Calculating Distance Traveled on an Inclined Plane: Mechanics Help Needed!"

  • Thread starter wuffle
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In summary, the discussion revolved around the mechanics of a block sliding down an inclined plane and being projected back up with an initial velocity. The two approaches presented different equations for calculating the distance traveled before the block comes to rest, with one taking into account the difference between static and kinetic friction. The question of whether the block will slide down again was also raised, but not fully resolved.
  • #1
wuffle
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Once again, need help with mechanics, this one I think I did right, but my friend did it somehow different, and I was wondering who of us 2 is right

Homework Statement


A block slides down an inclined plane of slope angle (alpha) with constant velocity. It is then projected up the same plane with an initial speed V0. How far up the incline will it move before coming to rest?Will it slide down again?

Homework Equations


F=ma

The Attempt at a Solution



What I did:Y coordinate
-mg * Cos(alpha)+N=ma(y)=0

X coordinate
ma(x)=-F(friction)+mgSin(alpha)

F(fric)=mgsin(alpha)

WHEN BLOCK SLIDES UP

mgsin(alpha)+F(gravity)=ma(x)
2mgsin(alpha)=ma(x)
a(x)=2gSin(alpha)

S=-V^2/(4gsin(alpha))

What my friend did:

F(fric)=N * μ = mg * cos(α) * μ
F(fric)=mg* sin(α)=mg* cos(α)* μ
μ = tg(α)
S=V0t -0.5at^2
a=μ * mg * sin(α)

t=V0/a

S=V0^2/a -V0^2/(2a),
where a= sin^2(α)/cos(α) * mgOh and I don't really know whether it will slide down or not, I hope you guys can help me!

Thanks in advance.
 
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  • #2


Your distance formula looks right but I figured acceleration, a = 2gsinα

You need to know that for a body on a ramp that static friction is greater then kinetic friction. At the instant the moving body stops evaluate the forces on the body and remember the static friction is greater then the kinetic friction.
 
  • #3


wuffle said:
a=μ * mg * sin(α)

where a= sin^2(α)/cos(α) * mg

I do not think the above are correct since the component of the weight is also contributing to the retardation up the plane.
 

1. How do you define mechanics?

Mechanics is a branch of physics that deals with the behavior of physical bodies when subjected to forces or displacements, and the subsequent effects on motion and equilibrium.

2. What are the main principles of mechanics?

The main principles of mechanics are Newton's laws of motion, conservation of energy, and conservation of momentum. These laws govern the behavior of objects in motion and explain the relationships between forces, mass, and acceleration.

3. What is the difference between statics and dynamics in mechanics?

Statics deals with the study of bodies in equilibrium, where there is no change in motion. Dynamics, on the other hand, deals with bodies in motion and the forces that cause that motion.

4. How can I apply mechanics in real-life situations?

Mechanics has a wide range of applications in everyday life, such as understanding the movement of vehicles, designing structures and machines, and analyzing sports movements. It also plays a crucial role in fields like engineering, architecture, and biomechanics.

5. What are some common misconceptions about mechanics?

One common misconception is that mechanics only applies to large and complex systems, but it can also be applied to small and simple systems. Another misconception is that mechanics is only relevant in the field of physics, when in reality, it has applications in various fields as mentioned before.

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