In a wheel and axle mechanism the diameters of the wheel and axle are 40cm and 8cm respectively. Given that the machine is 80% efficient, what effort is req...

In a wheel and axle mechanism the diameters of the wheel and axle are 40cm and 8cm respectively. Given that the machine is 80% efficient, what effort is required to lift a load of 100N?

Answer Details

The wheel and axle mechanism is a simple machine used for lifting heavy loads. The mechanical advantage of a wheel and axle mechanism is given by the ratio of the radius of the wheel to the radius of the axle. In this case, the diameters of the wheel and axle are given, and so we need to calculate their radii. The radius of the wheel, r_w, is half the diameter of the wheel, so r_w = 20 cm. Similarly, the radius of the axle, r_a, is half the diameter of the axle, so r_a = 4 cm. The mechanical advantage of the wheel and axle mechanism is given by: MA = r_w / r_a Substituting the values we get: MA = 20 cm / 4 cm = 5 The efficiency of the machine is given as 80%, which means that 80% of the work put into the machine is used to lift the load. The remaining 20% is lost due to friction and other factors. Efficiency = (Output work / Input work) x 100% Since the output work is equal to the weight lifted (100 N) times the distance moved by the load, and the input work is equal to the effort required to lift the load times the distance moved by the effort, we can write: Efficiency = (100 N x d) / (E x d) x 100% where d is the distance moved by both the load and the effort. Simplifying this expression gives: Efficiency = 100 / MA Substituting the value of MA gives: 80% = 100 / 5 So, the effort required to lift a load of 100N is: E = (100 N x d) / (Output work) E = (100 N x d) / (Efficiency x Input work) Substituting the values of efficiency, output work and input work, we get: E = (100 N x d) / (0.8 x E x 5 x d) Simplifying this expression, we get: E = 25 N Therefore, the effort required to lift a load of 100N is 25N. Hence, the correct option is 25N.