Q4.2 Work, force and displacement II (S)

A man pushes a trolley up a 30 hill, applying a constant force of 50 N at an angle of 20 to the trolley. What is the total amount of work the man does in raising the trolley by five meters?
Graphic - No title - trolley
Hide

Hint

Remember that both the force and the displacement are constant vectors.
 

Solution

Reveal
Hide

Solution

The displacement and the force are both constant vectors. We have to work out the magnitude of each, and the angle between them using (Equation 3.1)

\[ W = \vec{F} \cdot \vec{d} \]

  • The angle between the force vector and the displacement vector is 20. Therefore the work done by the man is
    W=(Fcos20)×d
    where F is the magnitude of the force vector, and d is the magnitude of the displacement vector.
  • If the trolley is raised by 5m, it must travel a distance d of
    d=5/sin30=10 m
  • The work done is then 50×10×cos204.7×102 J (2 s.f.)