Answer to Question #138915 in Mechanics | Relativity for Marilyn Recarte

Question

Imagine you’re pulling a sledge. That is: a massive
object with no wheels; scraping along the ground,
with friction, but pulled along by an ideal massless
rope under tension, inclined at an angle θ.
Obviously θ = 90◦ would not be a good angle at which to tug at the sledge, as you’d just be pulling it
straight up. Less obviously, θ = 0 would also not be the ideal angle for pulling the sledge. There is some
nonzero “optimum” angle θopt along which you can orient the rope that minimizes the amount of tension
you have to apply to the rope in order to overcome friction and get the sledge to move.
Explain in words why it is best to pull slightly upward. Try to explain succinctly, but completely. Answers
will be graded not only based on correctness, but also on completeness of the explanation. You do not need
to calculate θopt (or anything, really), you’re just trying to argue (in words) that θopt is nonzero

Answer 1

It is because When we pull the sledge Then angle of friction has some n0n zero value.

When we Pull the sledge the frictional force acting on the sledge is in backward direction.

But the normal reaction from ground should be in a direction that it oppose the Friction force,

So thee will be a lower tension in the rope as it was before.

Also the surface area included in friction i.e. the contact area between the sledge and the ground

decreases.

hence it is advised to pull the sledge slightly upwards.