# Worksheet: Resolution of Forces

In this worksheet, we will practice solving problems about the resolution of a force into two directions.

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,

Q2:

Resolve a force of 81 N into two perpendicular components and as shown in the figure. Give your answer correct to two decimal places. • A,
• B,
• C,
• D,

Q3:

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

• A,
• B,
• C,
• D,

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.

• Aparallel: 52.881 newtons, perpendicular: 153.578 newtons
• Bparallel: 153.578 newtons, perpendicular: 52.881 newtons
• Cparallel: 16.278 newtons, perpendicular: 47.276 newtons
• Dparallel: 47.276 newtons, perpendicular: 16.278 newtons
• Eparallel: 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

Q8:

Resolve a force of 110 N into two perpendicular components and as shown in the figure. Give your answer correct to two decimal places. • A,
• B,
• C,
• D,

Q9:

Resolve a force of 123 N into two perpendicular components and as shown in the figure. Give your answer correct to two decimal places. • A,
• B,
• C,
• D,

Q10:

A body weighing 18 N is placed on a plane that is inclined at to the horizontal. Resolve its weight into two components and , where is the component in the direction of the plane and is the component normal to the plane.

• A,
• B,
• C,
• D,

Q11:

A body weighing 12 N is placed on a plane that is inclined at to the horizontal. Resolve its weight into two components and , where is the component in the direction of the plane and is the component normal to the plane.

• A,
• B,
• C,
• D,

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 10 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,

Q16:

A force of magnitude 41 N acts due south. It is resolved into two components as shown on the diagram. Find the magnitudes of and . Give your answer to two decimal places. • A,
• B,
• C,
• D,

Q17:

A force of magnitude 99 N acts due south. It is resolved into two components as shown on the diagram. Find the magnitudes of and giving values to two decimal places. • A,
• B,
• C,
• D,
• E,

Q18:

The angle between two forces, and is . Their resultant is 2,900 N and makes an angle of with . Find the forces and . Give your answers to two decimal places.

• A,
• B,
• C,
• D,

Q19:

A force of magnitude 96 N acts vertically downward. It is resolved into two components as shown on the diagram. Find the magnitudes of and giving values to two decimal places. • A,
• B,
• C,
• D,

Q20:

A force , acting in a northerly direction, is the resultant of two forces and . The force has a magnitude of 172 N and is acting north of east, and the force acts in a westerly direction. Find the magnitudes and . • A,
• B,
• C,
• D,