# Finding angle to reduce friction

• maff is tuff
In summary, the car would have to be banked at an angle of 53.3 degrees to avoid any frictional force.
maff is tuff

## Homework Statement

A car is traveling around a curve that has a radius of 500 ft. at a speed of 60mph. To what angle must the curve be banked so that there is no frictional force?

## The Attempt at a Solution

I have attached mt solution below. I don't know the right answer to this question but I gave it a shot. The answer I got doesn't seem weird or anything so it has a a chance of being right. I don't think I understand the concept completely so I don't know if the moves or assumptions I made are valid. I kind of just wrote down the equations I know that might be relevant and used those. I know circular motion has acceleration proportional to the square of the speed and the radius so I used that equation. I am just not sure if my diagrams are correct and if I'm allowed to set equal the things that I set equal. So could you guys point out what is wrong and give me some hints on how to fix it? Or if it is right can you confirm? Thanks a lot for the help :)

#### Attachments

• Car Angle Friction.pdf
145.2 KB · Views: 291
4 forces really act in the car. Ff, Fc, P, N.
If we have N=0, we have Ff=0
N=PcosI - FcsenI
P=Fc tanI
so mg = mV²/R tanI
tanI = gR/V²

500ft = 152,4m
60mph = 26,8224 m / s

I>60º

I'm sorry you lost me. I have never seen that notation. I know N is normal force. Is Ff forward force? P parallel? And I don't know what Fc is. Why would normal force=0? Sorry I am not following.

kkk
That answer I've written in brazilian notation, I'm sorry.
I'm going to translate
Ff would go for friction force, that in BR is Força de atrito
Fc would go for centripetal force that in brazil is Força centrípeta
P would go for weght that in brazil is peso
N is normal

Ff = N.u, if Ff = 0, N is null

John

So could you tell me what I did wrong, like at which step I made my first error?

The centripetal acceleration is horizontal, not parallel to the ramp, because it points towards the center of the circle that the car traces out.

So that means my force diagram is incorrect?

The forces you drew were okay, but when you applied F=ma, the resulting equations were wrong because the centripetal acceleration has components in both the x and y directions for your choice of axes.

Ok thanks guys I'll work on the problem when I get home and I'll let you know if I have any more problems. Thanks again.

## 1. How does the angle affect friction?

The angle at which two surfaces are in contact can greatly affect the amount of friction between them. A higher angle means there is more surface area in contact, which leads to more friction.

## 2. What is the optimal angle to reduce friction?

The optimal angle to reduce friction depends on the specific materials and surfaces involved. In general, a lower angle will result in less friction, but it is important to consider other factors such as weight, speed, and surface texture.

## 3. How can I measure the angle to reduce friction?

The angle can be measured using a protractor or inclinometer. These tools can accurately measure the angle between two surfaces, allowing for precise calculations of friction.

## 4. Does the angle of the surface affect the direction of friction?

Yes, the angle of the surface can affect the direction of friction. Friction is always in the opposite direction of motion, so if the surface is angled, the direction of friction will also be angled.

## 5. Can the angle of friction be changed?

Yes, the angle of friction can be changed by altering the surface or materials in contact. For example, using lubricants or changing the texture of the surface can change the angle and reduce friction.

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