The Circular Motion of a Conveyor Belt

Ricardo D – Physics

The process of the circular motion on a pendulum, and whether or not the resultant speed is enough to physically damage a person walking by.

 

The steroid use and additives given to the chickens in this factory causes one of the chickens to grow too large for a conveyor belt’s processing. Because of the chicken’s enlarged size, the chicken becomes jammed inside of the conveyor belt resulting in the unhinging of screws and an entire side of the conveyor belt itself. This scenario converts the conveyor belt into a pendulum as it swings around an axis in circular motion. Taking into consideration the torque of the forces on the conveyor belt, and the circular motion of the pendulum after the conveyor belt snaps—the velocity will be able to be found, and in conclusion it will be decided whether or not the velocity has a great enough impact to hurt a human being. Even though in the scenario of the experiment, the pendulum will hit a vehicle in actuality and the impact of the collision will be discussed.

 

Torque and the Conveyor Belt

Prior to the accident, the chicken goes along the conveyor belt. The conveyor belt itself has two forces holding it up that cause the conveyor belt itself to stay up. As of this moment, the conveyor belt is at what is considered a rotational equilibrium—this occurs when there is the sum of the torques acting on the object equals zero. Therefore, the conveyor belt itself is staying still. However, when the chicken becomes jammed in the conveyor belt and causes the conveyor belt to become unhinged, rotational equilibrium will be broken. Which causes the belt itself to rotate around an axis as will be demonstrated. The hinge that breaks will be the hinge paired up with FA. 

  • -Force A: Holds up the right side of the conveyor belt.
  • -Force B: Holds up the left side of the conveyor belt.
  • -Force G: The force of gravity created by the mass of the conveyor belt.
  • -Force 1: The force of gravity created by the mass of the chicken.
  • Important equations associated with torque:
    • F=ma
    • T= F* r * sinΘ
    • FA + FB + (-FG) + (-F1) = 0
    • Since FA will be used as the reference point, the following equation will demonstrate torque and its relation with rotational equilibrium:
      • (TB) + (-T1) + (-TG) = 0
    • Important values given:
      • Acceleration of gravity (a)= 9.8 m/s2-
      • Mass of the conveyor belt= 296.4 kg—this is actual data used from a website estimating the mass of a conveyor belt (http://www.ckit.co.za), table 8 was used.
      • Mass of the chicken= 27 kg, this is experimental data used for the purpose of this experiment.
      • Length of the conveyor belt (r)= 12m
      • Length of the chicken from the end of the conveyor belt (r)= 8m
      • Length of the force of gravity on the conveyor belt (r)= 6m
    • Force and Torque Calculations
      • Force:
        • FA=?
        • FB =?
        • FG= ma, (296.4)(9.8), FG= 2904.72 N
        • F1=ma, (27)(9.8), F1= 264.6 N
      • Torque:
        • (TB) + (-T1) + (-TG) = 0
        • TB= FB*r
        • T1= F1*r
        • TG=FG*r
        • (FB*r) + (-F1*r) + (-FG*r)=0,  (FB*12) + (-264.6*8) + (-2904.72*12), (12FB) + (-2116.8) + (-17428.32), (12FB) + (-19545.12)=0,  (12FB) = 1945.12, FB= 1628.76 N
        • FA=?  FA + FB + (-FG) + (-F1) = 0,  FA + 1628.76 + (-2904.72) + (-264.6) = 0,  FA + (-1540.56) = 0,  FA = 1540.56 N

The resultant force of the broken hinge is 1540.56 N (FA). This force is a key factor in deciding the velocity of the conveyor belt as it transitions into a pendulum and follows a circular path. The force found will itself be the determinant factor in whether or not a person will be injured from contact with the pendulum. Also, the velocity will be found through other equations associated with circular motion and will be used to come to a sufficient conclusion.

Circular motion and the Pendulum

After the conveyor belt transitions into circular motion—air resistance and any type of friction caused by the attached hinge will be completely negligible. As a result of this, Newton’s 1st law of motion is very important when taking the swinging pendulum into consideration. Newton’s 1st law of motion states that “An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force” (www.physicsclassroom.com). With this in mind, it’s important to understand that the pendulum will not stop moving unless an outside force is acted upon, so until that happens, the pendulum will constantly move at the same velocity. A constant velocity also implies no acceleration, but since the pendulum is moving in circular motion and changing directions, there is an acceleration. Therefore, the force found in the previous section can be used in order to find the velocity and acceleration to see whether or not, a person (outside force) coming into contact with the pendulum would be injured.

  • Important equations associated with circular motion and velocity:
    • F= (m*v2)/r
    • F=ma
  • Important values given:
    • FA= 1540.56 N
    • Mass of the conveyor belt= 296.4 kg
    • Length of the conveyor belt= 12m
  • Force, Velocity, and Acceleration calculations
    • Velocity:
      • F= (m*v2)/r , 1540.56= (296.4*v2)/12, 18486.72= 296.4v2, v2=62.37,                v = 7.89 m/s
    • Acceleration:
      • F=ma, 1540.56=296.4a, a=5.198 m/s2
    • Force:
      • F=F, F= 1540.56 N

Conclusion

Through circular motion as a pendulum, the conveyor belt would generate a velocity of 7.89 m/s, an acceleration of 5.20 m/s2, and a total force of 1540.56 N. Within these conditions, it can be concluded that the speed and acceleration combined, do not generate a force strong enough to severely damage a human being—or really damage the body in general. Research shows that a blow of 3300 Newtons alone has only a 25% chance of breaking an average person’s rib (www.livescience.com). Compared to the 3300 Newtons experiment, the 1540.56 Newtons produced in the scenario have an even lesser chance of breaking the average person’s rib. Therefore it can be concluded that the person who comes into contact will not receive more damage than a possible blow to the ground and bruise from the impact. Also, the force would not be enough to deform or damage the vehicle it will come into contact with once the scenario is carried out.

 

Bibliography

“Dunlop Conveyor Belt Design Manual.” Dunlop Conveyor Belt Design Manual. N.p., n.d. Web. 31 Mar. 2016. <http://www.ckit.co.za/secure/conveyor/troughed/belt_tension/dunlop-belting.htm&gt;.

“Mathematics of Circular Motion.” Mathematics of Circular Motion. N.p., n.d. Web. 26 Mar. 2016. <http://www.physicsclassroom.com/class/circles/Lesson-1/Mathematics-of-Circular-Motion&gt;.

“Newton’s First Law.” Newton’s First Law. N.p., n.d. Web. 31 Mar. 2016. <http://www.physicsclassroom.com/class/newtlaws/Lesson-1/Newton-s-First-Law&gt;.

“What Is Torque?” Study.com. N.p., n.d. Web. 26 Mar. 2016. <http://study.com/academy/lesson/what-is-torque-definition-equation-calculation.html&gt;.

Q, By Charles. “Brute Force: Humans Can Sure Take a Punch.”LiveScience. TechMedia Network, 03 Feb. 2010. Web. 30 Mar. 2016. <http://www.livescience.com/6040-brute-force-humans-punch.html&gt;.