Exam 2 – Part 2

Problem 1:

Gear A starts from rest and accelerates uniformly with A=0.8 [rad/s2] in direction shown. Gears B and C are fastened together and rotate together. Radii of gears are: rA=5 [in], rB=8 [in], rC=4 [in], and rD=6 [in]. After A has rotated through A=3 [rev], determine the magnitude of acceleration of point P on gear D, aP [ft/s2].

Problem 2:

At the instant shown collar B moves with a velocity of vB=4 [m/s] and acceleration aB=2.4 [m/s2] to the right. Angle =50o, and length of the rod is L=650 [mm]. At the instant when =30o, determine (a) magnitude of angular acceleration of rod AB, AB [rad/s2], and (b) magnitude of acceleration of collar A, aA [m/s2].

A B

C

D

A

P

A

B

L

 

Problem 3:

A block A, WA= 350 [lb], on a frictionless slope is connected to a winch C, WC= 210 [lb]. The winch has radius r=1.8 [ft], and radius of gyration k=3.1 [ft]. A cable is wrapped around the winch and passes over massless, frictionless pulley B. If couple M= 450 [lb-ft] is applied to winch C, determine: (a) magnitude of acceleration of block A, aA [ft/s2], and (b) tension in the cable, T [lb]. Inclination angle =40o.

Problem 4:

A slender rod, mr=7 [kg] and L=650 [mm], is welded to the edge of a uniform disk, md= 14 [kg] and rd=320 [mm], as shown. The assembly swings freely about A in vertical plane. Knowing that P=250 [N] and that in position shown the assembly has an angular velocity A=15 [rad/s] counterclockwise, determine: (a) magnitude of the angular acceleration [rad/s2] of the assembly, (b) magnitude of X component of the reaction force [N] at A, and (c) magnitude of Y component of the reaction force [N] at A.

C

B

D

A

A

L/2

L/2

P

A

B

G

C

M

Problem 5:

When the slider-crank mechanism is at the position shown, link AB has an angular velocity of AB=2.5 rad/s, and an angular acceleration of AB=1.2 rad/s2. Assume that links AB and BC are massless and that slider C weighs 10 lbs. Determine: (a) magnitude of angular velocity of link BC, BC [rad/s], (b) magnitude of angular acceleration of link BC, BC [rad/s2], (c) magnitude of velocity [ft/s] of point C, vC, (d) magnitude of acceleration [ft/s2] of point C, aC, and (e) magnitude of force [lb] in link BC, FBC. The system parameters are as follows: LAB=1.5 ft, LBC=3.2 ft, =45o, =45o. Note that link BC is in horizontal position.

A

B

 

C

AB, AB

LAB