# Worksheet: Resolution of Forces

In this worksheet, we will practice resolving 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 above the -axis. Find and , its components in the and directions.

- A ,
- B ,
- C ,

**Q4: **

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

- A ,
- B ,
- C ,
- D ,
- E ,

**Q5: **

A particle weighing 69 N is placed on a plane inclined at an angle to the horizontal, where . Resolve the weight of the particle into two components, and , where is parallel to a line of greatest slope and is perpendicular to .

- A ,
- B ,
- C ,
- D ,

**Q6: **

An object weighing 50 newtons rests on a ramp that is inclined 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.

- A parallel: 52.881 newtons, perpendicular: 153.578 newtons
- B parallel: 47.276 newtons, perpendicular: 16.278 newtons
- C parallel: 153.578 newtons, perpendicular: 52.881 newtons
- D parallel: 16.278 newtons, perpendicular: 47.276 newtons
- E parallel: 50 newtons, perpendicular: 50 newtons

**Q7: **

A force of magnitude N acts on a particle in a direction south of west. and are two units vectors in the east and north directions, respectively. Express the force in terms of and .

- A N
- B N
- C N
- D N
- E N

**Q12: **

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

- A ,
- B ,
- C ,

**Q13: **

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

- A ,
- B ,
- C ,

**Q14: **

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

- A ,
- B ,
- C ,
- D ,
- E ,

**Q15: **

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

- A ,
- B ,
- C ,
- D ,
- E ,