a certain hydraulic jack in a gas station lifts a 900 kg car,a distance of 0.25 m when a force of 150 Newtons pushes a piston through a distance of 20 cm.What is the IMA,AMA and efficiency
AMA=force out/force in=900(9.8)/150= 58.6
IMA= workout/workin=900*9.8*.25/(150*.20 )=73.5
efficiency = ama/ima
This is indeed a great jack, worthy of lab study.
I got 73.5 as many Joules out as I put in ?
Yess, I want one.
Oh, I see we're getting technical here. Well, hold on to your lug nuts, because I'm about to break it down for you.
First, let's tackle the IMA, which stands for Ideal Mechanical Advantage. It represents the ratio of the force applied to the force exerted by the jack. In this case, the force exerted by the jack is equal to the weight of the car being lifted. So, IMA = Weight of the Car / Force Applied = 900 kg * 9.8 m/s^2 / 150 N. Let me grab my calculator... *beep boop beep* The IMA turns out to be 58.8.
Moving on to the AMA, or Actual Mechanical Advantage. This takes into account any losses or inefficiencies in the system. AMA is calculated by dividing the distance the force is applied by the distance the load is lifted. So, AMA = Distance Force Is Applied / Distance Load Is Lifted = 20 cm / 25 cm = 0.8.
Lastly, let's find the efficiency. Efficiency is the ratio of the AMA to the IMA, multiplied by 100% to get a percentage. Efficiency = (AMA / IMA) * 100% = (0.8 / 58.8) * 100%. Just give me a second to crunch the numbers... *clown noises* The efficiency comes out to be approximately 1.36%.
So, to sum it up, we have an IMA of 58.8, an AMA of 0.8, and an efficiency of 1.36%. Hope I was able to jack up your knowledge a little with some humorous assistance!
To calculate the IMA (Ideal Mechanical Advantage), AMA (Actual Mechanical Advantage), and efficiency of the hydraulic jack, we need to use the following formulas:
IMA = (output force)/(input force)
AMA = (output distance)/(input distance)
Efficiency = (AMA/IMA) * 100%
Let's begin by converting the given measurements to the SI unit system:
- Distance lifted by the car = 0.25 m
- Force applied on the piston = 150 Newtons
- Distance pushed by the piston = 20 cm = 0.2 m
- Mass of the car = 900 kg
Now we can calculate the IMA, AMA, and efficiency step by step:
Step 1: Calculate the output force (force on the car):
Using the formula F = m * g, where F is the force, m is the mass, and g is the acceleration due to gravity (approximately 9.8 m/s^2):
Output force = 900 kg * 9.8 m/s^2 ≈ 8820 Newtons
Step 2: Calculate IMA:
IMA = (output force) / (input force)
IMA = 8820 N / 150 N ≈ 58.8
Step 3: Calculate AMA:
AMA = (output distance) / (input distance)
AMA = 0.25 m / 0.2 m = 1.25
Step 4: Calculate efficiency:
Efficiency = (AMA / IMA) * 100%
Efficiency = (1.25 / 58.8) * 100% ≈ 2.12%
So, the IMA is approximately 58.8, the AMA is 1.25, and the efficiency is approximately 2.12%.
well 900 kg * 9.81 = 8829 Newtons lifted
work out doing lift = 8829 N * .25 m = 2207 Joules output
work in pushing piston = 150 N * 0.20 m = no way, typo