Calculating Frictional Force: Tension in Sleigh Rope & Mass of 47kg

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Homework Help Overview

The problem involves calculating the tension in a rope used to pull a sleigh with a total mass of 47 kg over level snow, considering the effects of friction and the angle of the rope. The coefficient of kinetic friction is given as 0.11, and the scenario requires maintaining a constant velocity.

Discussion Character

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Approaches and Questions Raised

  • Participants discuss the need to determine the normal force and its relationship with the applied force and gravitational force. There are attempts to set up equations based on the forces acting on the sleigh, including horizontal and vertical components of the applied force.

Discussion Status

Participants are exploring various equations related to the forces involved, with some guidance provided on separating the applied force into its components. There is recognition of the need to eliminate variables to solve for the unknowns, but no consensus has been reached on the approach to take.

Contextual Notes

There is a hint that the normal force is not simply equal to the gravitational force, which adds complexity to the problem. The discussion reflects uncertainty regarding the values of certain forces and how they interact within the context of the problem.

F.B
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I am really stuck on a few questions but i'll only post one.

An adult is pulling two small children in a sleigh over level snow. The sleigh and children have a total mass of 47 kg. The sleigh rope makes an angle of 23 degrees with the horizontal. The coefficient of kinetic friction between the sleigh and the snow is 0.11. Calculate the magnitude of the tension in the rope needed to keep the sleigh moving at a constant velocity. (Hint. The normal force is not equal to the force of gravity.)

I don't know what to figure out first. See i need Fn but i can't figure it out.
I think Fn=Fg - Fapp(in the y direction). But i don't have a force to help me out. So can anyone please help me.
 
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HINT: Now look at the horizontal forces and realize what "constant velocity" means.
 
a=0, so does it equal:
0=Fapp(in the x direction) - Ff
But i still don't know what Fapp is because i don't have a force there.
 
You now have two equations each of which contains Fapp. Use one equation to eliminate it in the other!
 
If i do that then i have:
Fapp=Fg - Fn
Fapp=Fnet + Ff

I can't use those because i still don't know Fn. It won't work.
 
You need to separate the applied force into horizontal and vertical components:

[tex]F_{app, y} = F_{app} \times \sin 23^o[/tex]

and

[tex]F_{app, x} = F_{app} \times \cos 20^o[/tex]

The normal force is therefore

[tex]F_n = -F_{app} \times \sin 20^o + mg[/tex]

and the horizontal force is

[tex]0 = F_{app} \times \cos 20^o - F_f[/tex]

Now use the fact that

[tex]F_f = \mu F_n = -\mu(- F_{app} \times \sin 20^o + mg)[/tex]

and you should be able to determine the magnitude of the applied force.
 

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