"Whatever," Leo grunted, wiping grease on his jeans. "I just want to go home. I grabbed the manual from the back shelf. It has the diagrams. Let's just copy the numbers."
A worker uses a ramp that is 6.0 meters long to lift a heavy crate up to a truck bed that is 1.5 meters high. What is the ideal mechanical advantage (IMA) of the ramp? Identify the Variables: Input Distance ( dinputd sub input end-sub ) = 6.0 m (the distance the crate is pushed) Output Distance ( doutputd sub output end-sub ) = 1.5 m (the vertical height the crate is raised) Step-by-step Solution:
A pulley system has an IMA of 6. Due to friction, the AMA is 4.5. Find the efficiency.
Leo flipped open the manual to a dog-eared page. "Look, here’s the answer key for the standard setup. It says right here: Section 14.3 Mechanical Advantage and Efficiency Answer Key . It lists the output force as 800 N and the input force as 200 N. So, the mechanical advantage is 4. Boom. We’re done."
Efficiency=(AMAIMA)×100%Efficiency equals open paren the fraction with numerator AMA and denominator IMA end-fraction close paren cross 100 % "Whatever," Leo grunted, wiping grease on his jeans
This accounts for real-world factors like friction and the weight of the machine's parts.
Output ForceInput Forcethe fraction with numerator Output Force and denominator Input Force end-fraction Decreases when friction increases. None (Ratio)
When searching for a , you will likely encounter these types of problems:
$\textEfficiency = \frac1500\text J1800\text J \times 100 = \mathbf83.3%$ It has the diagrams
assumes a perfect world where no energy is lost.
This accounts for real-world friction. It is the ratio of the output force (resistance) to the input force (effort). Ideal Mechanical Advantage (IMA):
Ideal Mechanical Advantage (IMA)=Input Distance (dinput)Output Distance (doutput)Ideal Mechanical Advantage (IMA) equals the fraction with numerator Input Distance open paren d sub input end-sub close paren and denominator Output Distance open paren d sub output end-sub close paren end-fraction
IMA=didoIMA equals the fraction with numerator d sub i and denominator d sub o end-fraction Identify the Variables: Input Distance ( dinputd sub
Because friction cannot be completely eliminated . Some input work is always wasted overcoming friction. Question: How can you increase the efficiency of a machine?
"Alright," Leo said, picking up the oil can. "Let's grease the gears. I want to get that Efficiency percentage up before we write this down."
Many educational publishers and online platforms provide study resources, answer keys, and teacher editions for physics curricula. When searching for "Section 14.3 Mechanical Advantage and Efficiency Answer Key PDF," you may want to look for:
Sam watched the spring scale attached to the chain. "Leo, stop! You’re pulling with 300 Newtons!"
If you push with 10 N and the machine pushes with 50 N, MA = 50/10 = 5.