The ratio of MA (mechanical advantage) to VR (velocity ratio) can be determined based on the work input and work output, considering the reduction caused by friction.
Let's assume that the input work is represented by WI and the output work is represented by WO. If 20% of the input work is reduced due to friction, it means that the effective work input is 80% of the original input work:
Effective work input (WE) = 80% of WI = 0.8 * WI
Now, the work output (WO) can be calculated using the equation:
WO = MA * WI
Given that WI = WE = 0.8 * WI, we can rewrite the equation as:
WO = MA * (0.8 * WI)
Simplifying, we find:
WO = 0.8 * MA * WI
To find the ratio of MA to VR, we need to relate the work output (WO) to the velocity ratio (VR). The equation relating these two quantities is:
WO = VR * WI
Substituting the expression for WO obtained earlier, we have:
0.8 * MA * WI = VR * WI
Canceling out the common factor of WI, we get:
0.8 * MA = VR
Therefore, the ratio of MA to VR is 0.8.