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
.
=
$$4√3
=
$$−4
x
(
t
) =
8 sin
t
,
v
(
t
) =
$$8
cos
(
t
)
a
(
t
) =
$$−8
sin
(
t
)
x
2
π
3
v
2
π
3

=
$$−4√3
In what direction is it moving at that time?
Since
<
0, the particle is moving to the
left
.
a
2
π
3
v
2
π
3

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
=
70
lb and
μ
=
0.5
, draw the graph of
F
as a function of
θ
.