A-Rothschild B- Goldberg C-Carey D-Narain

of 9 PY105 TEST 1 Oct 4, 2000 Name______ID______

Lecture Section: [ ] A-Rothschild [ ] B- Goldberg [ ] C-Carey [ ] D-Narain

Room: [ ] CGS 129

 Put your name and ID number on each page and lecture section and room of exam on the top of this page.  The test is 90 minutes long and has a total of 100 points  Answer ALL problems below. Indicate your answers in the space provided. If you need more space, write on the back of the pages.  Express all your numerical answers to the appropriate number of significant digits and with appropriate units.  It is very important to show ALL your work. Even if you have the right answer, you may not receive full credit if you don't show your work.

 This is a closed-book test with an equation sheet provided.

Grades

Problem 1 ______(/10)

Problem 2 ______(/20)

Problem 3 ______(/20)

Problem 4 ______(/25)

Problem 5 ______(/25)

Total ______(/100) Page 2 of 9 PY105 TEST 1 Oct 4, 2000 Name______ID______

PROBLEM 1. Quickies [10 points (2points each)]

1) The position vs. time graph of two riders is shown below. We will use “left” as negative displacement and “right” as positive displacement.

[ ] At t=0 s, rider C has a higher velocity than D and is on the right of D. [ ] At t=0 s, rider D has a higher velocity than C, but C is on the right of D. [ X ] At t=0 s, rider C has a higher velocity than D, but D is on the right of C. [ ] At t=0 s, rider D has a higher velocity than C and is on the right of C. [ ] At t=0 s, rider D and C are at rest. [ ] At t=0 s, rider C has a higher speed than D and both are at the same position. [ ] At t=0 s, rider D has a higher speed than C and both are at the same position.

2) Several projectiles are fired in the air. Which one must have been in the air longest? [ ] The one with the greatest range, R. [ ] The one with the greatest initial velocity. [ X] The one with the highest maximum elevation, h.

3) Consider a plane flying with ground speed Vg and airspeed Va in a wind with speed V. Which of the following relationships is true? [ ] Vg will always equal Va + V [ ] Vg is greater than Va + V [ ] Vg is less than Va - V [ X] Vg can have any value between Va + V and Va - V Page 3 of 9 PY105 TEST 1 Oct 4, 2000 Name______ID______

4) A toolbox, of mass M, is resting on a flat board. One end of the board is lifted up until the toolbox just starts to slide. The angle theta that the board makes with the horizontal for this to occur depends on the [ ] Mass, M. [ ] Acceleration of gravity, g. [ ] Normal force.

[ X] Coefficient of static friction, s.

5) Four students perform an experiment by pulling an object horizontally across a frictionless table. They repeat the experiment on several other objects of different masses, always applying the same force to produce acceleration. They each graph the results, individually. Which student's graph is correct?

[ X ] Graph 1 [ ] Graph 2 [ ] Graph 3 [ ] Graph 4 Page 4 of 9 PY105 TEST 1 Oct 4, 2000 Name______ID______

PROBLEM 2. Estimation? [20 points] A valley in Colorado is enclosed by mountains on three sides. On the forth side, a small stream, fed by rainfall in the valley, runs out into a lake. If the valley has an area of 20.0 square miles, and experiences an annual rainfall of 75 cm, then what is the average flow rate of water in the stream in units of (l/s)? (1 mile= 1.6km and 1liter=1000cm3)

Solution: flow rate = volume/time volume = area X depth =(20 sq mi) (1.6km/mi)^2(1000m/km)^2(0.750m) = 3.84x10^7m^3 time = 1 yr = 65days/yr)(24hr/day)(60min/hr)(60sec/min) =1536x10^7 sec flow rate = 3.84x10^7/3.1536x10^7 = 1.2177 m^3/s

1m^3=(100cm/m)^3 = 1000000cm^3; 1litre = 1000cm^3 so 1m^3 = 1000litres flow rate = 1217.7litres/sec. flow rate in sig figs flow rate = 1220 litres/sec Page 5 of 9 PY105 TEST 1 Oct 4, 2000 Name______ID______

PROBLEM 3. Kinematics [20 points]

A ball is dropped from the top of a tower by a man at the same time that a bowler rolls a bowling ball with a constant velocity, v, towards the base of the tower starting 10.0 m away. The two balls collide after 2.0 seconds. Neglect the height of the man, friction and air resistance. (Note: the diagram is not drawn to scale)

R= 100 m

a) (5 points) What is the height of the tower?

b) (5 points) What is the velocity of the dropped ball when it strikes the ground?

c) (5 points) What is the velocity of the bowling ball when it collides with the dropped ball?

d) (5 points) The experiment is repeated again by the man, but this time he drops a ball with twice the mass of the first. Do the bowling ball and the dropped ball collide at the base of the tower? Page 6 of 9 PY105 TEST 1 Oct 4, 2000 Name______ID______

PROBLEM 4. Projectile Motion [25 points]

You may assume that g=10.0 m/s2 and that the air resistance can be neglected.

A soccer ball is kicked in the air. It travels for 3.0 seconds and strikes the top of a 3.0 meter pole which is 60.0 meters away horizontally.

1) (5 points) What is the direction of the acceleration vector when the ball reaches the top of its trajectory? [ ] up [ X ] down [ ] parallel to the velocity

The acceleration in any projectile motion problem is always g, downward.

2) (5 points) What is the magnitude of the ball’s horizontal velocity at that same moment?

At the top of the motion, as everywhere on the trajectory, the x-velocity is = 60m/3 sec = 20 m/sec.

3) (8 points) What was the ball’s vertical velocity just after being kicked? Since the ball is 3 meters high (= y-y_0) after t=3 sec we can solve the displacement equation y = y_0 + v0_y*t -g*t2/2 for v0_y.

The solution is 16 m/sec.

4) (7 points) At what angle was the ball launched? Specify the direction with respect to the horizontal. Knowing the initial x and y velocities we can determine the initial angle from

tan(theta) = v0_y/v0_x = 16/20 theta = 38 degrees, or slightly less than 45 degrees, which would be the launch angle for equal x and y velocities Page 7 of 9 PY105 TEST 1 Oct 4, 2000 Name______ID______

PROBLEM 5. Forces and Newton’s laws [25 points]

A 4.0 kg aluminum block and a 12.0 kg copper block are placed on a wooden block. They are connected by a thin string which passes over a massless and frictionless pulley. The coefficient of kinetic friction between the Aluminum and wood is 0.6, and between Copper and wood is 0.45.

1) (8 points) Draw the free body diagrams for both blocks.

2) (8 points) Write down Newton’s second law equations for both the blocks.

For Al:

X direction: T - fAl = mAl a Y direction: FNAl – mAl g = 0 (no acceleration in y direction)

For Cu:

X direction: mcu g Sin(theta) – T - fCu = mCu a Y direction: FNCu – mCu g Cos(theta)= 0 (no motion in y dir) Page 8 of 9 PY105 TEST 1 Oct 4, 2000 Name______ID______

3) (7 points) Compute the acceleration of the blocks.

From part 2:

For Al we have:

T - fAl = mAl a

T –Alk FNAl = mAl a

but, FNAl = mAl g , we get T–Alk mAl g = mAl a

OR, T = Alk mAl g + mAl a

And for Cu:

mcu g Sin(theta) – T - fCu = mCu a

OR, mcu g Sin(theta) – T –Cuk FNCu = mCu a Using FNCu = mCu g Cos(theta),

We get, mcu g Sin(theta) – T –Cuk mCu g Cos(theta) = mCu a

Now substitute the value of T from Al:

mcu g Sin(theta) – Alk mAl g - mAl a –Cuk mCu g Cos(theta) = mCu a collect the two terms with “a” on the LHS and move rest to RHS

mAl a + mCu a = mcu g Sin(theta) – Alk mAl g –Cuk mCu g Cos(theta)

a = (mcu g Sin(theta) – Alk mAl g –Cuk mCu g Cos(theta) )/( mAl + mCu ) Page 9 of 9 PY105 TEST 1 Oct 4, 2000 Name______ID______

4) (2 points) Will the copper block move up the slide? Justify your answer.