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October 1, 2004 SAMPLE

PHYSICS 207: Mid-Term Exam I

Print your name and section clearly on all five 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 box 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 magnitudes. You are allowed one 8½ x 11" sheet of notes and no other references. The exam lasts exactly 50 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:

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PROBLEM 1: 5 pts. A particle undergoes a trajectory given by the expression $\vec{r}= a t {\bf i} + b t^2 {\bf j}$ where $a=1$ m/s and $b=1$ m/s$^2$.

What is the form (i.e., path) of the trajectory?

A.

Circular

B.

Linear

C.

Parabolic

D.

Elliptical

E.

None of the above

PROBLEM 2: 10 pts. In regards to PROBLEM 1 and at time $t=0$ seconds what is the velocity vector, $\vec{v}$? What are the magnitudes of the tangential and centripetal accelerations (again at $t=0$)?

$\vec{v}=~~$


$a_{\small\mbox{tangential}}=$  


$a_{\small\mbox{radial}}=$  

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PROBLEM 3: (10 pts.)

A force $\vec{F}$ is applied to a block of mass $m = 2$ kg as shown at an angle $\theta=30^\circ$ to the inclined plane. The inclined plane makes an angle $\theta$ with respect to the horizontal. The inclined plane is frictionless and gravity acts in the verical direction.
( $\theta=30^\circ$, $\sin \theta =0.5$ or $\frac{1}{2}$, $\cos \theta =0.83$ or $\frac{\sqrt{3}}{2}$)

a) First skectch a free body diagram of the forces.

b) Find the magnitude of $\vec{F}$ such that the block remains stationary.

$\vert F\vert=~$

PROBLEM 4:(10 pts.)

A force $\vec{F}$ is applied to a block of mass $M=2.0$ kg. The force is applied only along the horizontal. Gravity acts along the vertical. The interface between the block and the wall is characterized by static and kinetic coefficients of friction $\mu_s=0.4$ and $\mu_k=0.2$ respectively. The block is sliding down the wall with a constant velocity $-v_0~ \bf {j}$. What force $\vec{F}$ is necessary to keep the velocity constant ?

$\vec{F}=$  

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PROBLEM 5: 10 pts. A fish, that can swim at 2 km/hour, decides to swim upstream against a river (that flows from East to West) with a current of 1 km/hour for 30 minutes and then downstream for 30 minutes.
(a) What is the fish's final position relative to his start?

On another day the fish decides to swim facing North from the same starting point. Once again it swims 30 minutes out and then, facing South, it swims another 30 minutes.
(b) What is the fish's final position relative to his start?

(a)  


(b)  

PROBLEM 6: (10 pts.) On a dare a student has been given the task of driving a car (of mass 1000. kg) horizontally, at maximum acceleration, straight towards a brick wall 110. m away. The car accelerates at 6. m/s$^2$. The brakes are designed so that the car uniformly deaccelerates at 15. m/s$^2$. (When the brakes are applied the driver's foot is off the accelerator.)

If the car accelerates from rest for 5. seconds and then the brakes are applied until it once again until comes to rest. How far from the from the wall is the car when it stops?