What is the stopping distance for a round steel bar using friction braking?

In summary, the bar will brake by frictioning against a flat steel surface in a time of t=\frac{v}{\mu g} and a distance of d=v t - 0.5 \mu g t^2.
  • #1
capterdi
49
0
Hi,

Please help me with this problem:

Suppose a round steel bar of 25 mm diameter and 72 m lengh, which is traveling at 3.7 m/sec. I need to know which is the distance needed for the bar to brake by frictioning against a flat steel surface. Coefficient of friction is 0.3 and density of steel 7.85 ton/m3.

Thank you.
 
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  • #2
Do you need help finding an answer or do you just want someone to do this for you?

I would start by determining the mass of the rod and then finding the Lagrangian of the system.
 
  • #3
I gladly would like someone to solve this problem for me, so I can see which are the formulas involved, and also the solution.

Thanks
 
  • #4
It seems to me that you can just find the weight of the bar. Assuming the bar is horizontal, the weight will also be the normal force. Multiply said normal force by the coefficient of friction to obtain the friction force. Divide by the mass to get your acceleration. Divide the velocity by the acceleration to get the time needed.
 
  • #5
Minger,

Ok...let me try and see what I get...

Thanks
 
  • #6
The stopping time is,

[tex]t = \frac{v}{\mu g}[/tex]And the stopping distance is,

[tex]d = v t - 0.5 \mu g t^2[/tex]If you don't need to know the time then you can calculate the stopping distance directly from the equation,

[tex]d = \frac{v^2}{2 \mu g} [/tex]

Where [itex]\mu[/itex] is the coefficient of friction, v is the initial velocity and g is the gravitational aceleration aceleration (approx 9.8 m/s^2).
 
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  • #7
uart,

Ok...I can understand those equations, and have all needed data to solve them. Thanks a lot.
 
  • #8
Sorry...didn't notice before: The mass isn´'t involved in the equations? I suppose it's not the same distance and time for a mass of 1 kg than for 1,000kg.
 
  • #9
You should have derived these using my approach. You would have arrived at the same point, but with the knowledge of where they come from. The friction force again is the coefficient times the normal force:
[tex]F_f = \mu m g[/tex]
This will be the only force acting on the bar, so we can relate it with the famous equation:
[tex]F_f = \mu m g = m a[/tex]
Of course the masses will cancel out and you get the relationship between acceleration and coefficient of friction. From here, substitute the definition for acceleration:
[tex] \mu g = \frac{v}{t} [/tex]
and of course simply solve for time. So, theoretically in an ideal world, yes, both a 1kg and a 1000kg bar moving at the same initial velocity will stop at the same time.
 
  • #10
capterdi said:
Sorry...didn't notice before: The mass isn´'t involved in the equations? I suppose it's not the same distance and time for a mass of 1 kg than for 1,000kg.

Yes it actually is the same, the mass cancels out in the calculations. Think of it like this, the 1000kg object will experience 1000 times the frictional force compared with the 1kg object, but the deceleration (a=F/m) will be the same.
 
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  • #11
Right.

Thanks minger & uart for your help.
 

1. What is friction braking and how does it work?

Friction braking is a method of slowing down or stopping a bar by applying frictional force between the bar and a braking surface. This is typically achieved by pressing a brake pad against the surface of the bar, causing the two surfaces to rub against each other and create resistance, ultimately slowing down the bar.

2. What factors affect the effectiveness of friction braking?

There are several factors that can affect the effectiveness of friction braking, including the surface materials of the bar and the braking surface, the force applied to the brake pad, and the speed and weight of the bar. The type of brake pad and its condition can also play a role in the efficiency of friction braking.

3. How does friction braking compare to other types of braking?

Compared to other types of braking, such as regenerative braking, friction braking is less efficient and can cause more wear and tear on the braking surfaces. However, it is a simple and cost-effective method that is commonly used in many industries.

4. Can friction braking be used to control the speed of a bar?

Yes, friction braking can be used to control the speed of a bar. By adjusting the force applied to the brake pad, the amount of frictional force between the bar and the braking surface can be altered, allowing for precise control of the bar's speed.

5. What are some common applications of friction braking for bars?

Friction braking is commonly used in industrial machinery, such as conveyor belts, to control the movement and speed of bars. It is also used in vehicles, such as bicycles and cars, to slow down or stop the rotation of wheels. Additionally, friction braking is used in amusement park rides, such as roller coasters, to provide a smooth and controlled braking experience for riders.

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