8.3. Simple Machines http://www.ck12.org
Example Problem:
(a) How much force is required to lift a 500. kg stone using an ideal lever whose resistance arm is 10.0 cm and
whose effort arm is 2.00 m?
(b) What is the IMA?
(c) If the actual effort force required to lift the stone was 305 N, what was the AMA?
Solution:
(a)(resistance force)(resistance arm) = (effort force)(effort arm)
effort force=(resistance force(effort arm)(resistance arm) )=(^4900 (N 2. 00 )(^0 m.^100 ) m)=245 N
(b) IMA=resistance armeffort arm = 02 .. 10000 mm= 20
(c) AMA=resistance forceeffort force =^4900305 NN= 16
Pulley
Apulleyis a wheel on an axle that is designed to rotate with movement of a cable along a groove at its circumference.
Pulleys are used in a variety of ways to lift loads, apply forces, and to transmit power, but the simplest of pulleys
serves only to reverse the direction of the effort force. It consists of a single pulley attached directly to a non-moving
surface with a rope or cable through it. As a downward force is applied to one side of the pulley, the other side of
the pulley, with the attached resistance force, is pulled upward. This type of pulley is called a fixed pulley, and is
labeledAin the image below.
Another type of pulley is shown above asB. This type of pulley is called a movable pulley.A set of pulleys
assembled so they rotate independently on the same axle form a block. It is shown below in a system called a block
and tackle. A block and tackle consists of two blocks, in which one block is fixed and the other is movable; the
movable block is attached to the load.
The IMA of a pulley system can be determined by counting the number of supporting strands of rope in the system.
Be careful though, because in some systems the rope to which the effort force is applied will be a supporting strand,
but in others it is not. For example, in the image above with the five pulley systems, the rope to which the effort
force is applied (the one with the arrowhead) inAis not a supporting strand because it does not hold up any of the
weight of the load. The IMA ofAis 1. InB, however, the effort rope is supporting half of the weight of the load and
is therefore a supporting strand.Bhas 2 supporting strands and an IMA of 2.
Example Problem:Determine the IMA forC, D,andEin the image above.
Solution: