Mechanical Advantage and Efficiency

Chapter 14 Section 3

Mechanical Advantage

• The mechanical advantage of a machine is the number of times that the machine increases an input force

• Suppose a nut is in a nutcracker at position A

• In this position the nutcracker exerts a force on the nut about seven times greater than the force you exert on the nutcracker.

• In position A the nutcracker's mechanical advantage is about 7

A

Mechanical Advantage

• However, if the nut is moved to position B, the mechanical advantage decreases to about 3.

B

Actual Mechanical Advantage

• The mechanical advantage determined by measuring the actual forces acting on a machine is the actual mechanical advantage.

• The actual mechanical advantage (AMA) equals the ratio of the output force to the input force.

Actual Mechanical Advantage

• A loading ramp is a machine used to move heavy items into a truck.

• For instance, a long inclined ramp decreases the input force needed to lift a refrigerator into a truck.

• The mechanical advantage of a ramp with a rough surface is less than that of a similar smooth ramp because a greater force is needed to overcome friction.

Ideal Mechanical Advantage

• What can be done to increase the actual mechanical advantage of a ramp?

• One way is to reduce the friction of the ramp. • In fact, if any machine were frictionless, its

mechanical advantage would be the maximum possible value.

Ideal Mechanical Advantage

• The ideal mechanical advantage (IMA) of a machine is the mechanical advantage in the absence of friction.

• Because friction is always present, the actual mechanical advantage of a machine is always less than the ideal mechanical advantage.

• Because friction reduces mechanical advantage, engineers often design machines that use low-friction materials and lubricants.

Calculating Mechanical Advantage

• Ideal mechanical advantage is easier to measure than actual mechanical advantage

• Because it depends only on the locations of the forces and the distances over which they act.

Calculating Ideal Mechanical Advantage

• To calculate the ideal mechanical advantage of any machine, divide the input distance by the output distance.

• Remember that the effects of friction are neglected when calculating ideal mechanical advantage.

Mechanical Advantage

• The gondola makes use of the inclined plane formed by its supporting cable to more easily move people uphill.

• The increased horizontal distance (input distance) is greater than the vertical gain in height (output distance).

• Thus the inclined cable gives the gondola a mechanical advantage greater than 1.

Calculating Ideal Mechanical Advantage

• A woman drives her car up onto wheel ramps to perform some repairs. If she drives a distance of 1.8 meters along the ramp to raise the car 0.3 meter, what is the ideal mechanical advantage (IMA) of the wheel ramps?

Efficiency

• Because some of the work input to a machine is always used to overcome friction, the work output of a machine is always less than the work input.

• The percentage of the work input that becomes work output is the efficiency of a machine

• Because there is always some friction, the efficiency of any machine is always less than 100 percent.

Efficiency

• Efficiency is usually expressed as a percentage.

Efficiency

• Reducing friction increases the efficiency of a machine.

• Automobiles, for example, are designed so their wheels roll on bearings that contain many small steel rollers.

• Recall that rolling friction is less than sliding friction. • Thus, the roller bearings reduce the friction of the

rotating wheels. • To further reduce the rolling friction, the roller

bearings are also lubricated with grease.

1. A student working in a grocery store after school pushes several grocery carts together along a ramp. The ramp is 3 meters long and rises 0.5 meter. What is the ideal mechanical advantage of the ramp?

2. A construction worker moves a crowbar through a distance of 0.50 m to lift a load 0.05 m off of the ground. What is the IMA of the crowbar?

3. The IMA of a simple machine is 2.5. If the output distance of the machine is 1.0 m, what is the input distance?

4. You have just designed a machine that uses 1000 J of work from a motor for every 800 J of useful work the machine supplies. What is the efficiency of your machine?

5. If a machine has an efficiency of 40%, and you do 1000 J of work on the machine, what will be the work output of the machine?