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

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In summary, the problem involves pulling a sleigh with a total mass of 47 kg at a constant velocity over level snow with a coefficient of kinetic friction of 0.11. The rope makes an angle of 23 degrees with the horizontal and the goal is to calculate the magnitude of the tension in the rope needed to keep the sleigh moving. To solve this, the applied force must be separated into horizontal and vertical components and equations can be used to eliminate variables and determine the magnitude of the applied force.
  • #1
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 betwen 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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  • #2
HINT: Now look at the horizontal forces and realize what "constant velocity" means.
 
  • #3
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.
 
  • #4
You now have two equations each of which contains Fapp. Use one equation to eliminate it in the other!
 
  • #5
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.
 
  • #6
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.
 

1. What is frictional force?

Frictional force is a contact force that resists the motion of an object when it comes into contact with a surface.

2. How do you calculate frictional force?

Frictional force can be calculated by multiplying the coefficient of friction between two surfaces by the normal force acting on the object.

3. What is the tension in the sleigh rope?

The tension in the sleigh rope can be calculated by multiplying the mass of the sleigh by the acceleration due to gravity and adding it to the frictional force acting on the sleigh.

4. How does the mass of the sleigh affect the frictional force?

The mass of the sleigh affects the frictional force by increasing the normal force acting on the sleigh, which in turn increases the frictional force.

5. What is the significance of calculating frictional force in this scenario?

In this scenario, calculating the frictional force allows us to determine the amount of force needed to overcome the resistance and move the sleigh with a mass of 47kg. It also helps us understand the necessary tension in the sleigh rope to ensure a safe and smooth ride.

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