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October 5, 2006 Version A

PHYSICS 207: Mid-Term Exam I

Print your name and section clearly on all pages. (If you do not know your section number, write your TA's name.) Show all work in the space immediately below each problem. Your final answer must be placed in the boxes provided. Problems will be graded on reasoning and intermediate steps as well as on the final answer. Be sure to include units wherever necessary, and the direction of vectors. Each problem is worth between 5 and 10 points. In doing the problems, try to be neat. Check your answers to see that they have the correct dimensions (units) and are the right order of magnitude. You are allowed one 8½ x 11" sheet of notes and no other references. The exam lasts 90 minutes.

NOTE: for the purposes of this exam you should assume $g=10.$ m/s$^2$.

Do NOT write below this point.

SCORE

PROBLEM 1:

PROBLEM 2:

PROBLEM 3:

PROBLEM 4:

PROBLEM 5:

PROBLEM 6:

PROBLEM 7:

PROBLEM 8:

PROBLEM 9:

PROBLEM 10:

PROBLEM 11:

PROBLEM 12:

PROBLEM 13:

PROBLEM 14:

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PROBLEM 1: 6 pts.
The position of an object at equal time intervals is shown below:

Which graph below most correctly represents the position versus time for this object?
Circle the correct letter.

PROBLEM 2: 6 pts. The graph below shows the $y$ velocity versus time graph for a ball. For this ball the force of gravity is acting downward in the -$y$ direction and the $x$ axis is along the horizontal. Which explanation best fits the motion of the ball as shown by the velocity-time graph below?

Circle the correct letter.

(A)

The ball is falling straight down, is caught, and is then thrown straight down with greater velocity.

(B)

The ball is rolling horizontally, stops, and then continues rolling.

(C)

The ball is rising straight up, hits the ceiling, and then falls straight down.

(D)

The ball is falling straight down, hith the floor, and then bounces straight up.

(E)

The ball is rising straight up, is caught and held for awhile, and then is thrown straight down.

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PROBLEM 3: (6 pts.)
The equation for the change of position of a train starting at $x =0$ m is given by $x=\frac{1}{2} at^2 + b t^3$. The dimensions of $b$ are in

Circle the correct lettter.

(A)

$T^{-3}$

(B)

$LT^{-3}$

(C)

$LT^{-2}$

(D)

$LT^{-1}$

(E)

$L^{-1}T^{-1}$

PROBLEM 4: (6 pts.)A battleship simultaneously fires two shells at enemy ships. If the shells follow the parabolic trajectories shown, which ship gets hit first?

Circle the correct letter.

(A)

A

(B)

Both at the same time

(C)

B

(D)

More information is needed

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PROBLEM 5: (8 pts.) You are traveling in car at a speed of 20 m/s and crash into an another vehicle head on. The collision brings you to rest in a distance of 2 m. Thankfully the engine is designed to go under the passenger compartment. Assuming that your average acceleration in the crash is constant, what is your acceleration in terms of the number of $g$'s (assuming $g$ is 10 m/s$^2$)?

$a$ =  



PROBLEM 6: (8 pts.) Two identical, mass-less strings of length, $L$ = 10 m, are mounted to a rotating armature undergoing a circular rotation in the vertical direction. The strings are affixed to a small mass, $m = 10$ kg, that has a tangential velocity $v=5$ m/s at the bottom of its swing. What is the tension, $T$ in Newtons, in each string when the mass is at this bottom most position (as shown)?

$\vert\vec{T}\vert=$  

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PROBLEM 7: (6 pts.)
$\parbox{0.45\linewidth}{ \noindent A person pulls a block across a r... ...among the force magnitudes $W$, $f$, $N$\ and $F$\ {\bf must be true}? \vfill }$ $\parbox{0.30\linewidth}{~~ \begin{center} \includegraphics[width=2.5in]{f_4.eps} \end{center}}$

1. [(A)] $F = f$ and $N = W$
2. [(B)] $F = f$ and $N > W$
3. [(C)] $F > f$ and $N < W$
4. [(D)] $F > f$ and $N = W$
5. [(E)] None of the above

PROBLEM 8: (8 pts., )

A 80 kg man boards an elevator and goes up three flights. He happens to have a display that tells him his acceleration versus time (as shown at right).

What is his maximum apparent weight if he is standing on a scale?

$W=$  

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PROBLEM 9: (6 pts.)
Raindrops are falling straight downward in still air. When observed from a car traveling at 60 mi/h the drops form streaks on the side window at an angle of 60$^\circ$ with respect to vertical. What is the speed with which the drops are falling when they strike the side window?



















$s=$  


PROBLEM 10: (8 pts.)
A man starts out and walks first with a velocity ( $0.30 ~ \hat{\bf i} + 0.40 ~ \hat{\bf j}$) m/s for ten seconds and then moves at ( $0.5 ~ \hat{\bf i}$) m/s for 20 seconds. What is his average speed on the walk ?



















average speed $=$  

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PROBLEM 11: (8 pts.)

Two masses are connected by a string that goes over a frictionless, mass-less pulley. The mass on the horizontal surface is 2.0 kg and the coefficient of static friction is 0.80. The second mass sits on a frictionless 45$^\circ$ incline. What is the minimum mass (in kg) necessary to cause the pair of masses to slide?

$m=$  


PROBLEM 12: (6 pts.) The diagram below shows 3 vectors whose sum ( $\vec{\bf A}+\vec{\bf B}+\vec{\bf C}$) is zero and all of equal length. Which statement is true

Circle the correct letter.

(A)

$\bf {A} + \bf {B} = \bf {A} - \bf {C}$

(B)

$\bf {A} + \bf {B} = \bf {B} - \bf {C}$

(C)

$\bf {A} - \bf {B} = 2\bf {A} - \bf {C}$

(D)

$\bf {A} - \bf {B} = 2\bf {A} + \bf {C}$

(E)

2 $\bf {A} + 2\bf {B} = 2\bf {C}$

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PROBLEM 13:(8 pts, 2, 6)

A 1500 kg car is traveling at a constant speed of 25 m/s over the top of a perfectly semi-circular hill of radius 75 m.
(A) For the car to lose contact with the surface (and begin freefall) what will the normal force do?

(B) At what angle $\theta$, as shown, will this happen?

$\theta=$  

PROBLEM 14:(10 pts, 2,2,6)
Refer to the drawing and conditions of PROBLEM 13.
If we now assume that the angle $\theta$ is exactly 60$^\circ$, then
(A) What are the horizontal and vertical components of the car's velocity?
(B) Assuming the car now falls towards the ground. After falling for 2.0 seconds (just slightly before it hits the ground) what is the car's instantaneous speed?
(You should assume that the car does not encounter the hill once it begins free fall.)














$v_{\mbox{\tiny hor}} =$  

$v_{\mbox{\tiny vert}} =$  

$~~~~s=$