Solving the Toaster Friction Problem

  • Thread starter blackboy
  • Start date
  • Tags
    Friction
In summary, to make the toaster start moving, you need to pull on its electric cord at an angle so that the tension is as small as possible. With this angle and the cord tension you specified, the tension must be large enough to move the toaster.
  • #1
blackboy
61
0

Homework Statement



A 1.3kg toaster is not plugged in. The coefficient of static friction between the toaster and a horizontal countertop is 0.350. To make the toaster start moving, you carelessly pull on its electric cord. (a) For the cord tension to be as small as possible, you should pull at what angle above the horizontal? (b) With this angle, how large must the tension be?

Homework Equations





The Attempt at a Solution


Ok I know that there are two components to the tension, TCosθ and TSinθ. I got TSinθ<12.74 and TCosθ>4.459 so θ<70.7. We want TCosθ-4.459 to be as small as possible so

d(TCosθ-4.459)/dθ=0 and -TSinθ=0 so θ=0.

Somehow I don't think that is right. And for the second part are you giving T>x or a specified value for T? Thank you.
 
Physics news on Phys.org
  • #2
blackboy said:

Homework Statement



A 1.3kg toaster is not plugged in. The coefficient of static friction between the toaster and a horizontal countertop is 0.350. To make the toaster start moving, you carelessly pull on its electric cord. (a) For the cord tension to be as small as possible, you should pull at what angle above the horizontal? (b) With this angle, how large must the tension be?

Homework Equations





The Attempt at a Solution


Ok I know that there are two components to the tension, TCosθ and TSinθ. I got TSinθ<12.74 and TCosθ>4.459 so θ<70.7. We want TCosθ-4.459 to be as small as possible so

I don't quite understand what you did, so please forgive me if this sounds redundant:

Try drawing a free-body diagram of the toaster. There are 4 forces: gravity, tension, the normal force, and friction. Don't forget that friction is N*mu, not mg*mu. Write out Newton's second law for the x and y directions, get an expression for tension, and minimize it using calculus. Try it, and post back when you get an answer.
 
  • #3
Ok say there is a force T acting on the toaster at θ above the horizontal. The y component is TSinθ and the x component is TCosθ. We want TCosθ>fstatic so it will move. TCosθ>N(mu) TCosθ>12.74(.350), TCosθ>4.459. Now Cosθ ranges from 1 to 0. The higher Cosθ is, the lower T will be. The highest Cosθ goes is 1 so T>4.459. What am I doing wrong?
 
  • #4
Whats wrong if theta is zero? If you pull horizontally then the tension will be equal to the force of friction. If you make theta larger then your horizontal tension will decrease by a little but you vertical tension will increase by much more. mg is acting downward which is much larger than Nmu.
[tex]T=\frac{N-mg+F_s}{cos\theta - sin\theta}[/tex]
If theta is zero N and mg cancel out. If it isn't zero, the two don't cancel out and the denominator is greater than one.
 
  • #5
blackboy said:
Ok say there is a force T acting on the toaster at θ above the horizontal. The y component is TSinθ and the x component is TCosθ. We want TCosθ>fstatic so it will move. TCosθ>N(mu) TCosθ>12.74(.350), TCosθ>4.459. Now Cosθ ranges from 1 to 0. The higher Cosθ is, the lower T will be. The highest Cosθ goes is 1 so T>4.459. What am I doing wrong?
T*sinθ will act in the opposite direction to mg.. So the normal reaction will be ( mg - T*sinθ )
 
  • #6
Oh dang it, I put N=mg. Well I think I got it now. TCosθ-.35N>0, so T(Cosθ+.35Sinθ)>4.459. We want Cosθ+.35Sinθ to be max so T will be min. -Sinθ+.35Cosθ=0, θ=19.29. Then T>4.2. Right?
 
  • #7
Sorry for being rude, but am I right? Thank you.
 
  • #8
blackboy said:
Sorry for being rude, but am I right? Thank you.
Frictional force fr = μ( mg - T*sinθ ). To start motion T*cosθ > fr.
So write
μ( mg - T*sinθ ) = T*cosθ
Take the derivative and equate it to zεro to get θ
 
  • #9
Isn't that what I did in post 6? Then T=4.2 instead of T>4.2.
 
  • #10
blackboy said:
Isn't that what I did in post 6? Then T=4.2 instead of T>4.2.
Yes. You are right.
 
  • #11
Thank you come again.
 

1. How can the toaster friction problem be solved?

The toaster friction problem can be solved by identifying the source of the friction, such as a malfunctioning mechanism or debris buildup, and addressing it accordingly. This may involve cleaning, lubricating, or repairing the affected parts.

2. Why is the toaster friction problem important to solve?

The toaster friction problem can hinder the proper functioning of the toaster, leading to unevenly toasted bread or even damage to the appliance. It can also be a safety hazard if the friction causes overheating or sparks.

3. Are there any preventative measures to avoid the toaster friction problem?

Yes, regular cleaning and maintenance of the toaster can help prevent the buildup of debris or malfunctioning parts that can cause friction. It's also important to use the toaster according to the manufacturer's instructions and not overload it with too much bread or other food items.

4. Can the toaster friction problem be fixed by the average person, or should a professional be consulted?

In most cases, the toaster friction problem can be fixed by the average person with some basic tools and knowledge. However, if the problem is more complex or involves electrical components, it may be best to consult a professional.

5. How can the toaster friction problem be prevented in the future?

To prevent the toaster friction problem from recurring, it's important to continue with regular cleaning and maintenance. It's also a good idea to check for any signs of wear and tear on the toaster and replace any worn or damaged parts as needed.

Similar threads

  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
7K
  • Introductory Physics Homework Help
Replies
3
Views
2K
  • Introductory Physics Homework Help
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
3K
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
3K
  • Introductory Physics Homework Help
Replies
6
Views
1K
Replies
29
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
983
Back
Top