Calculating Time for Rectangular Block to Stop on Rough Ground

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In summary, the problem involves finding the time taken for a rectangular block traveling at a constant velocity on a smooth surface to come to a stop on rough ground with a coefficient of friction. The deceleration of the block depends on the length of the block in contact with the rough ground, with a maximum deceleration of (mu)g when the entire block is on the rough ground. The solution involves splitting the problem into two cases and using kinematics equations to find a relation between velocity and distance, and then using another equation to solve for time.
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gaobo9109
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Homework Statement


A rectangular block of length L is traveling on a smooth surface at velocity u. When it encounters rough ground with coefficient of friction mu, it decelerates to a stop. What is the time taken for the rectangular block to stop?

Homework Equations


F= (mu)mg

The Attempt at a Solution


Deceleration of the block is given by a = (mu)gx/L if only part of the block is on the rough ground. If the entire block is on the rough ground, the maximum deceleration is given by a = (mu)g. This means i have to split the question into two cases.
1. time taken when x is less than or equal to L
2. time taken when x is greater than L

But I am stuck here. I don't know how to relate x to t and u.
 
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  • #2
Friction force is independent of area of contact. So I think there is no need for taking a part of the block.

deceleration of the block is (mu)g
apply kinematics equation
v^2 - u^2 =2as
v=0 s=L
find a relation between u and s from here
use another equation - s=ut +0.5at^2
find out time from this equation. ( here discriminant will become 0 from previous equation.)
 

FAQ: Calculating Time for Rectangular Block to Stop on Rough Ground

How do you calculate the time for a rectangular block to stop on rough ground?

To calculate the time for a rectangular block to stop on rough ground, you will need to know the initial velocity of the block, the coefficient of friction between the block and the ground, and the distance the block travels. You can use the formula t = (mv - μmgd) / f, where t is the time, m is the mass of the block, v is the initial velocity, μ is the coefficient of friction, g is the acceleration due to gravity, d is the distance traveled, and f is the net force acting on the block.

How does the coefficient of friction affect the time for a rectangular block to stop on rough ground?

The coefficient of friction is a measure of the resistance between two surfaces in contact. In the context of a rectangular block stopping on rough ground, a higher coefficient of friction means there is more resistance between the block and the ground, resulting in a longer stopping time. On the other hand, a lower coefficient of friction means there is less resistance and the block will stop in a shorter amount of time.

Is there a difference in the time for a rectangular block to stop on rough ground compared to smooth ground?

Yes, there is a difference in the time for a rectangular block to stop on rough ground compared to smooth ground. This is because the coefficient of friction is different between the two surfaces. Rough ground has a higher coefficient of friction, resulting in a longer stopping time, while smooth ground has a lower coefficient of friction, resulting in a shorter stopping time.

Can the time for a rectangular block to stop on rough ground be affected by the shape of the block?

Yes, the time for a rectangular block to stop on rough ground can be affected by the shape of the block. This is because the shape of the block can affect the surface area in contact with the ground, which can in turn affect the coefficient of friction. A larger surface area in contact with the ground will result in a higher coefficient of friction, leading to a longer stopping time.

Are there any other factors that can affect the time for a rectangular block to stop on rough ground?

Yes, there are other factors that can affect the time for a rectangular block to stop on rough ground. These include the initial velocity of the block, the mass of the block, and any external forces acting on the block. Additionally, the roughness and condition of the ground can also have an impact on the stopping time. A rougher surface will result in a higher coefficient of friction and a longer stopping time, while a smoother surface will result in a lower coefficient of friction and a shorter stopping time.

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