exam 2 - weeklyjoys · exam 2 october 29, 2014 instructions: you have 60 minutes to complete this...

ME 274: Basic Mechanics IIFall 2014

October 29, 2014

Exam 2October 29, 2014

Instructions:

• You have 60 minutes to complete this exam.• This is a closed-book, closed-notes exam.• You are allowed to use the ME approved calculator only during the exam.• Usage of mobile phones and other electronic communication devices is NOT permitted during

the exam.

Problem Score

1 (20 pts)

2 (20 pts)

3 (20 pts)

Total

Name: −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

Instructor: Berger (9:30am-10:20am) Cappelleri (1:30pm-2:20pm)

Exam 2 of 9


October 29, 2014

Problem 1 (20 points):

Given: Conveyor belt OA is used to move packages in a manufacturing plant. An observer isattached to point A (not to the belt itself). At the instant shown, the conveyor is rotating aroundthe Y-axis with a constant angular velocity ω1 = 6 rad/s, while at the same time rotating upward(around the Z-axis) with θ = 4 rad/s (constant). The conveyor belt itself is running at a speed ofr = 5 ft/s, which is increasing at a rate of r = 8 ft/s2. Neglect the size of the package.

Find: When package P is at the position of r = 6 ft and θ = 45o:(a) determine the velocity of package P, expressed in the X-Y-Z coordinate frame. Solve this

problem to its completion.(b) to determine the acceleration of package P, we want to use this equation:

−→a P = −→a O +(−→a P/O

)rel

+ 2−→ω ×(−→v P/O

)rel

+−→ω ×(−→ω ×−→r P/O

)+−→α ×−→r P/O

Show all your work related to deriving expressions for each term in this equation, expressed inthe X-Y-Z coordinate system.

• −→a O =

•(−→a P/O

)rel

=

• −→α =

• 2−→ω ×(−→v P/O

)rel

=

r

x

y

X

Y

θ

ω1

P

O

A

Exam 2 of 9


October 29, 2014

This page is for extra work related to Problem 1.

Exam 2 of 9


October 29, 2014


Given: Just for fun, two engineering students A and B, each of mass m, intend to bungee jumpoff a bridge from rest. The elastic bungee cord has a stiffness of k. They want to just reach thesurface of the river, at which time A (attached to the cord), lets go of B, who falls harmlessly intothe river.

L

Find:(a) The proper unstretched length of the bungee cord to pull of this stunt(b) The maximum acceleration of student A(c) Determine if the maximum height reached by A after the rebound is safe, i.e., is it less than

the height of the bridge above the water, L?

Use the following parameters in your analysis: m = 70 kg, k= 1165 N/m, L = 35 m.

Exam 2 of 9


October 29, 2014

This page is for extra work related to Problem 2.

Exam 2 of 9


October 29, 2014


Part A (4 points):

The system shown below consists of three particles A, B, and E of mass m, 2m, and 2m respectively.The system starts from rest when θ = 0o. As the system moves from θ = 0o to θ = 90o, answer thefollowing. CIRCLE the correct choice for each case.

(a) TRUE or FALSE: energy is conserved for each particle individually(b) TRUE or FALSE: energy is conserved for the total system A+B+E(c) TRUE or FALSE: linear momentum is conserved in the horizontal direction for the total system

A+B+E(d) TRUE or FALSE: linear momentum is conserved in the vertical direction for the total system

A+B+E

Exam 2 of 9


October 29, 2014

Part B (4 points):

You are on a cart that is initially at rest on a smooth track. You throw a ball at the partition thatis rigidly mounted on the cart. If the ball bounces off the partition as shown in the figure, then atthe instant shown:

(a) The cart is moving to the right.(b) The cart is moving to the left.(c) The cart is stationary.(d) More information is needed about the impact of the ball with the partition in order to answer

this question.

Part C (4 points):

A race car is traveling on a track with banked turns (with bank angle θ as shown). At this instant,the car is on a part of the track where ρ = 500 m. The car is traveling at 80 m/s. Determine theminimum bank angle θ so that no friction force is required to keep the car on the track.

(a) θ = 37.5o

(b) θ = 0.93o

(c) θ = 21.7o

(d) θ = 52.5o

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October 29, 2014

Part D (4 points):

Particle A (having a mass mA) has a speed of v when it impacts a stationary particle B (having amass of mB). After impact, A and B have speeds 0.8v and 0.3v, respectively, along the directionsshown below. Circle the answer that most accurately represents the relative sizes of the masses ofA and B.

(a) mA = 0.3mB

(b) mA = 0.5mB

(c) mA = mB

(d) mA = 2mB

(e) The numerical value for the coefficient of restitution for the impact is needed to answer thisquestion.

Exam 2 of 9


October 29, 2014

Part E (4 points):

Blocks A and B (having masses of m and 2m, respectively) are connected by a lightweight, rigidrod. In System 1, a force F acts to the left on block A. In System 2, the same force acts to theleft on block B. Let F1 and F2 represent the magnitude of the load carried by the rod in Systems1 and 2, respectively. Circle the answer below that most accurately represents the magnitudes ofF1 and F2.

(a) F1 < F2

(b) F1 = F2

(c) F1 > F2

(d) More information is needed to answer this question.

Exam 2 of 9

exam 2 - weeklyjoys · exam 2 october 29, 2014 instructions: you have 60 minutes to complete this...

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