Physics 2004 JAMB Past Questions - Question 11: A machine whose efficiency is 60% has a velocity ratio of 5. If a force of 500N is applied to lift a load P, what is the magnitude of P?

Correct Answer

A

Explanation

To find the magnitude of the load, P, you can use the formula for mechanical advantage in a machine, which relates the input force (the force applied) and the output force (the force used to lift the load) in an idealized machine:

Mechanical Advantage (MA) = Output Force (P) / Input Force (F)

In this case, the machine's efficiency is 60%, which means it has an efficiency of 0.60 or 60/100.

Efficiency (η) = 0.60

Efficiency is defined as the ratio of useful work output to the work input. Therefore, you can express the relationship between the work done on the machine (input) and the work done by the machine (output) as follows:

Efficiency (η) = Work Output / Work Input

Given that Efficiency (η) = 0.60, you can say:

0.60 = Work Output / Work Input

Now, let's relate the work done by the machine to the input and output forces and the velocity ratio:

Work Output = Output Force (P) × Distance Output
Work Input = Input Force (F) × Distance Input

And the velocity ratio (VR) is defined as:

Velocity Ratio (VR) = Distance Input / Distance Output

In your problem, the velocity ratio (VR) is given as 5:

VR = 5

Now, we can rearrange the VR equation to find the relationship between the distances:

Distance Input = VR × Distance Output

Now, substitute these relationships into the efficiency equation:

0.60 = (P × Distance Output) / (F × VR × Distance Output)

Next, rearrange the equation to solve for P (the magnitude of the load):

P = (0.60 × F × VR × Distance Output) / Distance Output

Distance Output cancels out from the numerator and denominator, so you're left with:

P = 0.60 × F × VR

Now, you can plug in the given values:

F (Input Force) = 500 N
VR (Velocity Ratio) = 5

P = 0.60 × 500 N × 5

P = 0.60 × 2500 N

P = 1500 N

So, the magnitude of the load, P, is 1500 Newtons.