Page 47 - Fisika Terapan for Engineers and Scientists

8.2 The Curve of Potential Energy 247

(a) (b)

x = 9.0 m jump-off
point

U(x)

taut cord
0
point
10 000 J
E
5 000

x x
x 1 0
–20 –10 0 10 20 m
FIGURE 8.12 (a) The origin for the x
coordinate is at the point where the rubber
For x 0, the For x 0, the
turning cord becomes taut. The jump-off point is at
x 0 cord is taut, so cord is slack,
point 2
1
U = mgx + kx . so U = mgx. x 9.0 m, and the turning point is at some
2
negative value of x. (b) Curve of potential
energy for the bungee jumper. The red line
indicates the energy level.This line intersects
the curve at approximately x 15 m.This
is the turning point for the jumper.
COMMENTS: If there were no friction, the motion would reverse, and the jumper
would ascend to the bridge and bang against it. However, like a bouncing ball, the
rubber cord has some energy loss due to friction within the material, and the jumper
will not bounce back as high as the starting point.
Bungee jumping is a dangerous stunt.The human body has poor tolerance to
deceleration in the head-down position.The pooling of blood in the head can lead
to loss of consciousness (“redout”), rupture of blood vessels, eye damage, and tem-
porary blindness. And in several instances, jumpers were killed by smashing their
heads into the ground or by becoming entangled in their cords during the fall.

✔ Checkup 8.2

QUESTION 1: A particle moving in one dimension under the influence of a given con-
servative force has either no turning point, one turning point, or two turning points,
depending on the energy. Does the number of turning points increase or decrease
with the energy? Is there any conceivable value of the energy that will result in three
turning points?
QUESTION 2: By examining the curve of potential energy in Fig. 8.12, estimate at what
points the bungee jumper attains his maximum downward speed and his maximum
acceleration.
QUESTION 3: A particle moving under the influence of the spring force has a positive
energy E 50 J. How many turning points are there for this particle?
(A) 1 (B) 2 (C) 3 (D) 0