MECH 220 Midterm 2_2013
MECHANICS II MECH 220 MIDTERM EXAMINATION # 2 This test contains 3 questions
November 19, 2013
12:35 to 13:35
Closed book, one 8.5 in x 11 in crib sheet allowed PROBLEM 1
[8 marks]
A truck on an exit ramp is moving in such a way that at the instant shown a A = 6 m/s2 and φ = 13 . Let the distance between points A and B be dAB = 4 m. If at this instant the truck is turning clockwise, with θ = 60 , a Bx = 6.3 m/s2 and a By = −2.6 m/s2, determine the angular velocity and angular acceleration of the truck.
MECH II
1
MIDTERM/F09
MECH II
2
MIDTERM/F09
PROBLEM 2
[10 marks]
For the following problems from homework assignments and tutorials, please circle the answers True or False. For the 1kg ball dropped from rest above the smooth plane with a restitution coefficient of less than 1 (but not known precisely): a. The energy of the ball is conserved from A to C. True or False b. The linear momentum of the ball is conserved along the plane for motion between B and C. True or False c. Not enough information is given to determine the distance d. True or False For the plate and shaft rotating at a given angular velocity and angular acceleration, at the instant shown: a. Points C and D have the same speeds but opposite directions of motion. True or False b. The acceleration of point D does not depend on the angular velocity of the plate. True or False
Gears A and B have different moments of inertia IA = 3 and IB = 0.5 kg-m2 about their centers, respectively. If a torque of M=200(1-e-0.2t) N-m is applied to gear A, a. The angular acceleration of gear A is αA=(200/4.125)(1-e-0.2t) rad/s2 True or False b. The angular rates of the two gears are related as:
ωA / ω B = 3 / 2
True or False The 15-kg uniform slender rod starts from rest at θ = 0 and a constant force P = 200 N is applied as shown until the instant just before θ = 45 a. The work done by P on the rod for the stated period of motion is equal to 120 J. True or False b. The angular momentum of the rod about its center of mass is conserved True or False c. The work done by the force of gravity on the rod is negative. True or False
MECH II
3
MIDTERM/F09
PROBLEM 3
[12 marks]
A uniform pole of length L = 10 m, inclined at an angle θ = 30 with the vertical, is dropped and both ends have a velocity v = 7 m/s as end A hits the ground. Assume that end A pivots about its contact point during the remainder of the motion of the pole. a) Determine the angular velocity of the pole right after impact at end A. b) Determine the angular acceleration of the pole right after impact at end A. c) Determine the velocity v’ with which end B hits the ground.
MECH II
4
MIDTERM/F09
MECH II
5
MIDTERM/F09
November 19, 2013
12:35 to 13:35
Closed book, one 8.5 in x 11 in crib sheet allowed PROBLEM 1
[8 marks]
A truck on an exit ramp is moving in such a way that at the instant shown a A = 6 m/s2 and φ = 13 . Let the distance between points A and B be dAB = 4 m. If at this instant the truck is turning clockwise, with θ = 60 , a Bx = 6.3 m/s2 and a By = −2.6 m/s2, determine the angular velocity and angular acceleration of the truck.
MECH II
1
MIDTERM/F09
MECH II
2
MIDTERM/F09
PROBLEM 2
[10 marks]
For the following problems from homework assignments and tutorials, please circle the answers True or False. For the 1kg ball dropped from rest above the smooth plane with a restitution coefficient of less than 1 (but not known precisely): a. The energy of the ball is conserved from A to C. True or False b. The linear momentum of the ball is conserved along the plane for motion between B and C. True or False c. Not enough information is given to determine the distance d. True or False For the plate and shaft rotating at a given angular velocity and angular acceleration, at the instant shown: a. Points C and D have the same speeds but opposite directions of motion. True or False b. The acceleration of point D does not depend on the angular velocity of the plate. True or False
Gears A and B have different moments of inertia IA = 3 and IB = 0.5 kg-m2 about their centers, respectively. If a torque of M=200(1-e-0.2t) N-m is applied to gear A, a. The angular acceleration of gear A is αA=(200/4.125)(1-e-0.2t) rad/s2 True or False b. The angular rates of the two gears are related as:
ωA / ω B = 3 / 2
True or False The 15-kg uniform slender rod starts from rest at θ = 0 and a constant force P = 200 N is applied as shown until the instant just before θ = 45 a. The work done by P on the rod for the stated period of motion is equal to 120 J. True or False b. The angular momentum of the rod about its center of mass is conserved True or False c. The work done by the force of gravity on the rod is negative. True or False
MECH II
3
MIDTERM/F09
PROBLEM 3
[12 marks]
A uniform pole of length L = 10 m, inclined at an angle θ = 30 with the vertical, is dropped and both ends have a velocity v = 7 m/s as end A hits the ground. Assume that end A pivots about its contact point during the remainder of the motion of the pole. a) Determine the angular velocity of the pole right after impact at end A. b) Determine the angular acceleration of the pole right after impact at end A. c) Determine the velocity v’ with which end B hits the ground.
MECH II
4
MIDTERM/F09
MECH II
5
MIDTERM/F09
