Exam 1, Sample

Physics 172H fall 2007Purdue University

Print your name____ANSWER KEY_______________________ Lab section_______

Do not use other paper. Write on the back of this test if needed.

All problems except the last one are multiple-choice and only the correct answer isgraded.

For the last problem only you must provide the complete reasoning and solution asrequested in the problem:

• Correct answers without adequate explanations or with incorrect reasoning will becounted wrong. Cross out anything you don’t want us to read.

• Make explanations complete, but brief. Do not write a lot of prose.• Include diagrams where appropriate to explain your work.• Show what goes into a calculation, not just the final number: (2m)/(4 s) = 0.5 m/s• Give standard SI units with your results• Unless specifically asked to derive a result, you may start from the formulae given

on the equation sheet. All equations used must be derived from those on theequation sheet.

• Use correct vector notation• Your work must be legible and clear

Problem 1.

The x coordinate of the position of a mouse as a function of time is plotted below.

If each square on the grid is 1 [s] in time and 1 [m] in length, what is the average velocity

vx of the mouse during the 12 seconds shown?

a. 1 [m/s]b. –1 [m/s]c. 0.083 [m/s]

d. –0.083 [m/s],

vave =rf −ri

t f − ti

=ΔrΔt

e. 0 [m/s]

Problem 2

A pool ball of mass 0.10 kg, hits a side of the pool table with a velocity of <3, 0, 1.5>[m/s]. It rebounds with a velocity of <3, 0, -1.5> [m/s]. If the time of contact betweenthe ball and the pool table wall is 0.03 [s], calculate the force of impact that the balldelivers to the pool table.

a. <0, 0, 3> [N]b. <0, 0, -3> [N]c. <0, 0, 100> [N]d. <0, 0, -100> [N], apply the momentum principlee. <3, 0, 3> [N]f. <3, 0, -3> [N]g. <-6, 0, 100> [N]h. <-6, 0, -100> [N]

t

X

0

Problem 3.

Two small plastic balls, each of mass 2 grams, are rubbed all over with wool, and bothacquire the same amount of charge. If the balls are placed in a vertical line so that onefloats above the other by a distance of 5 mm, what is the magnitude of the charge on eachball?

a. 3.7E-11 [C]b. 1.1E-14 [C]c. 1.0E-7 [C]d. 7.4E-9 [C], equate Fg(by earth) with Felec by the ball.

Problem 4 – 5.

Problem 4.

A spaceship is set out for a long voyage. The captain hopes to make the trip faster bytraveling 0.94c. The spaceship accelerates from rest using a secret energy source thatproduces a 4.9E3 kg*m/s force on the spaceship. If the spaceship weighs only 1000 kg,will the captain live to see his goal?

a. Yes, apply the momentum principle, include gammab. No

Problem 5.

Will the captain reach the nearest star outside our solar system, which is about 2 lightyears away? (Use the constant force approximation for the average speed.)

a. Yes, apply position update formula, calculate a light-yearb. No

Problem 6.

An electron and proton are near each other. What is the direction of r in the electric

force law

Fon electron by proton =

14πε0

qeqpr 2 r ?

a. It points from the electron to the proton.b. It points from the proton to the electron.c. It points from the reference point to the electron.d. It points from the reference point to the proton.

Problem 7.

For the following speeds determine whether or not it is valid to approximate gamma as 1.

I. A proton zips by at 2.934E7 m/s.II. A cosmic ray flies by at 2.9E7 m/sIII. You ride your bike to school at 10 m/s

a. I and II onlyb. I and III onlyc. I, II and IIId. II and III only, remember precisione. I onlyf. II onlyg. III only

Problem 8 – 9.

The position and momentum of a bee is displayed by the vectors in the graph below.

Problem 8.

What is the significance of the location of the tip of the momentum vector on the graph(<-2, 4, 0>[m])?

a. It is where the bee is.

X

Y

b. It is where the bee will be at a later time.c. It has no significance on the position graph.d. It is where the bee was at an earlier time.

Problem 9

What is the significance of the location of the tip of the position vector on the graph (<3,3, 0>[m])?

a. It is where the bee is.b. It is where the bee will be at a later time.c. It has no significance on the position graph.d. It is where the bee was at an earlier time.

Problem 10 - 12.

Problem 10.

Which vectors are equal to r ?

a. a e.

a , b i.

c , d

b. b f.

a , c j.

b , c , d

c. c C g.

a , b , c

d. d h.

a , b , c , d

X

Y

Problem 11.

Which vectors have the same magnitude as r ?

a. a e.

a , b i.

c , d

b. b f.

a , c j.

b , c , d

c. c g.

a , b , c g

d. d h.

a , b , c , d

Problem 12.

Which share the same unit vector as r ?

a. a e.

a , b i.

c , d i

b. b f.

a , c j.

b , c , d

c. c g.

a , b , c

d. d h.

a , b , c , d

Problem 13.

Which of the following are vectors?I.

rII. rIII.

r

IV. r r

a. I and II onlyb. I and III onlyc. I , II and III onlyd. I, II , III and IVe. I, II and IV onlyf. I and IV onlyg. II, III and IV only

Problem 14.

About how big is an atom?a. 1E-6 [m]b. 1E-8 [m]c. 1E-10 [m]d. 1E-12 [m]e. 1E-15 [m]f. 1E-18 [m]

Problem 15.

For the following situations state whether an interaction occurred.I. A runner speeds up on a straight track.II. A spaceship travels at constant velocity in deep space.III. A balloon floats stationary in the air.

b. I onlyc. II onlyd. III onlye. I and II onlyf. I, II and IIIg. I and III onlyh. II and III only

Problem 16 – 17.

Remarkable data indicate the presence of a massive black hole at the center of our MilkyWay galaxy. The star nearest the center of our galaxy was observed to be about 1E14 mfrom the center, with a period of about 15 years. Assume the orbit is circular.

Problem 16.

What is the value of gamma for this speed?a. 1.1b. 1.01c. 1.001d. 1.0001e. 1.00001

f. 1.000001

Problem 17.

What is the mass of the black hole?a. 2.6E36 kgb. 3.2E37 kgc. 4.0E32 kgd. 2.2E34 kge. 2.4E35 kgf. 3.2E36 kg

Problem 18.

A spring has a relaxed length of 1.5 m and spring constant 300 N/m. You attach a massof 0.4 kg to one end of the spring, and then swing the ball around your head in a circle,causing the spring to stretch to a new length of 1.8 m. What is the speed of the ball?

a. 36.7 m/sb. 405 m/sc. 161 m/sd. 12.7 m/se. 20.1 m/s, equate circular motion to the spring forcef. 14.0 m/s

Problem 19.

Two cannon balls are dropped together from the top of the Leaning Tower of Pisa. Onehas mass M, the other has mass 4M. Ignore the effects of air on these two objects.Choose the correct statement:

a. The two balls experience equal forces, and hit the ground at the same time.b. The two balls had equal changes in velocity, and hit the

ground at the same time.c. The two balls had equal changes in momenta, and hit the ground at the same time.d. None of the above.

Problem 20.

A 500 kg car with velocity <20, 0, 0> [m/s] is traveling east on SR 26 and collides into a900 kg truck with velocity <0, 0, 5.0> [m/s] that is traveling south on 9th street inLafayette. If the two cars stick together because of the impact, what is their final velocityright after the collision?

a. <20, 0, 5.0> [m/s]b. <7.1, 0, 2.9> [m/s], conservation of momentumc. <2.4, 0, 7.7> [m/s]d. <3.3, 0, 2.1> [m/s]

Hand Written Problems

Name (print)__________________________________ TA Name__________________

Signature_____________________________________

Two blocks of mass m1 and m3, connected by a rod of mass m2, are sitting on a verysmooth table, and you push to the left on the right block (mass m1) with a constant force.State the system and surroundings and draw a force diagram every time your systemchanges.

a. What is the accelaration dvx /dt of the blocks?Sys: m1, m2 and m3Surr: table (negligible force, very smooth), hand (constant force

Fhand )

Force diagram:

Δp =FnetΔt →vc→ MtotΔ

v =FnetΔt

→ (m1 + m2 + m3 )Δv/Δt =Fhand

→ Δv/Δt =Fhand /(m1 + m2 + m3 )

→ Δv/Δt = −Fhand ,0,0 /(m1 + m2 + m3 )

→ Δvx /Δt = −Fhand /(m1 + m2 + m3 ) Note: When the quantities are kept in variableform (ie. Letters not numbers) then the units are implied with the variable (ie. m meansmass in units of kg). If your answer is numerical then units must be applied.Nevertheless, even in variable form it is useful to check the units to make sure they arecorrect.

m3 m1

m2

m3 m1

m2

y

xFhand

b. What is the compression force in the rod (mass m2) near its right end? Near its leftend?For the right compression force:Sys: m2 and m3Surr: table (negligible force, very smooth), m1 (compression force from the right

FcompR )

Force diagram:

Δp =FnetΔt →vc→ (m2 + m3 )Δv =

FnetΔt

→ (m2 + m3 )Δv/Δt =FcompR

plug in for Δv/Δt since the blocks all have the same acceleration

→ (m2 + m3 )Fhand /(m1 + m2 + m3 ) =

FcompR

→

m2 + m3

m1 + m2 + m3

⎛⎝⎜

⎞⎠⎟Fhand =

FcompR

→FcompR =

m2 + m3

m1 + m2 + m3

⎛⎝⎜

⎞⎠⎟−Fhand ,0,0 Note: the direction is in the –x as it should.

For the left compression force:Sys: m2Surr: table (negligible force, very smooth), m1 (compression force from the right

FcompR )

and m3 (compression force from the left FcompL )

Force diagram:

Δp =FnetΔt →vc→ (m2 )Δv =

FnetΔt

→ m2Δv/Δt =

FcompR +

FcompL

plug in for Δv/Δt since the blocks all have the same acceleration

→ m2

Fhand /(m1 + m2 + m3 ) −

FcompR =

FcompL

plug in for FcompR just found

m3 m1

m2

y

xFcompR

m3 m1

m2

y

xFcompR

FcompL

→

m2

m1 + m2 + m3

⎛⎝⎜

⎞⎠⎟Fhand −

m2 + m3

m1 + m2 + m3

⎛⎝⎜

⎞⎠⎟Fhand =

FcompL

→FcompL =

−m3

m1 + m2 + m3

⎛⎝⎜

⎞⎠⎟Fhand

→FcompL =

−m3

m1 + m2 + m3

⎛⎝⎜

⎞⎠⎟−Fhand ,0,0

→FcompL =

m3

m1 + m2 + m3

⎛⎝⎜

⎞⎠⎟

Fhand ,0,0 Note: the direction is in the +x as it should.

c. How would these results change if you pull to the left on the left block (mass m3) withthe same force, instead of pushing the right block?

For the acceleration the system won’t change and the net vector force is the same so theacceleration won’t change.

The systems for the left and right compression forces switch as well as the direction ofthe net vector forces so these two forces also switch (the solutions for the left and rightcompression forces switch with m1 and m3 switching as well.

→FcompR =

m1

m1 + m2 + m3

⎛⎝⎜

⎞⎠⎟

Fhand ,0,0 →FcompL =

m2 + m1

m1 + m2 + m3

⎛⎝⎜

⎞⎠⎟−Fhand ,0,0

m3 m1

m2Fhand

y

x

m3 m1

m2

y

xFcompL

m3 m1

m2

y

xFcompL

FcompR