Quiz05 Div3 Soln

ME 274 – Spring 2009 Quiz No. 5 – Div 3 Monday, February 23

SOLUTION

The slotted arm rotates within a horizontal plane with a constant rate of ω = 8 rad/sec about a vertical axis passing through point O. Block C, having a mass of m = 10 kg, is allowed to slide INWARD within the slot such that

r! = !4 m / sec and !! r = 2 m / sec 2 , with the tension in the cord controlling this rate. When r = 0.5 meters, determine: a) the tension in the cord. b) the normal force acting on the block by the slot in the arm. c) on which side of the slot (A or B) that block C is contacting the arm.

HORIZONTAL PLANE

Clearly show the four steps of analysis in your solution. Include a sketch of all relevant unit vectors in the FBD of your solution. FBD Newton

eθ

! Fr = "T = mar " F! = N = ma!

er

Kinematics

ar = !! r ! r" 2

T

a! = r!!! + 2 r!" = 2 r!" Solve Combining above:

(

!T = m !! r ! r" 2

)

#

2 T = m $% !!! r + r" 2 &' = (10 ) $ !2 + ( 0.5 ) ( 8 ) & = 300 newtons % '

N = 2m!r! = ( 2 ) (10 ) ( "4 ) ( 8 ) = "640 newtons ( N < 0

#

contacting B )

N