Physics homework help needed -- A mass sliding down a ramp with friction

In summary, the mass slides down the inclined part of the slide at a constant speed, and the coefficient of kinetic friction is equal to the normal force.
  • #1
pilot12
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Homework Statement
Trouble on this final problem of my physics homework
Relevant Equations
M g h + 1/2 mv^2 - (s1+s2)umg=0
h= 1.18sin(28.1) = .55579
When mass M is at the position shown, it is sliding down the inclined part of a slide at a speed of 2.19 m/s. The mass stops a distance S2 = 2.1 m along the level part of the slide. The distance S1 = 1.18 m and the angle θ = 28.10°. Calculate the coefficient of kinetic friction for the mass on the surface.
https://letu.loncapa.net/res/msu/physicslib/msuphysicslib/13_EnergyConservation/graphics/prob27a_MechEnWFriction.gif
38BC25BD-9D26-431A-A418-96FA31BC62A3.jpeg
 
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  • #2
Hello @pilot12 ,
:welcome: ##\qquad##!​

Here at PF we require an attempt at solution from you (see guidelines) before we are allowed to help.

Being confused is one thing, but being completely incapacitated is something else. What do you know that can help you here to get started ? (formulas, considerations, equations, etc)

##\ ##
 
  • #3
Sorry I did not know that @BvU , I was trying to use

mgh + 1/2mv^2 - (s1+s2)u m g=0

h= 1.18sin(28.1) = .55579
 
  • #4
pilot12 said:
Sorry I did not know that @BvU , I was trying to use

mgh + 1/2mv^2 - (s1+s2)u m g=0

h= 1.18sin(28.1) = .55579
Welcome to PF.

What you posted as the follow-up reply does not help. How are you gong to calculate the coefficient of friction to slow the mass in the specified distance?
 
  • #5
Also, this might be a trick question. Is the problem saying that the mass slides down the incline with a constant speed? What would be significant about that?
 
  • #6
@berkeman I believe it is saying it is sliding down at a constant speed. If it wasn’t, I think it would be an acceleration
 
  • #7
pilot12 said:
@berkeman I believe it is saying it is sliding down at a constant speed. If it wasn’t, I think it would be an acceleration
Good. So what can you say about a value of kinetic friction on a ramp that allows constant velocity down the ramp?
What two forces are equal in that situation? Can you post a Free Body Diagram (FBD) of the mass while it is sliding down the ramp?
 
  • #8
That the kinetic friction is equal to the Fnx? @berkeman
image.jpg
 
  • #9
##\mu_K## is not a force. ##\ \mu_K\times F_N\ ## is the friction force. What is ##F_N## in terms of ##F_g## and ##\theta## ?
 
  • #10
@BvU I figured it out, the masses cancel out and then you can solve it. Appreciate your help!
 
  • #11
DId you get a reasonable value for ##\mu## ?
 
  • #12
pilot12 said:
@berkeman I believe it is saying it is sliding down at a constant speed. If it wasn’t, I think it would be an acceleration
No, I'm pretty sure it is not saying that. It may well be accelerating.
If you allow for that possibility, and just assume the coefficient is the same both on the slope and on the flat, there is enough information to solve it.
What value did you get?
 
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  • #13
It definitely accelerates on the slope, yes.
 
  • #14
"When mass M is at the position shown, it is sliding down the inclined part of a slide at a speed of 2.19 m/s."
It is obvious from the text that it is sliding with that veleocity at that point and not for the whole length of the inclined plane. Otherwise, it should say "mass M is sliding down the inclined part of a slide at a speed of 2.19 m/s."
 
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  • #15
pilot12 said:
mgh + 1/2mv^2 - (s1+s2)u m g=0
The above equation looks like it is a correct application of the work energy theorem, however it is wrong. What is wrong is that the total work of friction is not ##(s_1+s_2)umg## because the normal force is not equal to ##mg## for the whole distance. It is equal to ##mg## only during the s2 distance.

Also we don't know if the friction coefficient is the same and equal to ##u## for the whole distance, we have to assume that otherwise it is not solvable by the data given.
 

FAQ: Physics homework help needed -- A mass sliding down a ramp with friction

1. How does friction affect the motion of a mass sliding down a ramp?

Friction is a force that opposes the motion of an object. In the case of a mass sliding down a ramp, friction will act in the opposite direction of the motion, slowing down the mass and causing it to move at a slower rate than it would without friction.

2. How do you calculate the force of friction on a mass sliding down a ramp?

The force of friction can be calculated using the equation F = μN, where μ is the coefficient of friction and N is the normal force. The normal force is equal to the weight of the object, which can be calculated using the equation N = mg, where m is the mass of the object and g is the acceleration due to gravity.

3. What factors affect the coefficient of friction on a ramp?

The coefficient of friction on a ramp can be affected by the type of surface the mass is sliding on, the weight of the mass, and the angle of the ramp. Rougher surfaces and heavier masses will generally have a higher coefficient of friction, while smoother surfaces and lighter masses will have a lower coefficient of friction.

4. How does the angle of the ramp affect the motion of a mass sliding down?

The angle of the ramp can affect the motion of a mass sliding down in two ways. Firstly, a steeper ramp will increase the force of gravity acting on the mass, causing it to accelerate at a faster rate. Secondly, a steeper ramp will also increase the normal force acting on the mass, which will in turn increase the force of friction and slow down the mass.

5. How do you calculate the acceleration of a mass sliding down a ramp with friction?

The acceleration of a mass sliding down a ramp with friction can be calculated using the equation a = (gsinθ - μcosθ) / (1 + μsinθ), where g is the acceleration due to gravity, θ is the angle of the ramp, and μ is the coefficient of friction. This equation takes into account both the force of gravity and the force of friction acting on the mass.

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