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Here are the solutions to questions 4 and 5.

Question 4: Truck on a Slope

4. (a) (i) Sketch a free body diagram for the truck as it ascends.

A free body diagram for the truck ascending the slope would show the following forces:

  • Weight (W=mgW = mg): Acting vertically downwards from the center of mass.
  • Normal Force (NN): Acting perpendicular to the slope, upwards from the surface.
  • Engine Force (FengineF_{engine}): Acting parallel to the slope, upwards (in the direction of motion).
  • Resistive Force (FresistiveF_{resistive}): Acting parallel to the slope, downwards (opposite to the direction of motion).

The weight can be resolved into two components: mgsin⁡θmg \sin\theta acting parallel to the slope downwards, and mgcos⁡θmg \cos\theta acting perpendicular to the slope downwards.

      ^ N
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