Page 68 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 5] LAWS OF MOTION 53

2
(a) w = mg = (5kg)(9.8 m/s ) = 49 N
(b) From the second law of motion F = ma, we have
F 100 N
a = = = 20 m/s 2
m 5kg

SOLVED PROBLEM 5.10
A force of 1 N acts on (a) a body whose mass is 1 kg and (b) a body whose weight is 1 N. Find their
respective accelerations.
F 1N
(a) a = = = 1 m/s 2
m 1kg
(b) The mass of a body whose weight is w is m = w/g. Hence, in general,
F F F
a = = = g
m w/g w
2
Here F = w = 1 N, so the acceleration is a = g = 9.8 m/s .

SOLVED PROBLEM 5.11
A net horizontal force of 4000 N is applied to a car at rest whose weight is 10,000 N. What will the car’s
speed be after 8 s?

To find the car’s acceleration from the second law, we need its mass, not its weight. The mass is
w 10,000 N
m = = = 1020 kg
g 9.8 m/s 2
The car’s acceleration when a 4000-N net force is applied is
F 4000 N 2
a = = = 3.92 m/s
m 1020 kg
The car’s speed 8 s after the acceleration began is
2
v = at = (3.92 m/s )(8s) = 31.4 m/s

BRITISH SYSTEMOFUNITS
In the British system, the unit of mass is the slug and the unit of force is the pound (lb). A net force of 1 lb acting
2
on a mass of 1 slug gives it an acceleration of 1 ft/s . Here is how units of mass and force in the SI and British
systems are related:
3
1kg = 10 g = 0.0685 slug (1 kg corresponds to 2.21 lb in the sense
that the weight of 1 kg is 2.21 lb)
1 slug = 14.6 kg (1 slug corresponds to 32 lb in the sense
that the weight of 1 slug is 32 lb)
1N = 0.225 lb
1lb = 4.45 N
Table 5.1 relates the SI and British systems to mass and weight.

SOLVED PROBLEM 5.12
(a) What is the weight of an object whose mass is 50 slugs? (b) What is the mass of an object whose
weight is 50 lb?