1. [1pt]
An angstrom is an older unit of length,
defined as 10-10m.
A ly is a light-year, the distance light travels in 1 year.
(Give ALL correct answers, i.e., B, AC, BCD...)
A) 8.0ly = 7.6x 1027 angstrom
B) 5.0m = 5.0x 1011 angstrom
C) 3.0 angstrom = 30nm
D) 9.0 angstrom = 9.0x 105fm
E) 9.0 angstrom = 9.0x 106fm
F) 3.0 angstrom = 0.3nm
G) 8.0ly = 7.6x 1026 angstrom
H) 5.0m = 5.0x 1010 angstrom
Correct, computer gets: DFGH
2. [1pt]
Calculate the volume of a spherical balloon which has a surface area of 0.0555
m2.
Area and Volume relations
Correct, computer gets: 1.23E-03 m^3
Hint: The area of a sphere is given by 4 times pi times r squared. this allows
you to calculate the radius. then, the volume of a sphere is given by: 4/3 pi r
cubed.
3. [1pt]
(This is a tough one! Read the hint which appears after you submit one wrong
answer.) The graph on your paper represents the function F(x)=ax b
Make a careful determination of the value of b. You have to get within 10\% of
the correct answer to get credit.
Correct, computer gets: 2.60E+00
Hint: Pick two points on the graph x1 and x2, and read F(x1) and F(x2). You
then have two equations F(x1)=a*x1^b and F(x2)=a*x2^b in two unknowns a
and b. Solve for b. A useful value of x to pick is x=1
4. [1pt]
Find the slope of the function at x = 1.5 for the curve above.
Correct, computer gets: 1.74E+01
5. [1pt]
Evaluate the definite integral from 1.90 to 3.70 of (x2 +3x)dx
Correct, computer gets: 2.972E+01
6. [1pt]
A Boeing 737 jet taking off from Denver airport accelerates from rest for 30.0 s
before leaving the ground. Its acceleration is 0.21 g's. Assuming that the
acceleration is constant, calculate the plane's speed at take off.
Correct, computer gets: 6.18E+01 m/s
Hint: The acceleration due to gravity g on the surface of the Earth is g=9.81
m/s^2.
7. [1pt]
How much work must be done to stop a 1360kg car traveling at 114km/hr?
Correct, computer gets: -6.82e+05 J
Hint: Is the work positive or negative?
8. [1pt]
How far above the Earth's surface will the acceleration of gravity be half of
what it is on the surface?
Correct, computer gets: 2.64e+03 km
9. [1pt]
The components of a vector V are often written (Vx, Vy, Vz). What is the z
component of a vector which is the sum of the two vectors, V1 and V2, whose
components are (3.43, 2.19, 0.00) and (2.34, -4.73, -1.26)?
Correct, computer gets: -1.26
10. [1pt]
Calculate the length of this vector.
Correct, computer gets: 6.43
Worked Out Answers:
1. Google calculator will do this if you have problems.
A  4r 2
A
4
r
2.
4 3 4  A 3 / 2
V  r 

3
3  (4 ) 3 / 2
A3 / 2
V 
3(4 )1 / 2



3. Choose two points on the graph. A convenient one is x=1
F (1)  a 2 b  F (1)  a
F ( 2)
 2b
a
 F ( 2) 


a


b  log
 2 




4. Plug in the values of a and b from problem 3.
x' 
dF
dx
x'
dF
 bax b 1
dx
5.
b
 (x
2
 cx)dx
a
x 3 cx 2


3
2
a
 a 3 ca 2   b 3 cb 2 
   

  
3
2
3
2
 

b 
6. V f  vi  at
7. This one is tricky because of units. Make sure you convert the initial velocity into m/s and use
your mass in kg.
Ke  Ke final  Keinitial 
1 2
1
mv final  mv 2 initial
2
2
v final  0
vinitial  vinitail *
1000m 1hr
*
1km 3600s
1
W   mv 2 initial
2
g r  kg s
GM E
r 2E
kGM
gs  2 E
r E
GM E kGM E
 2
8.
r2E
r E
2
r E
r2 
k
1
r
* rE
k
gr 

1

r  rE  rE 1 
k 

9.
V1  (V1x  V1 y  V1z )
V2  (V12  V2 y  V2 z )
V1  V2  V1x  V2 x  V1 y  V2 y  V1z  V2 z ) 
10.
length   (V 2 x  V 2 y  V 2 z )
V1  V2 length  (V1x  V2 x ) 2  (V1 y  V2 y ) 2  (V1z  V2 z ) 2