Optimizing Pulling Force: Solving for Theta and F in Newton's Laws

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Homework Help Overview

The problem involves a block being pulled along a horizontal surface with friction, and the goal is to determine the angle and force required for optimal pulling. The subject area pertains to Newton's laws of motion and frictional forces.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to understand the derivation of the answers they have, specifically questioning how the relationships involving angle and force were established. Some participants suggest finding the pulling force as a function of the angle theta.

Discussion Status

Participants are exploring the relationships between the forces acting on the block. There is an ongoing examination of the equations related to the forces in both the x and y directions, with some expressing confusion about the implications of their findings. No consensus has been reached, but there is engagement with the problem.

Contextual Notes

Participants are working under the constraints of Newton's laws and the conditions of constant velocity and friction. There is an indication of differing interpretations regarding the forces involved, particularly concerning the frictional force and its relationship to the angle.

Airsteve0
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A large block of mass M is going to be pulled with a constant velocity along a horizontal surface. The coefficient of friction between the surface and block is u.

(1) Find the angle theta=theta_naught that the direction of pull shall make with the direction of motion for the pulling force to be as small as possible.
(2) Find this smallest value of F.


Ok so I know the answers are:
(1) u = tan (thets_naught)
(2) F = (uMg)/sqrt(1 + u^2)

however I have no idea how these answers were arrived at. Could someone please offer some assisstance?
 
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Why don't you give it a try? Hint: Find the force as a function of theta.

(Five laws?)
 
Solving this system I was able to get to the solution:

tan(theta) = Fy/Fx (forces in x and y-directions)

However, I believe Fx equals the frictional force (uN) so the only way to arrive at the solution posted in the book would be if Fy = u^2N, which seems very strange.
 
Airsteve0 said:
However, I believe Fx equals the frictional force (uN) so the only way to arrive at the solution posted in the book would be if Fy = u^2N, which seems very strange.
Strange but true. (Not sure why you'd have an opinion about that.)
 
Doc Al said:
(Five laws?)

I think the five laws would be
3 laws of motion
1 of gravitation
1 of restitution
(though the last 2 arent applied here! :smile:)
 

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