the horizontal, where t a n 𝜃 = 4 3 . Resolve the weight of the particle into two components, 𝐹 1 and 𝐹 2 , where 𝐹 1 is parallel to a line of greatest slope and 𝐹 2 is perpendicular to 𝐹 1 .

Q6:

An object weighing 50 newtons rests on a ramp that is inclined 1 9 ∘ to the horizontal. Find the magnitude of the components of the force parallel and perpendicular to the ramp, giving your answer correct to three decimal places if necessary.

Q7:

A force of magnitude 4 √ 2 N acts on a particle in a direction 3 0 ∘ south of west. ⃑ 𝑖 and ⃑ 𝑗 are two units vectors in the east and north directions, respectively. Express the force in terms of ⃑ 𝑖 and ⃑ 𝑗 .

Q8:

Resolve a force of 110 N into two perpendicular components 𝐹 1 and 𝐹 2 as shown in the figure. Give your answer correct to two decimal places.

Q9:

Resolve a force of 123 N into two perpendicular components 𝐹 1 and 𝐹 2 as shown in the figure. Give your answer correct to two decimal places.

Q10:

A body weighing 68 N is placed on a plane that is inclined at 4 5 ∘ to the horizontal. Resolve its weight into two components 𝐹 1 and 𝐹 2 , where 𝐹 1 is the component in the direction of the plane and 𝐹 2 is the component normal to the plane.

Q11:

A body weighing 4 N is placed on a plane that is inclined at 4 5 ∘ to the horizontal. Resolve its weight into two components 𝐹 1 and 𝐹 2 , where 𝐹 1 is the component in the direction of the plane and 𝐹 2 is the component normal to the plane.

Q12:

A force of magnitude 44 N acts at the origin making an angle of 4 5 ∘ above the 𝑥 -axis. Find 𝐹 𝑥 and 𝐹 𝑦 , its components in the 𝑥 and 𝑦 directions.

Q13:

A force of magnitude 28 N acts at the origin making an angle of 6 0 ∘ above the 𝑥 -axis. Find 𝐹 𝑥 and 𝐹 𝑦 , its components in the 𝑥 and 𝑦 directions.

Q14:

Resolve a force of magnitude 52 N acting northwest into two components, 𝐹 1 and 𝐹 2 , acting north and west respectively.

Q15:

Resolve a force of magnitude 196 N acting northwest into two components, 𝐹 1 and 𝐹 2 , acting north and west respectively.

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