Page 166 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 12] SIMPLE MACHINES 151

THE INCLINED PLANE
In an inclined plane, the ratio between the input distance and the output distance is the same as the ratio between
the length L of the plane and its height h (Fig. 12-8). Hence the IMA of an inclined plane is
L
IMA =
h
Wedges, cams, and screws are all developments of the inclined plane.
A screw is an inclined plane wrapped around a cylinder in the form of a helix. The pitch p of a screw is the
distance from one thread to the next (Fig. 12-9). If the head of a screw is turned by a tangential force applied
at a distance L from its axis, the input force travels the distance s in = 2π L while the screw advances s out = p.
Hence the IMA of a screw is
s in 2π L
IMA = =
s out p

Fig. 12-8 Fig. 12-9

SOLVED PROBLEM 12.9

A ramp 25 m long slopes down 1.4 m to the edge of a lake. How much force is needed to pull out a
360-kg boat on a 90-kg trailer if friction in the trailer’s wheels reduces the efficiency to 90 percent?

The IMA of the ramp is
L 25 m
IMA = = = 17.9
h 1.4m
and its AMA is

AMA = (Eff)(IMA) = (0.9)(17.9) = 16.1
The output force is the combined weight of boat and trailer, which is
2
F out = w = (m 1 + m 2 )g = (450 kg)(9.8 m/s ) = 4410 N
The required input force is
4410 N
F out
F in = = = 274 N
AMA 16.1
SOLVED PROBLEM 12.10
The screw of a machinist’s vise has a pitch of 5 mm and a handle 20 cm long. If the efficiency is 40 percent,
how much force is developed between the jaws of the vise when a force of 40 N is applied to the end of
the handle?