Particle sliding across a surface with curved ends

In summary, rmunoz was trying to use the law of conservation of mechanical energy to describe the motion of a particle, but was unclear about how to start. He found help from tiny-tim, who explained the work-energy theorem and how to use it on the flat part of the track.
  • #1
rmunoz
30
0

Homework Statement


A particle can slide along a track with elevated ends and a flat central part, as shown below. The flat part has length L = 40 cm. The curved portions of the track are frictionless, but for the flat part the coefficient of kinetic friction is µk = 0.28. The particle is released from rest at point A, which is a height h = L/2. How far from the left edge of the flat does the particle finally stop? http://www.webassign.net/halliday8e/pc/halliday8019c08/halliday8019c08-fig-0057.htm


Homework Equations


Ugrav=mgh
K= 1/2mv^2
a(centripital)= v^2/r
Fric(kinetic)= [tex]\mu[/tex]mgsin90=> [tex]\mu[/tex]mg

Sorry to say, but the reason I'm having trouble with this problem is frankly that I have no idea how to start! The goal for me is to be able to use the law of conservation of mechanical energy to describe the particle's motion. At first glance, I feel like the equation for the kinetic energy of the particle, right after the first fall should take into account the velocity calculated by centripital acceleration. I can tell initially that the kinetic energy will be 0 since its not moving and that the Ugrav will describe the total mechanical energy within the system. Is this correct, or even relevant at all? Also, i have no idea how to describe the loss of kinetic energy as an increase in the amount of "heat" energy within the system due to the friction-surface. Any tips on how to get the ball rolling on this problem?

Sorry if this is at all unclear, this is my first post and as you can probably tell, I'm in dire need of some physics help, but more than willing to put in the effort with guidance!
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
Welcome to PF!

rmunoz said:
A particle can slide along a track with elevated ends and a flat central part, as shown below. The flat part has length L = 40 cm. The curved portions of the track are frictionless, but for the flat part the coefficient of kinetic friction is µk = 0.28. The particle is released from rest at point A, which is a height h = L/2. How far from the left edge of the flat does the particle finally stop?
…
The goal for me is to be able to use the law of conservation of mechanical energy to describe the particle's motion.

Hi rmunoz ! Welcome to PF! :wink:

As you say, this is an energy problem …

use conservation of energy on the curved part (the centripetal acceleration is irrelevant), and the work-energy theorem ( work done by friction = energy lost) on the flat part :smile:
 
  • #3
Wow, got it right on the first try! that was a lot easier than i thought it was going to be, thank you very much tiny-tim for the help... i think i like this website!
 

1. What is the difference between a particle sliding across a flat surface and a curved surface?

When a particle slides across a flat surface, it experiences a constant force due to the surface's uniform shape. However, on a curved surface, the particle experiences a varying force due to the changing curvature of the surface.

2. How does the shape of the curved ends affect the motion of the particle?

The shape of the curved ends can greatly impact the motion of the particle. A sharper curve will result in a greater force acting on the particle, causing it to accelerate more quickly. On the other hand, a more gradual curve will result in a smaller force and a slower acceleration.

3. What role does friction play in the motion of a particle sliding across a surface with curved ends?

Friction is a crucial factor in the motion of a particle on a curved surface. It acts in the opposite direction of the particle's motion, slowing it down and causing it to eventually come to a stop. The amount of friction present will depend on the type of surface and the force applied to the particle.

4. Can a particle sliding across a surface with curved ends ever achieve constant velocity?

Yes, it is possible for a particle to achieve constant velocity on a curved surface. This can occur when the force of friction is equal and opposite to the force of the curved ends, resulting in a net force of zero and a constant velocity.

5. How can the trajectory of a particle sliding across a surface with curved ends be predicted?

The trajectory of a particle on a curved surface can be predicted using mathematical equations and principles such as Newton's laws of motion. Factors such as the shape of the curved ends, the initial velocity of the particle, and the force of friction must be taken into account to accurately predict the trajectory.

Similar threads

Height to which rolling ball rises on a surface
    • Introductory Physics Homework Help
Replies
12
Views
2K
Particle constrained on a curve
    • Introductory Physics Homework Help
Replies
9
Views
1K
Two particles on a vertical ring
    • Introductory Physics Homework Help
Replies
16
Views
2K
A problem about momentum and energy,
    • Introductory Physics Homework Help
Replies
7
Views
1K
Mass sliding on rough and smooth surfaces
    • Introductory Physics Homework Help
Replies
13
Views
1K
Why Does a Rolling Sphere Climb Higher Than a Sliding Particle?
    • Introductory Physics Homework Help
Replies
2
Views
1K
What is the work-energy theorem for a block sliding on a frictionless incline?
    • Introductory Physics Homework Help
Replies
6
Views
4K
Energy Conservation: Puck on Wood on Frictionless Surface
    • Introductory Physics Homework Help
Replies
14
Views
2K
Particle sliding on a track (cons. of energy problem)
    • Introductory Physics Homework Help
Replies
2
Views
17K
Particle on a sliding inclined plane
    • Introductory Physics Homework Help
Replies
15
Views
3K

Hot Threads

Recent Insights

Back
Top