A simple wheel and axle has a wheel diameter of 2.3 m and requires an effort of 26 N to raise a mass of 16 kg. What is the efficiency of the machine?

To determine the efficiency of the simple wheel and axle, we start by calculating the theoretical mechanical advantage (MA) and then use that to find efficiency.

The mechanical advantage for this system can be calculated using the ratio of the load force (weight of the mass) to the effort force applied. The weight of the mass can be found using the equation:

Weight = mass × gravitational acceleration.

Assuming gravitational acceleration is approximately 9.81 m/s², the weight of the 16 kg mass would be:

Weight = 16 kg × 9.81 m/s² = 156.96 N.

Now, the mechanical advantage (MA) is:

MA = Load / Effort = 156.96 N / 26 N = 6.04.

Next, we can compute the efficiency of the machine using the formula:

Efficiency (%) = (MA / Ideal Mechanical Advantage) × 100%.

The ideal mechanical advantage (IMA) for a wheel and axle is defined as the radius of the wheel divided by the radius of the axle. The radius of the wheel would be half of the diameter, so:

Radius of the wheel = 2.3 m / 2 = 1.15 m.

If we assume the axle