Biomedical Engineering Reference
In-Depth Information
(a) Decompose the weight
W
of the child in orthogonal components
W
x
and
W
y
in
relation to the plane of the slide and obtain the value of these components.
(b) Find the value of the normal force exerted by the surface of the slide on the
child.
(c) Evaluate if the child will slide down when she or he lets go.
(d) Find the force of kinetic friction.
(e) Determine the acceleration of the child sliding down.
(f) Discuss what happens if the angle
θ
is greater than 45
.
(a) If the angle
θ
between the slide and the ground is 45
, the angle between
W
y
and
W
will also be 45
, since both sides of the angles are mutually perpendicular.
Then,
cos 45
¼
s
2
W
y
¼
W
cos
θ ¼
ð
20 kg
Þ
10 m
=
ð
200 N
Þ
0
:
707
¼
141
:
4N
:
sin 45
¼
s
2
W
x
¼
W
sin
θ ¼
ð
20 kg
Þ
10 m
=
ð
200 N
Þ
0
:
707
¼
141
:
4N
:
(b) As
N
¼
W
y
,
N
¼
141.4 N.
(c)
f
s
¼
¼
¼
113.1 N; the child goes down the slide, since
W
x
0.8 N
0.8(141.4 N)
is greater than
f
s
.
(d)
f
k
¼
0.6 N
¼
0.6(141.4 N)
¼
84.8 N.
2.83 m/s
2
.
(e)
a
¼
(
W
x
f
k
)/
m
¼
(141.4
84.8 N)/(20 kg)
¼
is increased, for example, to 60
, cos60
¼
0.5 and sin60
(f) If the angle
θ
¼
0.866. In these conditions,
W
y
¼
(200 N)0.5
¼
100 N decreases, and, as a
consequence,
the value of normal
force
N
decreases. Then,
f
s
¼
0.8
(100 N)
80 N will also be smaller, meaning that the child will slide more
easily and the acceleration will be greater. If, on the other hand, the angle is
decreased, the opposite happens.
¼
1.8 Pressure
The concept of pressure is associated with the force applied on a body. Pressure
p
is
defined as the force per unit area exerted perpendicularly on a surface.
Pressure
p
on the surface of the block exerted by the palm of the hand, as shown
in Fig.
1.13
, can be written by (
1.5
):
F
y
A
;
p
¼
(1.5)
where
F
y
is the component of force
F
perpendicular to the surface of block and
A
is
the area of the palm of the hand. Pressure is inversely proportional to area.
Therefore, for the same applied force, the pressure will be greater the smaller the
area. Knives and scissors also work in this same way. The sharper they are, the more
