exam 01: chapters 12 and 13 - uca

NAME:

Exam 01: Chapters 12 and 13

INSTRUCTIONS

• Solve each of the following problems to the best of your ability.• Read and follow the directions carefully.• Solve using the method required by the problem statement.• Show all your work. Work as neatly as you can. If you need additional paper, please be sure to staple all pages in the

proper order.• It is permissible to use your calculator or an online solver (like Wolframα) to perform derivatives or integrals. If you do,

state this explicitly.• Express your answer as directed by the problem statement, using three significant digits. Include the appropriate units.• You must submit your exam paper no later than Monday, February 05. You should submit the paper to me directly, or, if I

am not in my office, please turn it in to Mrs. McDaniel in the department office (LSC 171), no later than 12:00PM. You may not slide the paper under my door. Late papers will not be accepted.

Your work will be scored according to the following point structure:Problem 01: /15

Problem 02: /15

Problem 03: /15

Problem 04: /20

Problem 05: /15

Problem 06: /15

Problem 07: /20

Problem 08: /15

Problem 09: /20

ENGR 3311: DYNAMICS SPRING 2018

Problem 01

A particle is moving along a straight line with an initial velocity vi = 4m/s when it is subjected to an acceleration ,

where v is in m/s. Determine how far the particle travels before it stops, and how much time has elapsed.


EXAM 01 PAGE 2/10

Problem 02

Pegs A and B are restricted to move in the elliptical slots due to the motion of the slotted link. If the link moves with a constant speed v = 10m/s, determine the velocity and acceleration vectors of peg A when x = 1m.

Hint: Derivatives, chain rule, you know the drill. Careful! Pegs have vx and vy components!


EXAM 01 PAGE 3/10

Problem 03

The car travels around the circular track having a radius of r = 250m such that when it is at point A it has a velocity of vo = 3m/s, which is increasing at the rate of at = (0.15t)m/s2, where t is in seconds. Determine the magnitudes of its velocity and acceleration when it has traveled two-‐thirds of the way around the track.


EXAM 01 PAGE 4/10

Problem 04

The rod OA rotates clockwise with a constant angular acceleration α = –2 rad/s2. The rod starts from rest when θ = 180°. Two pin-‐connected slider blocks, located at B, move freely on OA and the curved rod whose shape is a limaçon described by the equation r = 100(3 − cosθ)mm. Determine the velocity and acceleration of the slider blocks at time t = 1s. (Hint: The slider’s angular velocity and acceleration are both negative according to the convention for deNining the displacement θ.)

400 mm

300 mm


EXAM 01 PAGE 5/10

Problem 05

The he 4m-‐long cord is attached to the pin at C and passes over the two pulleys at A and D. The pulley at A is attached to the smooth collar that travels along the vertical rod. When sB = 0.5m, the end of the cord at B is pulled downwards with an initial velocity vo = 1.5m/s and given an acceleration a = 0.75m/s2. Determine the velocity and acceleration of the collar at this instant.

1m 1m


EXAM 01 PAGE 6/10

Problem 06

The motor lifts the 60-kg crate with a constant acceleration a = 2m/s2. Determine the tension T in the cable, the reaction force at B, and the components of force reaction and the couple moment at the Nixed support A. Neglect the mass of beam AB.

2m/s2

3m

=T

mg

ma

= 0T T

Ay

Ax

⤴︎

MA


EXAM 01 PAGE 7/10

Problem 07

The 5-kg sack slides down the ramp. The coefNicient of kinetic friction between the ramp and the sack is µk = 0.30. If it has a speed v = 1.5m/s when x = 0.10m, determine the normal force on the sack and the normal and tangential components of the acceleration at this instant.

y=0.25e2x

=

N

mg

fk

mat man

t

n

θ


EXAM 01 PAGE 8/10

Problem 08

The 2-lb block is released from rest at A and slides down along the smooth cylindrical surface. If the attached spring has a stiffness k = 2 lb/ft, and an unstretched length lo = 1.35ft, determine the angle θ at which the block leaves the surface.

=

N

mgk∆lman mat


EXAM 01 PAGE 9/10

Problem 09

Starting from rest when θ = 0°, arm OA rotates with a clockwise angular velocity ω = (1.5t)rad/s. Determine the force arm OA exerts on the smooth 2kg cylinder B when θ = 45°.

Hint: Let cw be (+)! This keeps θ, ω, and α positive. Write θ, ω, and α as functions of t, but since θ= π/4, solve for t. Express θ, ω, and α numerically!

1.2m

=

rθ

mar maθ

mg

NFA


EXAM 01 PAGE 10/10

exam 01: chapters 12 and 13 - uca

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