Solving Ramp with Friction Homework Problem

[alfredo24pr]

Homework Statement

When mass M is at the position shown, it is sliding down the inclined part of a slide at a speed of 2.15 m/s. The mass stops a distance S2 = 2.5 m along the level part of the slide. The distance S1 = 1.15 m and the angle θ = 30.30°. Calculate the coefficient of kinetic friction for the mass on the surface.

Homework Equations

1/2mv² + mgh = ?

The Attempt at a Solution

I do not know where to start..

 

[SammyS]

PE_I + KE_I = PE_F + KE_F - W_Friction, where W_Friction is the work done by friction.

W_Friction is itself negative, so subtracting it from zero will give a positive number.

 

[alfredo24pr]

PE_I + KE_I = PE_F + KE_F - W_Friction, where W_Friction is the work done by friction.

W_Friction is itself negative, so subtracting it from zero will give a positive number.

PEi can be found using mgh, in which h is found using S1 and the angle

KEi is 1/2mv2 in which v is given

PEf is where I have doubt

KEf equals 0 since the object is at rest

Am I correct?

 

[SammyS]

PEi can be found using mgh, in which h is found using S1 and the angle
...

PEf is where I have doubt
...
Am I correct?

If h is the elevation above the level, then what is h on the level?

 

[alfredo24pr]

If h is the elevation above the level, then what is h on the level?

So, PEi + KEi = - Wfriction?

How do I calculate work done by friction?

Is it considering just the 1.15m from the ramp, the 2.5m or both?

 

[alfredo24pr]

anyone? :\

 

[SammyS]

Both !

Find the force of friction for each surface.

 

[alfredo24pr]

I cannot get an answer. How do I use friction?

 

[SammyS]

I cannot get an answer. How do I use friction?

The normal force for S₂ is obviously mg.

What is the normal force for S₁, when the block is on the ramp?

I do have a question about the problem. It does not indicate whether or not S₁ has friction. It's clear that S₂ has friction. I would suggest solving it both ways.

.

 

[alfredo24pr]

The normal force for S₂ is obviously mg.

What is the normal force for S₁, when the block is on the ramp?

I do have a question about the problem. It does not indicate whether or not S₁ has friction. It's clear that S₂ has friction. I would suggest solving it both ways.

.

The professor told me that it is the same coefficient for both

 

[SammyS]

The professor told me that it is the same coefficient for both

OK !

What is the normal force, when the block is on the ramp?

 

[alfredo24pr]

OK !

What is the normal force, when the block is on the ramp?

mg cos 30.3?

 

[SammyS]

mg cos 30.3?

Yes, that's right. (Make sure that's 30.3° , not 30° & 30 minutes. The latter is sometimes written 30:30° or 30°30'. 30° & 30 minutes = 30.5° )

The frictional force is μ times the normal force & is in the direction opposite the direction of the motion.