Question

An effort of 9.2 N was applied to a differential wheel and axle operating at 52% efficiency to raise a load. If the machine has the following measurements: radii of axles are 9.8 m and 12.2 m, radius of wheel 30 m, calculate the value of the load lifted.

a) 110.4 N
b) 125.8 N
c) 142.3 N
d) 155.6 N

Answer 1

To calculate the load lifted with a differential wheel and axle, determine the mechanical advantage (MA) using the radii of the wheel and axle, then adjust for efficiency to find the effective mechanical advantage (EMA). Multiply the effort by EMA to find the value of the lifted load.

Step-by-step explanation:

The question pertains to calculating the load lifted using a differential wheel and axle with given dimensions and efficiency. To solve this, we first need to calculate the mechanical advantage (MA) of the system, which is the ratio of the radii of the wheel to the larger axle (since we are lifting the load). The MA of the system is given by:

• MA = radius of wheel / radius of larger axle = 30 m / 12.2 m

Given the efficiency of the system (52%), read as a decimal (0.52), the effective mechanical advantage (EMA) is:

• EMA = MA × efficiency

Then, considering the effort applied (9.2 N), the load lifted (L) is found using:

• L = effort × EMA. By substituting the values, we will find the actual load lifted, which can be matched to one of the given answer choices.