Math 317, Section 202, Homework no. 6
(due Wednesday (!) March 3, 2010)
[10 problems, 48 points + 8 bonus points]
Problem 1
(6 points)
.
An object of mass
m
= 2 moves along the trajectory
(1)
r
(
t
) =
t
4
2
i

t
4
j
+
t
4
4
k
,
0
≤
t
≤
1
,
(2)
r
(
t
) =
1
√
2
cos
t
i

1
√
2
cos
t
j
+ sin
t
k
,
0
≤
t
≤
2
π.
Time is denoted by
t
. For each trajectory (1) and (2),
(a) determine the tangential and the normal component of acceleration,
(b) find the force
F
(
t
) that acts on the object, as a function of time,
(c) compute the work done by
F
in moving the object along the trajectory.
(1 point for each combination of part (a) to (c) with a trajectory (1) or (2))
Problem 2
(8 points)
.
Consider the force given by the vector field
F
(
x, y, z
) =
c
h
z, x, zy
i
,
with some constant
c
.
(a) (6 points, 2 points for each trajectory) Compute the work done by the force
F
in moving
a particle of mass
m
= 1 along each of the following trajectories.
t
denotes time.
(1)
r
(
t
) =
h
t,
0
,
3

3
t
i
, 1
≤
t
≤
2,
(2)
r
(
t
) =
h
2
t,
0
,
3

6
t
i
, 1
/
2
≤
t
≤
1,
(3)
r
(
t
) =
t,
0
,
1

t
2
, 1
≤
t
≤
2.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '10
 phfiier
 Force, Continuous function, Line segment

Click to edit the document details