Coefficient of Friction between slide/girl

In summary: How much work was done against gravity? How much work was done by gravity? What is the relationship between work and energy? How does that relate to the relationship between PE and KE?In summary, a 36kg girl slides down a slide that is 4.5m long at an angle of 35 degrees. At the bottom of the slide, she is moving at 3 m/sec. Using the equations for kinetic and potential energy, the total energy at the top of the slide is calculated to be 911.15 J. However, at the bottom of the slide, the girl has a kinetic energy of only 162 J. This difference in energy can be attributed to the work done by friction and gravity.
  • #1
cdsnig
2
0

Homework Statement


A 36kg girl slides down a slide that is 4.5m long. At the bottom of slide she is moving at 3 m/sec. If slide is inclined at 35 degrees find the coefficient of friction between slide and girl.



Homework Equations



Ff = μ*Force normal
Total energy = KE + PE
KE = 1/2 mv^2
PE = mgh
Total energy = F cosθ


The Attempt at a Solution



KE = 162 using above formula, PE = 911.15. Total energy = 1073.15
F = 1310.32 using the cosθ formula.

And that is where I am stuck - is the F the normal force or the Ff (from friction) how would I solve for the coefficient from this point? And have I even approached it in the right way so far?
 
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  • #2
cdsnig said:

Homework Statement


A 36kg girl slides down a slide that is 4.5m long. At the bottom of slide she is moving at 3 m/sec. If slide is inclined at 35 degrees find the coefficient of friction between slide and girl.

Homework Equations



Ff = μ*Force normal
Total energy = KE + PE
KE = 1/2 mv^2
PE = mgh
Total energy = F cosθ

The Attempt at a Solution



KE = 162 using above formula, PE = 911.15. Total energy = 1073.15
F = 1310.32 using the cosθ formula.

And that is where I am stuck - is the F the normal force or the Ff (from friction) how would I solve for the coefficient from this point? And have I even approached it in the right way so far?

Firstly; how did you get that PE figure - not enough to say using the formula above as I need to know what values you used for m, g and h.

Secondly; why did you add KE and PE together? Surely we had pE at the top and KE at the bottom, but never both at the same time [perhaps half and half on the way down, but you were considering the top and the bottom, I hope]
You said,
Total energy = KE + PE

At the top that would be Total energy = 0 + PE
At the bottom that would be Total energy = KE + 0

And those two totals are different, due to the friction.

Edit: Total energy = F cosθ makes you group of formulas look like a grab-bag of possibilities, rather than a reasoned list of what actually applies.
 
  • #3
cdsnig said:

Homework Statement


A 36kg girl slides down a slide that is 4.5m long. At the bottom of slide she is moving at 3 m/sec. If slide is inclined at 35 degrees find the coefficient of friction between slide and girl.

Homework Equations



Ff = μ*Force normal
Total energy = KE + PE
KE = 1/2 mv^2
PE = mgh
Total energy = F cosθ

The Attempt at a Solution



KE = 162 using above formula, PE = 911.15. Total energy = 1073.15
F = 1310.32 using the cosθ formula.

And that is where I am stuck - is the F the normal force or the Ff (from friction) how would I solve for the coefficient from this point? And have I even approached it in the right way so far?

At the top of the slide the girl has PE = 911 J. At the bottom, her KE is only 162 J. What happened to the rest of the PE? How much work was done by friction?
 

1. What is the coefficient of friction between a slide and a girl?

The coefficient of friction between a slide and a girl is a measure of the amount of resistance the girl experiences while sliding down the slide. It is a dimensionless value typically represented by the symbol 'μ' and is dependent on the materials of the slide and the girl's clothing, as well as other factors such as surface roughness and temperature.

2. How is the coefficient of friction between a slide and a girl calculated?

The coefficient of friction is calculated by dividing the force required to move the girl down the slide by the weight of the girl. This can be done by conducting experiments and measuring the force and weight, or by using mathematical formulas that take into account the materials and surface properties of the slide and the girl.

3. Why is the coefficient of friction between a slide and a girl important?

The coefficient of friction is important because it determines the ease and safety of sliding down a slide. A higher coefficient of friction means there is more resistance, making it harder for the girl to slide down the slide. This can result in slower speeds and a rougher, less enjoyable experience. A lower coefficient of friction means less resistance, allowing the girl to slide down the slide more easily and smoothly. This can also impact safety, as a lower coefficient of friction may increase the risk of the girl slipping or losing control while sliding.

4. Can the coefficient of friction between a slide and a girl be changed?

Yes, the coefficient of friction can be changed by altering the materials or surface properties of either the slide or the girl. For example, using a different type of slide material or applying a lubricant to the slide can decrease the coefficient of friction. Similarly, changing the girl's clothing or adding grips to her hands or feet can also affect the coefficient of friction.

5. Are there any safety precautions that should be taken into consideration when measuring the coefficient of friction between a slide and a girl?

Yes, it is important to take proper safety precautions when conducting experiments to measure the coefficient of friction. This may include wearing appropriate protective gear, using a controlled and safe environment, and having adult supervision. It is also important to carefully follow experimental procedures and use accurate measurements to ensure reliable results.

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