5.
7/7 points |
Previous Answers
SCalcET7 3.3.035.MI.
A mass on a spring vibrates horizontally on a smooth level surface (see the figure). Its equation of motion is
where
t
is in
seconds and
x
is in centimeters.
(a) Find the velocity and acceleration at time
t
(b) Find the position, velocity, and acceleration of the mass at time
t
=
2
π
/
3
=
x
(
t
) =
8 sin
t
v
(
t
) =
$$8
cos
(
t
)
a
(
t
) =
$$
−
8
sin
(
t
)
x
2
π
3
.
.
,

In what direction is it moving at that time?
.

6.
5/5 points |
Previous Answers
SCalcET7 3.3.038.
An object with weight
W
is dragged along a horizontal plane by a force acting along a rope attached to the object. If the rope makes an
angle
θ
with the plane, then the magnitude of the force is
where
μ
is a constant called the
coefficient of friction
(a) Find the rate of change of
F
with respect to
θ
F
=
µ
W
μ
sin
θ
+ cos
.
.
θ

(b) When is this rate of change equal to 0?

(c) If
W
=
60
lb and
μ
=
0.5
, draw the graph of
F
as a function of
Use the graph to locate the value of
θ
for which
dF
/
d
θ
= 0. (Round your answer to two decimal places.)
θ
.