A ROBOT UNLOADS A FINISHED COMPONENT FROM A

MACHINE AND PLACES IT ON A GRAVITY CONVEYOR. THE CONVEYOR ACCELERATES FROM REST

UNTIL IT REACHES THE BOTTOM OF THE CONVEYOR 4.5 SECONDS LATER. THE COMPONENT IS

TRAVELLING AT A VELOCITY OF 1.35 M/S WHEN IT REACHES THE BOTTOM OF THE CONVEYOR

WHERE , IT IS THEN STOPPED BY HITTING A BUFFER. THE COMPONENT SITS STATIONARY

AWAITING PACKAGING.

A) DETERMINE THE LINEAR ACCELERATION

OF THE COMPONENT AS IT TRAVELS DOWN THE GRAVITY CONVEYOR (IGNORING FRICTIONAL

FORCES.

B) THE CONVEYOR SECTION LENGTH IS

LATER MODIFIED AND EXTENDED BY A FURTHER 1.5M. DETERMINE THE NEW VELOCITY OF

THE COMPONENTS WHEN THEY REACH THE BUFFER.

C) EXPLAIN THE CAUSE OF THE

COMPONENTS ACCELERATING FROM REST DOWN THE CONVEYOR.

D) DETERMINE THE FORCE EXERTED BY THE

COMPONENT, OF MASS 4.5KG, DOWNWARD ON THE CONVEYOR AS IT SITS AT THE

BUFFER.

E) EXPLAIN WHY THE COMPONENT DOES NOT

ACCELERATE DOWN THROUGH THE CONVEYOR WHILST RESTING AT THE BUFFER.

A)

FOR THE FIRST PART, USE EQUATION VF

= V0 + AT, WHERE V0 = 0, T = 4.5 S AND VF =

1.35 M/S

A = 1.35/4.5 = 0.3 M/S2B)

KNOWING ACCELERATION AND NEW DISTANCE, YOU

CAN DETERMINE THE NEW FINAL SPEED USING EQUATION:

(VF)2 = V02 + 2A*D

THE PROBLEM STATES THAT IT IS EXTENDED BY AN ADDITIONAL 1.5 M, SO YOU’LL HAVE

TO FIRST DETERMINE THE INITIAL LENGTH BEFORE THE EXTENSION:

D = VF2/2A = (1.35)^2/(2*.3) = 3.0375 M

NOW YOU ADD 1.5 TO THAT DISTANCE ABOVE AND USE THE FORMULA TO DETERMINE VF:

VF = ROOT(2*.3*4.5375) = 1.65M/S

C) GRAVITY

D)

WE KNOW THAT

VELOCITY (V) = ACCELERATION (A) X TIME (T)

1.35 = A X 4.5 ———à A=0.3 M/S2

FORCE (F) = MASS (M) *ACCELERATION (A)

=

4.5 KG *0.3 M/S2 =1.35

E)

THE FORCE EXERTED WILL BE EQUAL TO MASS

TIMES THE GRAVITY. THAT IS 4.5*9.81= 44.145 N.

THE COMPONENT DOES NOT ACCELERATE DOWN THE

CONVEYOR BELT BECAUSE WHEN ENTIRE ASSEMBLY IS CONSIDERED AS A SYSTEM, IT DOES

NOT AFFECT OUR SOLUTION AND AS IT DOES NOT AFFECT THE SOLUTION. THE

ACCELERATION OF ALL PARTS IS SAME AND HENCE, COMPONENT MAINTAINS ITS INERTIA

UNDER THE EFFECT OF GRAVITY

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