Physics 207 – 05S Exam 1 March 11th, 2005

A 1

Last Name:______________________________ First Name:_____________________________________

Discussion Section: ___________ Instructions-

This is a closed book exam. No memory aids of any kind, electronic or otherwise, may be used. You have fifty (50) minutes to complete it.

1. Before starting work, check to make sure that your test is complete. You should have 7 numbered pages plus a formula sheet.

2. When you are done, you MUST hand in all 7 pages of the exam.

Exam Grading Policy- This exam consists of 13 questions; true-false questions are worth 2 points each, three-choice multiple choice questions are worth 3 points each, five-choice multiple choice questions are worth 6 points each. The maximum possible score is 69. Basic questions are marked by a single star *. More difficult questions are marked by two stars **. The most challenging questions are marked by three stars ***. Circle only ONE answer. If you decide to change an answer, erase vigorously. If you circle no answer, or circle more than one answer, you earn zero (0) points for that problem.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

Total

Please do not write in this box

Physics 207 – 05S Exam 1 March 11th, 2005

A 2

1. (*) At a certain instant of time, the acceleration and velocity vectors of an object are shown to the right. Which statement most correctly describes the motion of this object?

(a) it is slowing down and turning upwards (b) it is speeding up and turning downwards (c) it is maintaining its speed but turning upwards (d) it is slowing down but not changing direction (e) it is undergoing uniform circular motion

2. (*) This question and the next question are about the following situation

A 3-kg block sits on a 10-kg block resting on a frictionless table, as shown. A string along the horizontal direction with a force F pulls the lower block. The two blocks move ahead together with an acceleration of 1 m/s2.

What is the pulling force?

(a) F = 10 N (b) F = 7.0 N (c) F = 16 N (d) F = 13 N (e) F = 39 N

3. (*) What horizontal force does the bottom block exert on the upper block?

(a) Fb,u = 0.0 N (b) Fb,u = 7.0 N (c) Fb,u = 3.0 N (d) Fb,u = 1.0 N (e) Fb,u = 2.0 N

Acceleration

Velocity

3kg

10 kg

a = 1 m/s2

F

Physics 207 – 05S Exam 1 March 11th, 2005

A 3

4. (**) At the right is a graph of the acceleration of a

point particle as a function of time:

Which choice below is a possible graph of the position of the particle as a function of time?

(a) (b) (c) 5. (**) A mass m is attached to a spring with spring constant k, the other end of which is attached to the

ceiling. It is pulled and allowed to oscillate up and down. Using dimensional analysis, determine which one of the following is a valid expression for the time, T, it takes to complete each oscillation.

Accel [m/s2]

Time [sec]

Position [m]

Time [sec]

Position [m]

Time [sec]

Position [m]

Time [sec]

k

m

3

2

(a) 2

(b) 2 -

(c) 2

(d) 2

(e) 2

T km

T m k

T m k

T k m

T m k

= π

= π

= π

= π

= π +

Physics 207 – 05S Exam 1 March 11th, 2005

A 4

6. (*) This and the next question are about the following situation.

A car undergoing uniform acceleration, a = 3 m/s2, is traveling at a velocity of 36 m/s as it enters a tunnel. When the car exits the tunnel, its velocity is 60 m/s.

How long is the tunnel?

(a) 267 m (b) 307 m (c) 346 m (d) 384 m (e) 442 m

7. (*) For how long is the car in the tunnel? (a) 8.0 s (b) 7.0 s (c) 6.0 s

8. (**) An empty car is driven off of a cliff as part of a stunt for a new movie. The car starts at rest and

then undergoes constant acceleration of a = 4.5 m/s2 for a distance of r = 100 m. The car then goes off the cliff, leaving the cliff traveling parallel to the ground. The cliff is a height h = 78.4 m above the ground below.

What is the distance D away from the cliff that the car lands? (a) 108 m (b) 120 m (c) 132 m (d) 144 m (e) 156 m

Physics 207 – 05S Exam 1 March 11th, 2005

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9. (***) Buckingham fountain in Chicago has several water jets with the geometry shown in the figure. The initial speed of the water coming out of the jet is v0 = 8 m/s.

How from the edge of the upper pool does the water fall? This distance is labeled x in the figure. (a) The water does not make it all the way to the upper pool. (b) 1.3 m (c) 2.2 m (d) 3.1 m (e) 4.6 m

10. (*) A boat captain guides his boat across the river at an angle ? as shown. The river flows towards the east. If the speed of the boat with respect to the river, /b rv

r, is 12 mph, the angle ? = 60° and she ends

up on the opposite bank directly across from her starting point, what is the speed, rvr

, of the river?

(a) rvr

= 6.0 mph

(b) rvr

= 10.4 mph

(c) rvr

= 12 mph

(d) rvr

= 7.2 mph

(e) rvr

= 8.4 mph

river East

?

vboat/river

Physics 207 – 05S Exam 1 March 11th, 2005

A 6

11. (**) This and the next question are about the following situation:

A tennis ball of mass m is attached to a rope and swung in a vertical circle. The rope has a length, L = 2 m. The weight of the ball is W = 0.5 N. When the ball is at its highest point, the tension in the rope is 1 N. What is the tangential velocity (speed) of the ball at its highest point?

(a) vt = 2.8 m/s (b) vt = 4.7 m/s (c) vt = 5.3 m/s (d) vt = 6.8 m/s (e) vt = 7.7 m/s

12. (*) When the rope is exactly horizontal to the ground the speed of the ball is v. Which of the following expressions for the tension, T, is correct? (a) T = W (b) T = mv2/L (c) T = mv2/L – W

13. (***) An inclined plane with angle ? = 30° has a smooth frictionless surface. A mass, m = 5-kg, sits on the plane and is attached by a massless rope strung over a pulley to a hanging mass, M = 7-kg.

What is the displacement of mass m two seconds after the system of two masses is released from rest?

(a) 3.7 m (b) 3.0 m (c) 7.4 m (d) 5.6 m (e) 8.1 m

g

W=0.5 N

L=2m

frictionless

ground

Physics 207-05S Exam 1 Formula Sheet

A 7

Kinematics

( )( )

02

0 02 2

0 0

0 02

0

= = + 2

v = v + 2 x - xx - x v + v 2x - x v - 2

tt ta

tt at

++

==

v v ar r v a

29.81 m sg =

2D Motion

2 2max

2

sin 2

sin2i

i

h v g

Range v g

θ

θ

=

=

Uniform Circular Motion 2 2

2 2

a v r rv r

T f

= = ω= ω

ω = π = π

Galilean Transformations

0

0

r r v tv v v

′ = −′ = −

r r rr r r

Dynamics

, ,

NET

A B B A

m== −

F aF F

( )2

12 1 211 2 2

(gravity near earth's surface)

; 6.67 10 N m kgspring

F mg

F G m m rF k x

G −=

= −= − ∆

= × •

2 2 2

sin2 2sin cos

sin30 0.50; cos30 0.866

sin60 0.866; cos60 0.50

x y rθ θ θ

° °

+ ==

= =

= =o o

2

2

if 0 then

4

2

ax bx c

b b acx

a

+ + =

− ± −=