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Ground Level / / I ,\III/B \',-~.~~-""""'"-----'('-------'---D150m', ,A

CD (a)

(b)\\ .•..,\,...,(c)

Cd)

An underground pipe carries water of density 1000 kg/ m ' to a fountain at ground level, as shown above. At

point A, 0.50 m below ground level, the pipe has a cross-sectional area of 1.0 x 10-4 m2. At ground level, the

pipe has a cross-sectional area of 0.50 x 10-4 m2. The water leaves the pipe at point B at a speed of 8.2 m/s.

Calculate the speed of the water in the pipe at point A.

Calculate the absolute water pressure in the pipe at point A.

Calculate the maximum height above the ground that the water reaches upon leaving the pipe vertically atground level, assuming air resistance is negligible.

Calculate the horizontal distance from the pipe that is reached by water exiting the pipe at 60° from thelevel ground, assuming air resistance is negligible.

A B c

Three objects of identical mass attached to strings are suspended in a large tank of liquid, as shown above.

(a) Must all three strings have the same tension?

Yes No

Justi fy your answer.

Object A has a volume of 1.0 X 10-5 m' and a density of 1300 kg/m3. The tension in the string to which

object A is attached is 0.0098 N.

(b) Calculate the buoyant force on object A.

(c) Calculate the density of the liquid.

(d) Some of the liquid is now drained from the tank until only half of the volume of object A is submerged.Would the tension in the string to which object A is attached increase, decrease, or remain the same?

Increase Decrease Remain the same

Justify your answer.

.2.0 Ill!~--,50 kg ~ ~ zoo kg

I'~'-- 15m ----II

Se;eral, students are riding in bUI~lper cars at an amusement park. The combined mass of car A and its occupantsIS _50 .k~. ~he?comblne~ I.llass of car B and Its occupants IS200 kg. Car A is IS m away from car B and movingto the right at _.0 m/s, as shown, when the driver decides to bump into car B, which is at rest.

(a) Car A accelerates at 1.5 m/ S2 to a speed of 5.0 m/s and then continues at constant velocity until it strikescar B. Calculate the total time for car A to travel the 15m.

(b) After the collision, car B moves to the right at a speed of 4.8 m/s.

I. Calculate the speecl of car A after the collision.

II. Indicate the direction of motion of car A after the collision.

__ To the left __ To the right

(c) Is this an elastic collision?__ None; car A is at rest.

Yes No

Justify your answer.

The procedure is repeated, and the period P is determined for four different values of m2, where

m, = 0.012 kg and r = 0.80 m. The data, which are presented below, can be used to compute anexperimental value for g.

/112 (kg) 0.020 0.040 0.060 0.080

P (s) 1.40 l.05 0.80 0.75

(b) What quantities should be graphed to yield a straight line with a slope that could be used to determine g?

(c) On the grid below, plot the quantities determined in part (b), label the axes, ancl draw the best-fit line to thedata. You may Lise the blank rows above to record any values you may need to calculate.

_ -l __ .J. __ I...__ I__

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(d) Use your graph to calculate the experimental value of g.

----------- ----

An experiment is performed using the apparatus above. A small disk of mass m, on a frictionless table isattached to one end of a string. The string passes through a hole in the table and an attached narrow, verticalplastic tube. An object of mass m2 is hung at the other end of the string. A student holding the tube makes thedisk rotate in a circle of constant radius r, while another student measures the period P.

m1r(a) Derive the equation P = 2n that relates P and m2'/11.2g

WaterVapor

The cylinder represented above contains 2.2 kg of water vapor initially at a volume of 2.0 m' and an absolutepressure of 3.0 x 105 Pa. This state is represented by point A in the PV diagram below. The molar mass ofwater is 18 g, and the water vapor can be treated as an ideal gas.

P (Pa)

B C4.0 x I()~ -----------------n,3.0 x 10) ----------------11.1 :

1 I1 I1 II II I1 II I1 I

1.0 X 105

2.0 X 105.

o+---i---f---+---I--+--+-- V (rn ')o 0.5 1.0 1.5 2.0 2.5 3.0

(a) Calculate the temperature of the water vapor at point A.

The absolute pressure of the water vapor is increased at constant volume to 4.0 x 10s Pa at point B, and then thevolume of the water vapor is increased at constant pressure to 2.5 m3 at point C, as shown in the PV diagram.

(b) Calculate the temperature of the water vapor at point C.

(c) Does the internal energy of the water vapor for the process A ~B ~C increase, decrease, or remain thesame?

Increase __ Remain the sameDecrease

Justi fy your answer.

(d) Calculate the work done on the water vapor for the process A~B~C.

~ !4.0N.~ __ 8_.(_)_k_g_J......• -_

Block A of mass 2.0 kg and block B of mass 8.0 kg are connected as shown above by a spring of spring constant80 N/m and negl igi ble mass. The system is being pulled to the right across a horizontal frictionless surface by ahorizontal force of 4.0 N, as shown, with both blocks experiencing equal constant acceleration.

(a) Calculate the force that the spring exerts on the 2.0 kg block.

(b) Calculate the extension of the spring.

The system is now pulled to the left, as shown below, with both blocks again experiencing equal constantacceleration.

A-+.()N~

4 2.0 k~

/3

'j

(c) Is the magnitude of the acceleration greater than, less than, or the same as before?Greater Less The same

Justify your answer.

(e1) Is the amount the spring has stretched greater than, less than, or the same as before?Greater

Justify your answer.

(e) In a new situation, the blocks and spring are moving together at a constant speed of 0.50 m/s to the left.Block A then hits and sticks to a wall. Calculate the maximum compression of the spring.

Less The same

wrute Light

I I I I I I Air____ ....L_--L_-..!...._---.!...._----!._----!. Oil

Air

A wiele beam of white light is incielent normal to the surface of a uniform oil film. An observer looking down atthe film sees green light that has maximum intensity at a wavelength of 5.2 x lO-7 m . The index of refraction ofthe oil is 1.7.

(a) Calculate the speed at which the light travels within the film.

(b) Calculate the wavelength of the green light within the film.

(c) Calculate the minimum possible thickness of the film.

(d) The oil film now rests on a thick slab of glass with index of refraction 1.4, as shown in the figure below. Alight ray is incident on the film at the angle shown. On the figure, sketch the path of the refracted light raythat passes through the film and the glass slab and exits into the air. Clearly show any bending of the ray ateach interface. You are NOT expected to calculate the sizes of any angles.

~ Air n = 1.0II Oil n = 1.7I

Glass n = 1.4

Air n = 1.0