SME
Grade 11 Science · Problem type
A block and tackle
Use this for “Four strands hold up an 800 N crate and the pulleys are 80% efficient. What pull lifts it, and how much rope do you pull to lift it 0.5 m?”
Diagram
Ideal MA = supporting strands = 4
Effort = load/(MA × efficiency) = 800/(4 × 0.8) = 250 N
Pull 4 m of rope to lift the load 1 m: less force, more distance.
This is an example. Type your own values to start a new problem.
FL
Load
example
n
Supporting strands
example
IMA
Ideal mechanical advantage
calculated
e
Efficiency
example · %
FE
Effort
calculated
dL
Load lifted
example
dE
Rope pulled
calculated
Formulas
IMA
=
n
4 = 4
FE
=
FL/(IMA
×
e
100
)
250
=
800/(4
×
80
100
)
dE = IMA × dL
2 = 4 × 0.5
Assumptions
•
Each supporting strand holds an equal share of the load: the ideal mechanical advantage IMA is the number of strands.
•
Less force, more distance: pull the rope IMA times as far as the load rises.
•
Friction in the pulleys wastes some work: divide the ideal effort by the efficiency.
Step-by-step
WE KNOW
FL = 800 N, n = 4, e = 80%, dL = 0.5 m
FIND
ideal mechanical advantage (IMA), effort (FE), rope pulled (dE)
Step 1 · Find ideal mechanical advantage (IMA)
Use IMA = n
Count the strands holding up the moving pulley.
IMA = 4
Step 2 · Find effort (FE)
Use FE = FL/(IMA × e/100)
The ideal effort is the load over IMA; friction makes it bigger: divide by the efficiency too.
FE
=
800/(4
×
80
100
)
FE = 800/3.2
FE = 250 N
Step 3 · Find rope pulled (dE)
Use dE = IMA × dL
Each strand shortens by the lift, so pull IMA times as much rope.
dE = 4 × 0.5
dE = 2 m
Check
Put the numbers back in. Both sides should match.
4 = 4 ✓
250
=
800/(4
×
80
100
)
✓
2 = 4 × 0.5 ✓
Topic check
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