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October 1, 2004 Version B

PHYSICS 207: Mid-Term Exam I

Print your name and section clearly on all seven 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 15 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: 15 pts.

A driver of a car sweeps out a series of two arcs that move the car in the following way: In the initial 20 second period the car drives along a circular arc, sweeping out 1/2 of a circle of radius 100 m, first directly north, then east and finally south. In the second 20 second period the car moves again sweeping out 1/2 of a circle of radius 50 m, at first due west, then north and finally ending east.

(a) What is the net displacement (in terms of east, west, north south)?
(b) What is the magnitude of the average velocity?
(c) What is the average speed?

displacement $=~$


$\vert\vec{v}\vert=$  


$s=$  

PROBLEM 2: 10 pts. A student measures the length of three different rectangular blocks and places them end to end so that their lengths add together. The lengths are given as $10\pm1$ cm, $20\pm3$ cm and $30\pm5$ cm. Using the explicit procedure given in Serway in Chapter 1, what is the total length and uncertainty?

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PROBLEM 3: (5 pts.)
Which of the following products of ratios gives the conversion factor to convert miles per hour to METERS per MINUTE?

Circle the correct answer.

(A)

$\frac{5280~{\small\mbox f}}{1~{\small\mbox {mi}}} \cdot \frac{12~{\mbox {in}}... ...}{100~{\small\mbox {cm}}} \cdot \frac{60~{\mbox {min}}}{1~{\small\mbox {hr}}}$

(B)

$\frac{1~{\small\mbox {mi}}}{5280~{\small\mbox f}} \cdot \frac{1~{\small\mbox ... ...box {cm}}}{1~{\mbox {m}}} \cdot \frac{1~{\small\mbox {hr}}}{60~{\mbox {min}}}$

(C)

$\frac{1~{\small\mbox {mi}}}{5280~{\small\mbox f}} \cdot \frac{1~{\small\mbox ... ...box {cm}}}{1~{\mbox {m}}} \cdot \frac{60~{\mbox {min}}}{1~{\small\mbox {hr}}}$

(D)

$\frac{5280~{\small\mbox f}}{1~{\small\mbox {mi}}} \cdot \frac{12~{\mbox {in}}... ...}}{100~{\small\mbox {cm}}} \cdot \frac{1~{\mbox {h}}}{60~{\small\mbox {min}}}$

(E)

$\frac{1~{\small\mbox {mi}}}{5280~{\small\mbox f}} \cdot \frac{12~{\mbox {in}}... ...}}{100~{\small\mbox {cm}}} \cdot \frac{1~{\mbox {h}}}{60~{\small\mbox {min}}}$

PROBLEM 4:(12 pts., 4, 4, 4)

Two identical masses are stacked one on top of the other and these masses sit on a frictionless table top. A force $\vec{T}$ is applied horizontally to the bottom block of mass $M=1.0$ kg by means of an attached rope. The force is applied only along the horizontal. Gravity acts along the vertical. The interface between the two blocks is characterized by static and kinetic coefficients of friction $\mu_s=0.4$ and $\mu_k=0.2$ respectively.
(a) Considering only the top block what force $\vec{F}$ applied directly to the top block is necessary to cause the top block to slide relative to the bottom one?
(b) Draw a free body diagram of the forces on the bottom block.
(c) What tension $T$ is necessary to achieve the result of part (a)?

$\vert\vec{F}\vert=$  


$\vec{T}=$    

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PROBLEM 5: (8 pts.)

Two rectangular horses are walking eastward as shown towing a 100 kg boat at a constant 7 km/hour (perfectly eastward as well). The tension in each of the identical length ropes is 200 N. The angle between the ropes is 45 degrees.

What is the force $\vec{F}$ of the water on the boat? (Remember vectors require both magnitude and direction. )

$\vec{F}=$  

PROBLEM 6: (10 pts.) A person is test driving a car (of mass 1000. kg) in a northwards direction. Initially they accelerate at 5. m/s$^2$ for 2 seconds, next drive at constant velocity for 2 seconds and then brake (at constant acceleration) to a stop in 2 seconds .

What total distance $d$ have they travelled?

$d=$

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PROBLEM 7: 5 pts. A 10 kg mass undergoes motion along a line with a velocities as given in the figure below. Indicate by circling one of the given letters the region in which the magnitude of the force on the mass at its greatest?

(You do not need to consider the points at which the curve is discontinuous.)

PROBLEM 8: (5 pts.)

The power radiated per unit surface area ($P/A$) by a blackbody (as you will study later in the semester) is proportional to its absolute temperature (i.e., degrees Kelvin or K) to the fourth power. Thus $P/A=c T^4$ or power $P=cAT^4$ where $A$ is the area of the blackbody in m$^2$ and $c$ is a fundamental constant. If power, $P$, is in units of Force $\times$ Distance / Time the find the units of $c$ in terms of kg, m, s and K.

Units of $c$ =  

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PROBLEM 9: (10 pts.) A very short (point-like) person throws a ball into the air in an eastward direction at a 45$^\circ$ angle from the horizontal and at a speed of 100. m/s. When the ball reaches its maximum height
(a) How long does it take?
(b) What is its new displacement relative to the person if the person remains stationary?
(You may let $\cos (45^\circ) = \sin (45^\circ) = 0.7$)













$t=$  


$r=$  

PROBLEM 10: (10 pts.)

A 2 kg miniature car is located 1 m from the center of a circular platform that is rotating clockwise at the rate of 1 revolution per second. The car itself, as viewed from a STATIONARY observer (NOT on the platform) is moving in a circular path on the platform in a counter-clockwise direction at a speed of 1 m/s.

(a) What is the magnitude of the centripetal force?
(b) What is the tangential velocity with respect to the rotating platform?

    

$\vert\vec{F}_{\mbox{\small radial}}\vert=$  


$v_{\small\mbox{tangential}}=$  

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PROBLEM 11: 5 pts.
Which of the following statements is most correct for two observers in different inertial frames of reference (i.e., moving at different but constant velocities) that are watching an object moving along a complicated path (i.e., changing position, velocity and acceleration).

Please circle the appropriate letter.

A.

The two people observe the same paths, velocities and accelerations.

B.

The two people observe the same paths, different velocities and the same accelerations.

C.

The two people observe different paths, different velocities and different accelerations.

D.

The two people observe different paths, the same velocities and different accelerations.

E.

The two people observe different paths, different velocities and the same accelerations.

F.

The correct answer has not been given.

PROBLEM 12: (5 pts.)

The gravitational force felt by the Earth arising from a 10 N apple hanging on a tree is

Please circle the correct letter.

A.

$6.7 \times 10^{-11}$ N

B.

$6.7 \times 10^{-10}$ N

C.

 0 N

D.

 1 N

E.

10 N