Friction and Newton's Laws

  • Thread starter jared69sib
  • Start date
  • #1
38
0

Homework Statement



A child slides down a slide with a 34 degree incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.

Homework Equations



[tex]\Sigma[/tex]F = ma
[tex]\Sigma[/tex]FR=[tex]\mu[/tex]FN

The Attempt at a Solution



set x-axis along incline.
Got FN=mgcos[tex]\theta[/tex] and gsin[tex]\theta[/tex]-gtan[tex]\theta[/tex]cos[tex]\theta[/tex]=a
Now I don't know what to do. I have a = 4.92 m/s2, but I feel I can't proceed without [tex]\Delta[/tex]x or t....

Thanks in advance!
 

Answers and Replies

  • #2
ehild
Homework Helper
15,543
1,913
Check your equation for a. Now it is equivalent to a=0.

Try to apply the Work-Energy theorem.

ehild
 
Last edited:
  • #3
HallsofIvy
Science Advisor
Homework Helper
41,847
965
What I would do is use "energy". Taking the bottom of the slide as the 0 point for potential energy, at the top of the slide the child's gravitational potential energy is mgh where m is the child's mass and h is the vertical height of the slide. At the bottom the child's gravitational potential energy is 0 so all of that potential energy is converted to kinetic energy or lost to friction. But we are told that the speed was only 1/2 what it would be without friction. Since kinetic energy increases as the square of the speed, and the child's speed is half what it would be without friction, its kinetic energy is 1/4. If there were no friction, the kinetic energy would be equal to the original potential energy, mgh, but now is 1/4 that- mgh/4. That means that the energy lost to friction is 3mgh/4.

Let the coefficient of kinetic friction by [itex]\mu[/itex]. Now you can calculate the component of the child's weight normal to the slide from the given angle and the length of the slide assuming height h and the given angle. The work done by the friction force is the coefficent of friction times the friction force times the length of the slide and that must be equal to 3mgh/4.

You will find that m, g, and h all cancel.
 

Related Threads on Friction and Newton's Laws

  • Last Post
Replies
17
Views
3K
  • Last Post
Replies
2
Views
7K
  • Last Post
Replies
16
Views
3K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
16
Views
8K
  • Last Post
Replies
1
Views
3K
Replies
1
Views
1K
  • Last Post
Replies
2
Views
5K
Replies
1
Views
3K
  • Last Post
Replies
8
Views
4K
Top