AEROSPACE ENGINEERING JANUARY 2015

PHYSICS I FINAL EXAM

Solve the three following problems. Each one is scored with 20 points.

1. A semicircular slot of 25-cm radius is cut in a flat platewhich rotates about the vertical AD at a constant rateof 14 rad/s. A small block E of mass 350 grams isdesigned to slide in the slot as the plane rotates. Know-ing that the coefficients of friction are s = 0.35 andk = 0.25, determine whether the block will slide in theslot if it is released in the position corresponding to (a) = 80o, (b) = 40o. Also determine the magnitude andthe direction of the friction force exerted on the blockimmediately after it is released.

65 cm

2. The sleeve at A slides upward at a constant ve-locity of 10 m/s. Bar AC slides through thesleeve at B. Determine (a) the angular veloc-ity of bar AC and the velocity at which the barslides relative to the sleeve at B, (b) the angularacceleration of bar AC and the rate of changeof the velocity at which the bar slides relativeto the sleeve at B.

Problem 17.130 The sleeve at A slides upward at aconstant velocity of 10 m/s. Bar AC slides through thesleeve at B. Determine the angular velocity of bar ACand the velocity at which the bar slides relative to thesleeve at B. (See Example 17.8.)

10 m/sA

C

B

30!

1 m

Solution: The velocity of the sleeve at A is given to be vA =10j (m/s). The unit vector parallel to the bar (toward A) is

e = 1(cos 30i+ sin 30j) = 0.866i+ 0.5j.Choose a coordinate system with origin at B that rotates with the bar.The velocity at A is

vA = vB + vArele+ AC rA/B

= 0+ vArele+ i j k0 0 AB0.866 0.5 0

vA = (0.866i+ 0.5j)vArel + AC(0.5i+ 0.866j) (m/s).The given velocity is vA = 10j (m/s). Equate like components in thetwo expressions for vA:

0 = 0.866vArel 0.5AC,

10 = 0.5vArel + 0.866AC.

Solve: AC = 8.66 rad/s (counterclockwise),

vArel = 5 m/s from B toward A.

CB

Ay

x

vAvArel

Problem 17.131 In Problem 17.130, the sleeve at Aslides upward at a constant velocity of 10 m/s. Deter-mine the angular acceleration of bar AC and the rate ofchange of the velocity at which the bar slides relative tothe sleeve at B. (See Example 17.8.)

10 m/sA

C

B

30!

1 mSolution: Use the solution of Problem 17.130:

e = 0.866i+ 0.5j,

AB = 8.66 rad/s,

vArel = 5 m/s.The acceleration of the sleeve at A is given to be zero. The accelerationin terms of the motion of the arm is

aA = 0 = aArele+ 2AB vArele+ AB rA/B 2ABrA/B .

aA = 0 = aArele+ 2vArel i j k0 0 AB0.866 0.5 0

+ i j k0 0 AB0.866 0.5 0

2AB(0.866i+ 0.5j)0 = (0.866i+ 0.5j)aArel 43.3i+ 75j

+ AB(0.5i+ 0.866j) 64.95i 37.5j.

Separate components:

0 = 0.866aArel 43.3 0.5AB 64.95,

0 = 0.5aArel + 75+ 0.866AB 37.5.

Solve: aArel = 75 (m/s2) (toward A).

AB = 86.6 rad/s2 , (clockwise).

421

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3. A 1.2-m diameter homogeneous cylinder ofmass 150 kg rests on the bed of a flatbedtruck as shown. The truck accelerates fromrest at a rate of 0.9 m/s2 for 20 s and thenmoves with a constant velocity. If the cylin-der rolls without slipping, determine (a) theangular acceleration of the cylinder, (b) the

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A 4ft diameter homogeneous cylinder that weighs 300 lb rests on the bed of aflatbed truck as shown. The truck accelerates from rest at a rate of 3 ft/s2 for20s and then moves with a constant velocity. If the cylinder rolls withoutslipping, determine the distance traveled by the truck before the cylinder rollsoff the truck. Please show all force diagrams.

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3.6 m

acceleration of the cylinder relative to the ground, (c) the minimum value of the coefficientof static friction between the truck and the cylinder, (d) the distance traveled by the truckbefore the cylinder rolls off the truck.

Data: Moment of inertia of a cylinder of mass m and radius r about its axis IG =12mr2