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Worksheet: The Work Done by a Constant Force in the Vector Notation

Q1:

A particle moves in a plane in which and are perpendicular unit vectors. A force, acts on the particle. The particle moves from the origin to the point with position vector m. Find the work done by the force.

Q2:

A force acts on a particle, causing a displacement . If the work done by the force is 0.02 J, what is the value of ?

Q3:

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 .

Q4:

A particle moved on a plane from the point 𝐴 ( βˆ’ 8 , 6 ) to the point 𝐡 ( 2 , 5 ) under the action of a force of 17 N whose line of action made an angle of πœƒ with the π‘₯ -axis where s i n πœƒ = 8 1 7 . Find the work done by this force over the displacement οƒ  𝐴 𝐡 .

  • A βˆ’ 1 4 2 or 158 work units
  • B65 or 95 work units
  • C βˆ’ 6 5 or βˆ’ 9 5 work units
  • D142 or βˆ’ 1 5 8 work units

Q5:

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 ,

Q6:

A particle moved from point 𝐴 ( 7 , βˆ’ 3 ) to point 𝐡 ( βˆ’ 9 , 2 ) along a straight line under the action of a force F of magnitude 8 √ 1 0 N acting in same direction as the vector c i j = βˆ’ 3 βˆ’ . Calculate the work done by the force, given that the magnitude of the displacement is measured in meters.

  • A 8 J
  • B 424 J
  • C βˆ’ 2 4 8 J
  • D 344 J

Q7:

A particle moved from point 𝐴 ( 2 , 2 ) to point 𝐡 ( βˆ’ 9 , 1 0 ) along a straight line under the action of a force F of magnitude 3 0 √ 5 N acting in same direction as the vector c i j = βˆ’ 3 βˆ’ 6 . Calculate the work done by the force, given that the magnitude of the displacement is measured in meters.

  • A 420 J
  • B 810 J
  • C βˆ’ 9 0 0 J
  • D βˆ’ 1 5 0 J

Q8:

A body of mass 3 kg is moving under the action of a force F , such that its displacement s i j ( 𝑑 ) = ο€Ή 5 𝑑  + ( 7 𝑑 ) 2 . 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 𝑑 in seconds.

  • A 7 560 J
  • B 900 J
  • C 2 700 J
  • D 5 400 J

Q9:

The displacement of a particle of mass 30 g is given as a function of time by the relation s i ( 𝑑 ) = ο€Ή 5 𝑑 βˆ’ 6 𝑑  2 , where i is a constant unit vector, 𝑠 is measured in centimetres, and 𝑑 in seconds. Given that the particle started its motion at 𝑑 = 0 , find the force 𝐹 acting on the particle and the work done π‘Š by this force during the first 7 seconds of motion.

  • A 𝐹 = βˆ’ 2 1 0 i d y n , π‘Š = 5 4 3 9 0 e r g
  • B 𝐹 = βˆ’ 3 5 5 i d y n , π‘Š = 9 1 9 4 5 e r g
  • C 𝐹 = βˆ’ 3 0 i d y n , π‘Š = 7 7 7 0 e r g
  • D 𝐹 = βˆ’ 3 6 0 i d y n , π‘Š = 9 3 2 4 0 e r g

Q10:

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

Q11:

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 .

Q12:

A body of mass 2 kg is moving under the action of three forces, F 1 , F 2 , and F 3 , where F i j 1 = 𝑏 βˆ’ 3 , F i j 2 = βˆ’ 4 + 3 , and F i j 3 = βˆ’ 1 0 + π‘Ž , and i and j are two perpendicular unit vectors, π‘Ž and 𝑏 are constants, and each force is measured in newtons. The displacement of the body is expressed by the relation s i j ( 𝑑 ) = ο€Ή 4 𝑑  + ο€Ή 3 𝑑 βˆ’ 8 𝑑  2 2 , where the displacement is measured in meters, and the time 𝑑 is in seconds. Determine the work done by the resultant of the forces in the first 6 seconds of motion.

  • A βˆ’ 7 6 8 J
  • B 3 120 J
  • C 1 584 J
  • D 3 024 J

Q13:

A body moves in a plane in which and are perpendicular unit vectors. At time seconds, its position vector is given by . Given that from to , the change in the body’s kinetic energy was 414 J, find the body’s mass.

Q14:

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 seconds.

Q15:

An object moves 10 m in the direction of j i + . There are two forces acting on this object: F i j k 1 = + 2 + 2 N and F i j k 2 = 5 + 2 βˆ’ 6 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 3 0 √ 2 Nβ‹…m
  • B 1 0 √ 2 Nβ‹…m
  • C 6 0 √ 2 Nβ‹…m
  • D 5 0 √ 2 Nβ‹…m
  • E 40 Nβ‹…m

Q16:

An object moves 10 m in the direction of j . There are two forces acting on this object: F i j k 1 = + + 2 N and F i j k 2 = βˆ’ 5 + 2 βˆ’ 6 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.

Q17:

An object moves 20 meters in the direction of k j + . There are two forces acting on this object: F i j k 1 = + + 2 N and F i j k 2 = + 2 βˆ’ 6 N. Find the total work done on the object by the two forces.

  • A 5 0 √ 2 Nβ‹…m
  • B 1 0 √ 2 Nβ‹…m
  • C βˆ’ 2 0 √ 2 Nβ‹…m
  • D βˆ’ 1 0 √ 2 Nβ‹…m
  • E 2 0 √ 2 Nβ‹…m

Q18:

A body moves under the force F i j = 6 βˆ’ 9 from point 𝐴 ( βˆ’ 2 , 8 ) to point 𝐡 ( 1 , βˆ’ 7 ) . Determine the work done by the force, where the displacement is measured in meters and the force in newtons.

  • A βˆ’ 8 4 J
  • B βˆ’ 1 5 3 J
  • C 69 J
  • D 153 J

Q19:

A force of F i k = 6 + 4 newtons acts on a body and moves it from point 𝐴 ( βˆ’ 9 , βˆ’ 2 , βˆ’ 3 ) to point 𝐡 ( 8 , βˆ’ 7 , βˆ’ 1 ) . Determine the work done by the force F , where the displacement is measured in meters.

  • A βˆ’ 6 6 J
  • B βˆ’ 1 1 0 J
  • C 44 J
  • D 110 J

Q20:

A body moves from point 𝐴 ( 1 , 2 , 5 ) to 𝐡 ( 5 , 5 , βˆ’ 4 ) under a force F . Determine the work done if the force has magnitude √ 5 7 newtons and direction cosines ο“’ 5 √ 5 7 5 7 , 4 √ 5 7 5 7 , 4 √ 5 7 5 7 ο““ , taking the displacement as measured in meters.

  • A 4 √ 5 7 5 7 J
  • B βˆ’ 4 √ 5 7 5 7 J
  • C 4 J
  • D βˆ’ 4 J

Q21:

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