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? |
Solution
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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)
![\[ W = \vec{F} \cdot \vec{d} \]](mastermathpng-0.png)
- The angle between the force vector and the displacement vector
is 20∘. Therefore the work done by the man is
W=(Fcos20)×dwhere 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×cos20∼4.7×102 J (2 s.f.)