Answer to Question #86828 in Mechanics | Relativity for Nada

Question

An elephant pulls the wooden lump of mass 0.5 ton by a rooe along the ground where the rope makes an angle 60° to the horizontal at uniform velocity. Given that the frictional force between the lump and the ground is 200 N, find: 1. the tension force in the rope.
2. the tension force in the rope required to make the lump move at acceleration 2 m/s2

Answer 1

1. Uniform velocity means no acceleration.

$T\cos\alpha = F_f;\\ T = \frac{F_f}{\cos\alpha} = \frac{200~\text{N}}{0.5} = 400~\text{N}. \\$

2.

$T = \frac{F_f+ma}{\cos\alpha} = \frac{200~\text{N}+500~\text{kg}*2\frac{\text{m}}{\text{s}^2}}{0.5} = 2400~\text{N}. \\$