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Faculty of Engineering and Department of Physics

Engineering Physics 131

Midterm Examination

Monday February 24, 2014; 7:00 pm – 8:30 pm

1. No notes or textbooks allowed. 2. Formula sheets are included (may be removed). 3. The exam has 9 problems and is out of 50 points. Attempt all parts of all problems. 4. Show all work in a neat and logical manner. Questions 1 to 4, 8(a) and 9 do not require detailed calculations and only the final answers to these questions will be marked. For the rest of the questions, details and procedures to solve these problems will be marked. 5. Write your solution directly on the pages with the questions. Indicate clearly if you use the backs of pages for material to be marked. 6. Non-programmable calculator allowed. Turn off all cell-phones, laptops, etc. and put them in your backpack.

DO NOT separate the pages of the exam containing the problems.

LAST NAME: ______________________________________

FIRST NAME: ______________________________________

ID#: ___________________

Please circle the name of your instructor:

B01: Kaminsky

B02: Beach

B03: McDonald

B04: Tang

B05: Wheelock

B06: Ropchan

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Please do not write in the table below.

Question Value (Points) Mark

1 5

2 2

3 5

4 2

5 7

6 7

7 8

8 8

9 6

Total 50

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1. [5 Points] Cars A and B begin at distances sA = 1.0 km and sB = 1.5 km from an intersection, as measured bumper to stopping line. The vehicles are initially travelling at 18 km/h and 36 km/h, respectively, and they are accelerating at constant rates aA = 0.05 m/s2 and aB = 0.10 m/s2. Neither vehicle, however, will exceed the posted speed limit of 54 km/h. Each lane is 4.0 m wide. Expressed in a coordinate system centered on the intersection, and whose axes are aligned with the two roads, the vehicle positions are rA = ( sA4.0, 2.0) m and rB = (2.0, sB+4.0) m. The distance between the vehicles is |rA/B| = |rA rB|.

Of the 11 lines shown on the three graphs below, 5 correctly describe the evolution in time of sA, sB, vA (speed of A), vB (speed of B) and |rA/B|. Match those 5 lines to the corresponding quantity by writing the appropriate numbers in the blanks provided.

sA is described by curve

sB is described by curve

vA is described by curve

vB is described by curve

|rA/B| is described by curve

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2. [2 Points] A baseball was thrown from a cliff and the projectile motion was simulated by using a computer. The relationship between the vertical position (in the y-direction) and the horizontal position (in the x-direction) is shown graphically below. One of the curves was generated for the case when there was no air resistance, and the other curve was generated when air resistance was present. The initial velocities and angles of the baseball are the same.

Answer the following questions regarding the curves and the motion. (a) [1]Which curve represents the motion when air resistance was present? Circle

your choice.

Curve I Curve II (b) [1]The curves were drawn and extended below the line y = 0. What does this

mean physically? Circle your choice.

(A) The balls stopped moving.

(B) The balls changed direction of motion.

(C) The balls fell below the height from which they were thrown.

(D) Insufficient information to answer.

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3. [5 Points] The block is initially given a push, then it slides down a frictionless track (under the influence of gravity) and remains in contact with the track all the way around the loop. Five locations along the track (A, B, C, D, E) are indicated on the diagram.

In the table below, circle the location(s) (A, B, C etc.) that have the following attributes. If there are no such locations, circle “none”.

Tangential acceleration (at) = 0 at … A B C D E none

Normal acceleration (an) = 0 at … A B C D E none

Normal component of velocity (vn) is nonzero at …

A B C D E none

Speed is decreasing at … A B C D E none

Acceleration and velocity vectors are perpendicular at …

A B C D E none

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4. [2 Points] In the figure shown below, the pulley is massless and frictionless, the rope is massless, and 45 . Block B moves down the incline with a constant speed vB. The relative velocity of B with respect to A is given by vB/A and has components (vB/A)x and (vB/A)y with respect to the coordinate system shown.

Now consider a similar arrangement with the angle of the incline replaced by 2 and the masses of blocks A and B adjusted so that block B moves down the incline with the same speed vB. Using the same coordinate system, do the following quantities increase, decrease, remain the same, or is it impossible to say? Circle one answer for each. (vB/A)x Increase Decrease Remain the same Impossible to say (vB/A)y Increase Decrease Remain the same Impossible to say |(vB/A)x| Increase Decrease Remain the same Impossible to say |(vB/A)y| Increase Decrease Remain the same Impossible to say

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5. [7 Points] A body travels along a smooth horizontal surface in the positive x direction and is subject to a quadratic drag force whose magnitude also increases linearly with position. Thus, the body’s acceleration is given by:

a = −2xv2 m/s2 (with x in m, and v in m/s). At t = 0, the body is at x = 0, and its velocity v is +4 m/s. (a) [2] In terms of M, L and T, what dimensions must the ‘2’ carry? (b) [5] Find the velocity of the body as a function of position. (Hint: you can still

separate the appropriate variables as always.)

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6. [7 Points] On a planet where g = 10 m/s2, a football is kicked from the origin (point A) at a speed of 6.0 m/s, directed θA = 53.13° above the horizontal (so cos θA = 3/5, sin θA = 4/5). At t = 0.75 s, what is the football’s: (a) rate of change of speed; (b) normal component of acceleration; (c) radius of curvature.

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7. [8 Points] The car travels along a circular path having a radius of 30 m at a speed of v = 5 m/s. At s = 0, it begins to accelerate with v = dv/dt = (0.05 s) m/s2, where s is in meters. Determine its speed and the magnitude of its total acceleration when it has moved s = 18 m.

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8. [8 Points] Consider the system shown. Both blocks move at a constant speed. The relative velocity of B with respect to A, vB/A, is directed downwards towards the right at an angle as measured from the usual

positive x axis . (a) [1] Does B move up or down the incline? Circle

one answer.

Up Down If the speed of B is 3 m/s determine: (b) [3] the velocity of A, expressed as a magnitude and direction with respect to the

nearest horizontal; and (c) [4] the angle that vB/A makes with respect to the nearest horizontal.

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9. [6 Points] Two stacked blocks are traveling horizontally along a rough horizontal surface as shown when the bottom block encounters a spring anchored on one side to a wall. The surface between the two blocks is also rough. While the spring is being compressed and while the top block remains at rest relative to the bottom block (figure on the right), draw the complete free-body and kinetic diagrams for both blocks. Be sure to clearly indicate the correct directions of any vector on each diagram. All symbols shown in your diagrams are assumed to take on positive values. In addition, YOU MUST USE the following symbols for forces (IF APPLICABLE): mig for gravitational forces fk for kinetic frictional forces Nij for normal forces i acting on j fs for static frictional forces Fspring for elastic restoring forces Tij for tensional forces

Free Body Diagram for A: Kinetic Diagram for A: = Free Body Diagram for B: Kinetic Diagram for B: =

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