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Lesson Worksheet: Work Done by a Force Expressed in Vector Notation Mathematics

In this worksheet, we will practice calculating the work done by a constant force vector acting on a body over a displacement vector using the dot product.

Q1:

A particle moves in a plane in which i and j are perpendicular unit vectors. A force Fij=(9+)N acts on the particle. The particle moves from the origin to a point with the position vector (9+6)ij m. Find the work done by the force.

Q2:

A body moves under the force Fij=69 from point 𝐴(2,8) to point 𝐵(1,7). Determine the work done by the force, where the displacement is measured in meters and the force in newtons.

Q3:

A body moves in a plane in which i and j are perpendicular unit vectors. Two forces, Fij=(92)N and Fij=(97)N act on the body. The particle moves from the point with position vector (6+2)ij m to the point (2+3)ij m. Find the work done by the resultant of the forces.

Q4:

A particle moves in a plane in which i and j are perpendicular unit vectors. Its displacement from the origin at time 𝑡 seconds is given by rij=2𝑡+7+(𝑡+7)m and it is acted on by a force Fij=(6+3)N. How much work does the force do between 𝑡=2s and 𝑡=3s?

Q5:

A force Fij=(49) N is acting on a particle whose position vector as a function of time is given by rij(𝑡)=(9𝑡8)+3𝑡+2 m. Calculate the work 𝑊 done by the force F between 𝑡=3 and 𝑡=8seconds.

Q6:

A body of mass 3 kg is moving under the action of a force F, such that its displacement sij(𝑡)=5𝑡+(7𝑡). Find the work done by this force in the first 6 seconds of its motion, given that the displacement is measured in meters, the force in newtons, and the time 𝑡 in seconds.

Q7:

A force Fij=(𝑚9)N acts on a particle, causing a displacement sij=[5+(𝑚+6)]cm. If the work done by the force is 0.02 J, what is the value of 𝑚?

Q8:

A particle moved from point 𝐴(7,1) to point 𝐵(4,6) along a straight line under the action of the force Fij=𝑎+𝑏. During this stage of motion, the work done by the force was 106 units of work. The particle then moved from 𝐵 to another point 𝐶(8,3) under the effect of the same force. During this stage of motion, the work done by the force was 138 units of work. Determine the two constants 𝑎 and 𝑏.

  • A𝑎=12, 𝑏=10
  • B𝑎=12, 𝑏=10
  • C𝑎=12, 𝑏=10
  • D𝑎=12, 𝑏=10

Q9:

A particle moved from point 𝐴(7,3) to point 𝐵(9,2) along a straight line under the action of a force F of magnitude 810 N acting in the same direction as the vector cij=3. Calculate the work done by the force, given that the magnitude of the displacement is measured in meters.

Q10:

A particle moved from point 𝐴(2,2) to point 𝐵(6,10) along a straight line under the action of the force Fij=𝑘6 acting in the opposite direction to the displacement 𝐴𝐵. Find the work done by the force F.

This lesson includes 43 additional questions and 232 additional question variations for subscribers.

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