Page 95 - Schaum's Outline of Theory and Problems of Applied Physics

80 ENERGY [CHAP. 7

The gravitational potential energy of a body of mass m at a height h above a given reference level is

Gravitational potential energy = PE = mgh

where g is the acceleration of gravity. In terms of the weight w of the body,

PE = wh

SOLVED PROBLEM 7.19
A 1.5-kg book is held 60 cm above a desk whose top is 70 cm above the floor. Find the potential energy
of the book (a) with respect to the desk, and (b) with respect to the floor.
(a) Here h = 60 cm = 0.6m,so

2
PE = mgh = (1.5kg)(9.8 m/s )(0.6m) = 8.8J
(b) The book is h = 60 cm + 70 cm = 130 cm = 1.3 m above the floor, so its PE with respect to the floor is

2
PE = mgh = (1.5kg)(9.8 m/s )(1.3m) = 19.1J

SOLVED PROBLEM 7.20
Compare the potential energy of a 1200-kg car at the top of a hill 30 m high with its kinetic energy when
its velocity is 100 km/h (27.8 m/s).

5
2
PE = mgh = (1200 kg)(9.8 m/s )(30 m) = 3.5 × 10 J
1 2 2 5
1
KE = mv = (1200 kg)(27.8 m/s) = 4.6 × 10 J
2 2
The KE of the car at this velocity is greater than its PE at the top of the hill. This means that a crash at 100 km/h
(62 mi/h) into a stationary obstacle will yield more work—that is, do more damage—than dropping the car from a
height of 30 m (98 ft).

SOLVED PROBLEM 7.21
(a) A 125-lb woman jumps off a wall 3 ft high and lands on a concrete road with her knees stiff. Her
body is compressed by 3 in. at the moment she hits the road. What is the average force exerted on her
by the road? (b) If the woman bends her knees on impact so that she comes to a stop over a distance of
12 in., what would the force on her be?

(a) The woman’s potential energy with respect to the road is converted to work done on her body. Here s = 3 in.
= 0.25 ft. Setting her initial PE equal to the work done,

wh = Fs
wh (125 lb)(3ft)
F = = = 1500 lb
s 0.25 ft
(b)Now s = 12 in. = 1 ft, and

wh (125 lb)(3ft)
F = = = 375 lb
s 1ft
Clearly it is safer to land with bent knees rather than rigid knees after falling through even a short distance.