Time required to reach to Speed of Roller table for a bar

[Kaustubh]

Homework Statement

If rolling mill is running at 10 meters per second and roller table after mill is running at 20 meters per second.
Before cutting of bar, it will move at 10 meters per second.

Before cutting, roller table is trying to pull the bar, but since bar is not cut, it will slip on roller.

After cutting, bar has to move with the speed of 20 meters per second on roller table.
How much time bar will take to reach to that speed?

Coiff of friction of roller is 0.5

Homework Equations

F = Mass x a.
Coiff of friction x g = a

 

[tiny-tim]

Welcome to PF!

Hi Kaustubh! Welcome to PF!

Show us what you've tried, and where you're stuck, and then we'll know how to help!

 

[Kaustubh]

Hi there,
I am unable to formulate the friction factor, which will affect speed of bar after cutting.

 

[tiny-tim]

I don't understand …

the coefficient of friction is given as 0.5

 

[rwisz]

The bar will experience a force of friction as it moves along the roller table. This force will act in the opposite direction of the bar's motion and will cause the bar to accelerate at a slower rate. The equation F=ma can be used to calculate the acceleration of the bar, where F is the force of friction, m is the mass of the bar, and a is the acceleration.

The coefficient of friction is a measure of the resistance to motion between two surfaces in contact. In this case, it represents the friction between the bar and the roller table. The equation μg = a can be used to calculate the acceleration due to friction, where μ is the coefficient of friction, g is the acceleration due to gravity, and a is the acceleration.

To calculate the time it takes for the bar to reach a speed of 20 meters per second, we can use the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. In this case, u is 10 meters per second, a is the acceleration due to friction, and v is 20 meters per second.

Substituting the values into the equation, we get:

20 m/s = 10 m/s + (μg)t

Solving for t, we get:

t = (20 m/s - 10 m/s)/(μg)

Using the given coefficient of friction (μ = 0.5) and the acceleration due to gravity (g = 9.8 m/s^2), we can calculate the time it takes for the bar to reach a speed of 20 meters per second on the roller table.

t = (20 m/s - 10 m/s)/(0.5 x 9.8 m/s^2)

t = 1 second

Therefore, it will take 1 second for the bar to reach a speed of 20 meters per second on the roller table after cutting.