Solving Frictional Force of Sand on Conveyor Belt

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NIn summary, the frictional force acting on the sand poured onto a conveyer belt at a constant rate of 25kg/s and moving horizontally at a constant speed of 4m/s can be calculated using the formula F_f=v_{conveyer}\frac{dm}{dt}, resulting in a force of 100N. This approach is based on the true definition of force, taking into account the constant addition of mass to the conveyer belt and the lack of acceleration from the belt itself.
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Homework Statement


Sand is poured onto a converyor belt at a constant rate of 25kg/s. The belt keeps moving horizontally at a constant speed of 4m/s.


Homework Equations


What is the fricional force acting on the sand?


The Attempt at a Solution


According to the solution, the answer can be calucated using "impulse":
Taking right hand side be positive.
friction =[ 25 X (+4) - 0 ] /1
= 100 N
I don't understand why such approach works. The teacher said that the sand experience kinetic friction at the instant when it touches the belt, and that some time(though very small) is required for the sand to accelerate from 0m/s to 4m/s. However, I don't know why the above equation can solve the problem. Why the time of impulse can be regarded as 1? It is not given that the sand accelerates from 0m/s to 4m/s in 1 second.
 
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You're right, this is a bogus solution. The problem really ought to be done with the true definition of F.

[tex]\Sum F_{ext} = \frac{dp}{dt} = m \frac{dv}{dt} + v \frac{dm}{dt}[/tex]

where p is momentum.

So there is no acceleration from the conveyer belt, which makes dv/dt=0. There is however mass constantly being added to the conveyer belt at 25kg/s.

[tex]F_f=v_{conveyer}\frac{dm}{dt}[/tex]

so F_f = 4m/s*25kg/s
 

1. What is frictional force and how does it affect a conveyor belt?

Frictional force is a resistive force that occurs when two surfaces are in contact and moving relative to each other. In the case of a conveyor belt, the sand particles on the belt create frictional force as they rub against the belt, which can slow down the movement of the belt and affect its efficiency.

2. How is the frictional force of sand on a conveyor belt calculated?

The frictional force of sand on a conveyor belt can be calculated using the formula F = μN, where F is the frictional force, μ is the coefficient of friction between the sand and the belt, and N is the normal force exerted by the sand on the belt. The coefficient of friction can be determined through experiments or by consulting reference tables.

3. What factors can affect the frictional force of sand on a conveyor belt?

There are several factors that can affect the frictional force of sand on a conveyor belt, including the type of sand, the speed and angle of the belt, the texture and material of the belt, and the presence of any lubricants or contaminants on the belt or sand particles.

4. How can the frictional force of sand on a conveyor belt be reduced?

One way to reduce the frictional force of sand on a conveyor belt is by choosing a belt material with a low coefficient of friction, such as Teflon or silicone. Another method is to use a lubricant, such as water or oil, to reduce the friction between the sand particles and the belt. Additionally, keeping the belt clean and free of debris can also help reduce frictional force.

5. What are some ways to optimize the efficiency of a conveyor belt with sand?

To optimize the efficiency of a conveyor belt with sand, it is important to minimize the frictional force and ensure smooth movement of the belt. This can be achieved by regularly maintaining and cleaning the belt, using a suitable belt material and lubricant, and adjusting the speed and angle of the belt to reduce excessive friction. It is also helpful to regularly monitor and adjust the tension of the belt to prevent slippage and maximize its efficiency.

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