# Worksheet: Work Done by a Force Expressed in Vector Notation

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.

**Q3: **

A particle moved from point to point along a straight line under the action of the force . During this stage of motion, the work done by the force was 106 units of work. The particle then moved from to another point under the effect of the same force. During this stage of motion, the work done by the force was units of work. Determine the two constants and .

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

**Q4: **

A particle moved from point to point along a straight line under the action of the force acting in the opposite direction to the displacement . Find the work done by the force .

**Q5: **

A particle moved on a plane from the point to the point under the action of a force of 17 N whose line of action made an angle of with the -axis where . Find the work done by this force over the displacement .

- A142 or work units
- B or work units
- C or 158 work units
- D65 or 95 work units

**Q6: **

A particle moved from point to point along a straight line under the action of a force of magnitude N acting in the same direction as the vector . Calculate the work done by the force, given that the magnitude of the displacement is measured in meters.

**Q7: **

A body of mass 3 kg is moving under the action of a force , such that its displacement . 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 in seconds.

**Q8: **

The displacement of a particle of mass 30 g is given as a function of time by the relation , where is a constant unit vector, is measured in centimeters, and in seconds. Given that the particle started its motion at , find the force acting on the particle and the work done by this force during the first 7 seconds of motion.

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

**Q9: **

A particle moves in a plane in which and are perpendicular unit vectors. Its displacement from the origin at time seconds is given by and it is acted on by a force . How much work does the force do between and ?

**Q10: **

The position vector of a particle of mass 3 kg moving under the action of a force is given as a function of time by the relation , where and are two perpendicular unit vectors. Calculate the work done by the force between to .

**Q11: **

A body of mass 2 kg is moving under the action of three forces, , , and , where , , and , and and are two perpendicular unit vectors, and are constants, and each force is measured in newtons. The displacement of the body is expressed by the relation , where the displacement is measured in meters, and the time is in seconds. Determine the work done by the resultant of the forces in the first 6 seconds of motion.

**Q12: **

A force N is acting on a particle whose position vector as a function of time is given by m. Calculate the work done by the force between and .

**Q13: **

An object moves 10 m in the direction of . There are two forces acting on this object: N and N. Find the total work done on the object by the two forces.

*Hint*: You can take the work done
by the resultant of the two forces or you can add the work done by each force.

- A Nβ m
- B Nβ m
- C Nβ m
- D40 Nβ m
- E Nβ m

**Q16: **

A body moves under the force from point to point . Determine the work done by the force, where the displacement is measured in meters and the force in newtons.

**Q17: **

A force of acts on a body and moves it from point to point . Determine the work done by the force , where the displacement is measured in metres.

**Q18: **

A body moves from point to point under a force . Determine the work done if the force has a magnitude of newtons and direction cosines , taking the displacement as measured in meters.

**Q19: **

A particle is moving in a straight line under the action of the force from point to point . Find the work done by the force .

- A units of work
- B units of work
- C units of work
- D units of work
- E units of work

**Q20: **

A body is displaced by m with a force N. What is the work done?

**Q21: **

A force of 8 newtons moves a body from to . Taking 1 unit to equal 1 meter, what is the work done?

- A J
- B24 J
- C664 J
- D J

**Q22: **

A body moves in a plane in which and are perpendicular unit vectors. Two forces, and act on the body. The particle moves from the point with position vector m to the point m. Find the work done by the resultant of the forces.