Lesson Worksheet: Resolution of Forces Mathematics

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

Q1:

True or False: In the given figure,FFRcossinsin(90𝜃)=𝜃=90.

  • ATrue
  • BFalse

Q2:

Complete the following: In the given figure, FR=×(𝜃+𝜃)sin.

  • Atan𝜃
  • Bsin𝜃
  • Csin𝜃
  • Dcos𝜃
  • Ecos𝜃

Q3:

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

  • AF=57.98N, F=57.98N
  • BF=30.01N, F=36.76N
  • CF=28.99N, F=28.99N
  • DF=112.01N, F=36.76N

Q4:

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

  • AF=218.07N, F=196.00N
  • BF=59.58N, F=88.98N
  • CF=131.24N, F=196.00N
  • DF=131.24N, F=218.07N
  • EF=218.07N, F=131.24N

Q5:

A force F, acting in a northerly direction, is the resultant of two forces F and F. The force F has a magnitude of 172 N and is acting 60 north of east, and the force F acts in a westerly direction. Find the magnitudes of F and F.

  • A||=863FN, ||=863FN
  • B||=172FN, ||=863FN
  • C||=863FN, ||=86FN
  • D||=86FN, ||=863FN

Q6:

In the given figure, the force R with magnitude 12 N is resolved into two components F and F, and the force R bisects the angle between the directions of F and F, where the angle between the directions of F and F is 70. Find the magnitude of F to the nearest newton.

Q7:

The diagram shows a body of weight 69 N suspended by 2 light, inextensible strings, 𝐴𝐶 and 𝐵𝐶. Both strings make an angle of 37 with the horizontal. Resolve the weight of the body into two components in the direction of 𝐴𝐶 and in the direction of 𝐵𝐶. Give your answers to the nearest newton.

  • A𝑊=57N, 𝑊=57N
  • B𝑊=43N, 𝑊=43N
  • C𝑊=69N, 𝑊=69N
  • D𝑊=83N, 𝑊=83N

Q8:

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

  • A𝐹=137.81N, 𝐹=65.53N
  • B𝐹=47.61N, 𝐹=65.53N
  • C𝐹=100.12N, 𝐹=137.81N
  • D𝐹=47.61N, 𝐹=137.81N

Q9:

A body weighing 72 N is placed on a plane that is inclined at 45 to the horizontal. Resolve its weight into two components 𝐹 and 𝐹, where 𝐹 is the component in the direction of the plane and 𝐹 is the component normal to the plane.

  • A𝐹=362N, 𝐹=362N
  • B𝐹=362N, 𝐹=36N
  • C𝐹=722N, 𝐹=723N
  • D𝐹=36N, 𝐹=36N

Q10:

A particle weighing 69 N is placed on a plane inclined at an angle 𝜃 to the horizontal, where tan𝜃=43. Resolve the weight of the particle into two vector components, F and F, where F is parallel to a line of greatest slope and F is perpendicular to F, and find their intensities F and F.

  • AF=34.5N, F=34.5N
  • BF=41.4N, F=55.2N
  • CF=55.2N, F=55.2N
  • DF=55.2N, F=41.4N

This lesson includes 30 additional questions and 198 additional question variations for subscribers.

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