Physics 2018 JAMB Past Questions - Question 37: What effort will a machine of efficiency 90% apply to lift a load of 180N if its efforts arm is twice as long as its load arm?

Correct Answer

A

Explanation

M.A = Effort x V.R /100 = 90x2 /100 = 1.8therefore E = L /M.A = 180 /1.8 = 100N
To determine the effort required to lift a load using a machine, we can use the principle of mechanical advantage. In this case, the machine has an efficiency of 90% and an effort arm that is twice as long as the load arm.

The mechanical advantage (MA) of a machine is calculated by dividing the length of the effort arm (EA) by the length of the load arm (LA). In this case, since the effort arm is twice as long as the load arm, the mechanical advantage can be expressed as MA = EA / LA = 2.

The efficiency (Eff) of a machine is given by the formula: Eff = (MA / (MA + 1)) * 100%. In this case, the efficiency is given as 90%, so we can substitute the values into the formula and solve for MA:

90% = (MA / (MA + 1)) * 100%
0.9 = MA / (MA + 1)
0.9(MA + 1) = MA
0.9MA + 0.9 = MA
0.9 = 0.1MA
MA = 0.9 / 0.1
MA = 9

Now that we have the mechanical advantage, we can calculate the effort (E) required to lift the load (L) using the formula: E = L / MA.

Given that the load is 180N, we can substitute the values into the formula:

E = 180N / 9
E = 20N

Therefore, the machine with an efficiency of 90% would apply an effort of 20N to lift a load of 180N if its effort arm is twice as long as its load arm.