# Solving Friction Problems: Calculate Coefficient & Height

• JoanF
In summary: Unfortunately, I'm finding your work a little difficult to follow. My answer differs from yours, so one of us is making an error.
JoanF

## Homework Statement

mass of the body: 1,0 kg
A is the minimum height that the body must be abandoned to describe a circular path.

there is friction ONLY between A and C

the circular path has radius 1,0 m

1. Calculate the coefficient of kinetic friction between A and C.

2. Calculate the height from the ground that the body will leave the circular path, if left in B. (use as coefficient of friction the value of question 1.)

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The problem description is incomplete--there is key information missing. Please provide the full statement of the problem, word for word as it was given.

Also, show what you've tried.

Doc Al said:
The problem description is incomplete--there is key information missing. Please provide the full statement of the problem, word for word as it was given.

Also, show what you've tried.

1) A is the minimum height that a body of 1,0 kg must be abandoned to describe the circular path of the figure. We know that there is friction ONLY between A and C and that the circular path has radius 1,0 m.

1.1) The normal reaction in C is...
A) 50 N
B) 40 N
C) 10 N
D) 60 N

1.2) The coefficient of kinetic friction between A and C is...
A) 0,33
B) 0,50
C) 0,22
D) 0,15

1.3) Calculate the height from the ground that the body will leave the circular path, if left in B. (use as coefficient of friction the value of question 1.)

I tried and my answer was 0,22 to 1.2) but how do I do 1.3)?

JoanF said:
I tried and my answer was 0,22 to 1.2)
Good.
but how do I do 1.3)?
What would be the criterion for the body leaving the circular path? Express it mathematically. Then realize that the energy the body will have on entering the circular portion will be different than before.

Doc Al said:
Good.

What would be the criterion for the body leaving the circular path? Express it mathematically. Then realize that the energy the body will have on entering the circular portion will be different than before.

I've done this:

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JoanF said:
I've done this:

Is it correct??

JoanF said:
Is it correct??
Unfortunately, I'm finding your work a little difficult to follow. My answer differs from yours, so one of us is making an error.

What I did:
Found the total energy of the mass when let go from A.
Found the new total energy of the mass when let go from B.
Found the condition for losing contact with the surface.
Combined the last two to solve for the height at which the mass leaves the surface.

If you summarize the results you get for each of those steps, perhaps I can see where we differ.

using g=10, I got: h=1,64 m

using g=9,8, I got: h=1,4456 m

I've done just like you

JoanF said:
using g=10, I got: h=1,64 m

using g=9,8, I got: h=1,4456 m

If you were to solve the problem symbolically, only plugging in numbers at the last step to get a numerical answer, you'd see that the answer does not depend on g or m. (They cancel out.) Whenever possible, that's the best way to go, since it reduces the chance for arithmetic error.

## 1. How do I calculate the coefficient of friction?

To calculate the coefficient of friction, you will need to know the force of friction and the normal force acting on an object. The coefficient of friction is equal to the force of friction divided by the normal force.

## 2. What is the significance of calculating the coefficient of friction?

The coefficient of friction is a measure of the resistance between two surfaces in contact. It helps determine how much force is needed to move an object over a surface and can be used to predict the motion of objects in various scenarios.

## 3. How do I determine the height of an object based on friction?

To determine the height of an object based on friction, you will need to know the coefficient of friction, the force of friction, and the normal force acting on the object. The height can be calculated using the equation: height = force of friction / (coefficient of friction x normal force).

## 4. What are some common examples of friction problems?

Some common examples of friction problems include calculating the force required to push a heavy object across a surface, determining the angle at which an object will start to slide down an inclined plane, and predicting the speed of an object sliding down a ramp with friction.

## 5. How can I use the coefficient of friction to improve the efficiency of machines?

The coefficient of friction can be used to identify areas of high friction in machines and find ways to reduce it, thus improving the overall efficiency. By selecting materials with lower coefficients of friction or using lubricants, the amount of energy needed to overcome friction can be reduced, making the machine more efficient.

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