Lesson 4 Objective

At the end of this section, you should be able to:

• determine whether the machines are force multipliers, speed multipliers,
  or direction changers;
• define the terms work input, work output, effort, load, mechanical advantage
  (M.A), velocity ratio (V.R) and efficiency (ƞ´);
• derive the expression for efficiency;
• calculate mechanical advantage and efficiency of simple machines.

Brainstorming Question

Simple machines in real world are not 100% efficient. Why? Is it possible to transfer all input energy to output energy using simple machines?

key terms and concepts

• AMA= load/effort.
• V.R=distance moved by effort/distance moved by the load.
• Efficiency ( ƞ) = M.A/V.R.
  

Mechanical Advantage (M.A)

Different simple machines can be used to perform the same task. For instance, nails can be pulled from wood using either a pair of pliers or a claw hammer. A claw hammer, which acts as a first-class lever, requires less effort by converting a small input force into a much larger output force. This conversion gives the hammer mechanical advantage.

Mechanical Advantage (M.A) = Output Force / Input Force

For example, if a load of 400 N is lifted with a force of 160 N using a lever, the mechanical advantage is:

M.A = Load / Effort = 400 N / 160 N = 2.5

Mechanical advantage has no units; it’s a ratio comparing input to output forces. When the input and output forces are equal, the mechanical advantage is 1. Machines with a mechanical advantage greater than 1 act as force multipliers.

There are two types of mechanical advantages:

• Actual Mechanical Advantage (AMA): Compares the output force (load) to the input force (effort).
• Ideal Mechanical Advantage (IMA): Theoretical mechanical advantage assuming no energy losses.

In practice, IMA is always greater than AMA due to factors like friction.

Velocity Ratio (V.R)

The term velocity ratio describes the ratio of the distance moved by the effort to

the distance moved by the load.

Velocity ratio (V.R) = distance moved by the effort/distance moved by the load

                               = d_E/d_L

Velocity ratio has no units.

Example 5.2

A load of 200 N is lifted by applying a force of 80 N on the lever. If the load is 10 cm

from the fulcrum and the effort is 40 cm from the fulcrum, calculate the V.R of the

lever.

Given: d_L= 10 cm, d_E = 40 cm, Required: V.R=?

Solution:

The velocity ratio of the lever is V.R = dE/dL = 40cm/10cm = 4

Efficiency of Machines(ƞ)

Efficiency measures how well a machine converts input energy into useful output energy. Due to friction, efficiency is always less than 100%. It’s calculated as the ratio of work output to work input, often expressed as a percentage.

Efficiency (ƞ) = power output/power input = work output/work input

Similar to M.A and V.R, efficiency has no units since it is ratio.

Efficiency can also be expressed in terms of M.A and V.R.

ƞ = work output/work input = load x distance moved by load/effort x distance moved by effort

But

$\frac{ load}{effort}$ = M.A

 and  

$\frac{distance moved by load}{distance moved by effort}$ = $\frac{1}{V.R}$

ƞ= $\frac {M.A}{V.R}$

Example: If a motor uses 1000 joules of energy to lift a box but only 800 joules of energy is effectively used to lift the box, the efficiency of the motor is 800 J/1000 J×100=80%

Designing Simple Machine

Now that you understand the six types of simple machines and their mechanical advantages, you’ve likely noticed how people in your community work. Many tasks, like lifting water from a deep well or carrying heavy loads, could be made easier with simple machines.

1. List activities which need simple machine in your community;

2. Prioritize and select one activity in group,

3. Collect the necessary materials,

4. Design a machine that includes at least two simple machines.