Force is a vector quantity, and a force can be resolved into its components to get the effect of the force.
The responses are;
- a) The force exerted by the first person towards the right is approximately 280.96 Newtons.
- b) To move the railroad car, the second person must exert a force of approximately 356.49 Newtons.
Reasons:
a) The force with which the person is pulling the railroad car, F = 310 N
The vector force on the rope [tex]\vec {v}_{rope}[/tex] = 310 × cos(25°)·i + 310 × sin(25°)·j
Which gives;
- [tex]\vec {v}_{rope}[/tex] = 280.96·i + 131.01·j
The component of the vector acting along the railroad, towards the right is the i component
Therefore, the force the person exerts toward the right while trying to move the car is approximately
b) The direction of the rope of the second person, θ = 18°
The force required to get the railroad car moving = 620 N
The force the second person has to exert to the right is therefore;
F × cos(18°) = 620 - 310 × cos(25°)
Therefore;
[tex]\displaystyle F = \mathbf{\frac{620 - 310 \times cos(25^{\circ})}{ cos(18^{\circ})}} \approx 356.49[/tex]
The force the second person must exert in the given direction, is therefore;
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