Physics

Version 054 – Exam 1 – Chiu – (56645)

This print-out should have 16 questions.

Multiple-choice questions may continue on

the next column or page – find all choices

before answering.

10.0 points

001

A proton of mass

mp = 1.7 × 10−27 kg

1

Substituting the appropriate values we obtain

∆r = 0.238 m

Note : For relativistic calculations it is convenient to work with dimensional quantities

such as

v

= 0.3961

c

β=

and with a constant momentum of

0, 0, 2.2 × 10−19 kg.m/s

γ=

is created in an accelerator experiment. How

far did the proton travel in 2 ns? (Given that

the speed of light is 3 × 108 m/s)

1. 0.381

2. 0.397

3. 0.277

4. 0.387

5. 0.308

6. 0.418

7. 0.364

8. 0.238

9. 0.26

10. 0.312

1

1−

γβ =

v2

c2

|p|

= 0.4314

mc

There is a useful identity which takes the form

β=

γβ

1 + (γβ )2

Hence, the position update formula becomes

∆r = β c ∆t = 0.238 m

Correct answer: 0.238 m.

Explanation:

Let : |p| = 2.2 × 10−19 kg.m/s ,

c = 3 × 108 m/s ,

mp = 1.7 × 10−27 kg , and

∆t = 2 × 10−9 s .

The expression for the displacement is given

by

1

rf − ri =

2

1+

|p|

mp 2 c2

p

mp

Thus, the expression for |rf − ri | is

=

1

|p|2

1+

mp 2 c2

|p|

mp

∆t

∆t

002 10.0 points

A star with mass M is located at the origin

and a planet m is located at

r = (x, y, 0)

where x = 3.1 × 1011 km, y = 4.7 × 1011 km.

Let us write the y-component of the gravitational force which the star is pulling the planet

GmM

by the expression Fy =

K . Determine

r2

the value of K

1. 0.749

2. 0.718

3. 0.835

4. 0.805

5. 0.871

6. 0.824

7. 0.695

8. 0.845

9. 0.855

Version 054 – Exam 1 – Chiu – (56645)

2

10. 0.628

4. Id, IIb correct

Correct answer: 0.835.

5. Id, IIa

Explanation:

6. Ia, IIb

Let : x = 3.1 × 1011 km ,

y = 4.7 × 1011 km ,

z = 0 km .

and

8. Ic, IIb

Here, ˆ is the unit vector and r =

r

2 + y 2 + z 2 The gravitational force is

x

given by

F=

GM m...