# Dynamics Question -- packages discharged from a conveyor belt

• RoyalFlush100
In summary, the force exerted by the conveyor belt on a 4 kg package just after passing Point A is 23.24 N, which is equal to the normal force. The frictional force is assumed to be negligible in this scenario.
RoyalFlush100

## Homework Statement

A series of small packages, each with a mass of 4 kg, are discharged from a conveyor belt as shown. Assume that the coefficient of static friction between each package and the conveyor belt is 0.4.

Determine the force exerted by the belt on a package just after it has passed Point A

I attached the picture below

F = ma

## The Attempt at a Solution

So I began by drawing a FBD:
-W: Weight pointed downwards
-N: Normal pointed upwards
-f: Friction pointed left
-B: Force from the belt pointed right.
From what I understand, we are trying to solve for B.
Also, it is about to enter a circular region, which makes me think that the net acceleration is -mv^2/r in the y direction and dv/dt in the x direction.

So, I began by solving the forces in the y direction:
-mv^2/r = -W + N
-(4)(1^2)/(0.250) = -(4)(9.81) + N
--> N = 23.24 N

From there, I setup the equation in the x direction:
dv/dt = B - (u)N
dv/dt = B - (0.4)(23.24)
Now the thing is, I assumed that the speed is consistent which would imply B = (0.4)(23.24) = 9.296 N.

However, this answer was wrong, so I am not sure how to approach it from here.

#### Attachments

• problem 1.jpeg
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When the package passes point A, what value for ##\theta## are you assuming?

PeroK said:
When the package passes point A, what value for ##\theta## are you assuming?
0 degrees as shown in the picture. But 90 degrees, counterclockwise from the (+) x-axis (assuming the center of the circle is the origin).

RoyalFlush100 said:
0 degrees as shown in the picture. But 90 degrees, counterclockwise from the (+) x-axis (assuming the center of the circle is the origin).

So, what force is causing the acceleration in the x-direction?

PeroK said:
So, what force is causing the acceleration in the x-direction?
I assumed the conveyor belt was pushing horizontally on it, to offset frictional impacts.

RoyalFlush100 said:
I assumed the conveyor belt was pushing horizontally on it, to offset frictional impacts.

Friction is a resisting force. Unless an external force is trying to accelerate an object, the frictional force will be zero. In the case of a block at rest or a block moving with constant velocity horizontally, there can be no frictional force; if there were the block would accelerate.

PeroK said:
Friction is a resisting force. Unless an external force is trying to accelerate an object, the frictional force will be zero. In the case of a block at rest or a block moving with constant velocity horizontally, there can be no frictional force; if there were the block would accelerate.
Okay, so then we're left with its weight and the normal force. So would the normal force be defined as the "the force exerted by the belt on a package." In which case the answer would simply be 23.24 N?

RoyalFlush100 said:
Okay, so then we're left with its weight and the normal force. So would the normal force be defined as the "the force exerted by the belt on a package." In which case the answer would simply be 23.24 N?

I think so!

RoyalFlush100

## What is a conveyor belt and how does it work?

A conveyor belt is a continuous moving system used to transport materials or packages from one location to another. It is typically made up of a belt, rollers, and a motor that drives the belt forward. The packages are placed on the belt and moved along by the rotating motion of the rollers.

## What is the purpose of discharging packages from a conveyor belt?

The purpose of discharging packages from a conveyor belt is to move them from the conveyor system to their desired destination. This allows for efficient and organized transportation of goods or materials.

## How do dynamics play a role in the discharge of packages from a conveyor belt?

Dynamics, or the study of forces and motion, plays a crucial role in the discharge of packages from a conveyor belt. The speed and direction of the conveyor belt, as well as the weight and size of the packages, all affect how they will be discharged from the belt.

## What factors can affect the dynamics of packages discharged from a conveyor belt?

The speed and direction of the conveyor belt, the weight and size of the packages, the surface and slope of the discharge point, and any external forces such as wind or friction can all affect the dynamics of packages discharged from a conveyor belt.

## How can the discharge of packages from a conveyor belt be optimized for efficiency?

To optimize the discharge of packages from a conveyor belt, factors such as the speed and direction of the belt, the size and weight of the packages, and the surface and slope of the discharge point should be carefully considered and adjusted accordingly. Additionally, regular maintenance and monitoring of the conveyor system can help identify any issues that may affect efficiency.

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