# Lesson Worksheet: Resultant of Coplanar Forces Mathematics

In this worksheet, we will practice finding the resultant of a group of forces acting on a point.

Question 1

The diagram shows three coplanar forces acting at point . Their magnitudes are 2 N, 2 N, and 8 N in the directions , , and respectively. Given that and , what is the magnitude of the resultant force? Give your answer to the nearest newton. Question 2

The forces , , and act on a particle, where and are two perpendicular unit vectors. Given the forces’ resultant , determine the values of and .

• A,
• B,
• C,
• D,

Question 3

Three forces, , , and act at a point. Their resultant is N northwest. Determine the values of and .

• A,
• B,
• C,
• D,

Question 4

Three forces, N, N, and N act on a particle. Given that the resultant of the forces is N, what are the values of and ?

• A,
• B,
• C,
• D,
• E,

Question 5

Determine the magnitude of the resultant of the forces shown in the figure that are measured in newtons. • A N
• B N
• C N
• D N

Question 6

Four forces act on a particle as shown in the diagram. Determine , the magnitude of their resultant, and find , the angle between their resultant and the -axis. Give your answer to the nearest minute if necessary. • A,
• B,
• C,
• D,

Question 7

The diagram shows a system of three forces measured in newtons. Given that and , determine , the magnitude of their resultant, and find , the angle between their resultant and the positive -axis. Give the answer rounded to the nearest minute. • A,
• B,
• C,
• D,
• E,

Question 8

The diagram shows a square, , of side 8 cm. The point is on where . Forces of magnitudes 8 N, 20 N, N, and 12 N act at as indicated on the diagram. Find the magnitude of their resultant. • A32 N
• B N
• C16 N
• D N
• E N

Question 9

is an equilateral triangle, where is the point of intersection of its medians. Three forces of magnitudes 48, 26, and 42 newtons are acting at in the directions of , , and . Determine the magnitude of the resultant and its angle of inclination with the positive direction of the -axis rounded to the nearest minute.

• A,
• B,
• C,
• D,

Question 10

The diagram shows a regular hexagon, , whose diagonals intersect at the point . The 6 forces shown acting at are measured in newtons. Find the magnitude of their resultant and , the angle between their resultant and the positive -axis. Round your value of to the nearest minute if necessary. • A,
• B,
• C,
• D,

This lesson includes 43 additional questions and 356 additional question variations for subscribers.

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