SME
Grade 11 Science · Problem type
A ramp
Use this for “A 900 N crate is pushed up a 3 m ramp onto a 1 m platform. What is the ideal mechanical advantage and the effort? What if the ramp is 75% efficient?”
Diagram
Ideal MA = length/height = 3/1 = 3
Effort = load/MA = 900/3 = 300 N
Push 3 m along the ramp for each 1 m of height: less force, more distance.
This is an example. Type your own values to start a new problem.
FL
Load
example
L
Ramp length
example
h
Ramp height
example
e
Efficiency
example · %
IMA
Ideal mechanical advantage
calculated
FE
Effort
calculated
Formulas
IMA
=
L
h
3
=
3
1
FE
=
FL/(IMA
×
e
100
)
300
=
900/(3
×
100
100
)
Assumptions
•
The ideal mechanical advantage of a ramp is its length over its height.
•
Friction wastes some of the work: the actual effort is the ideal effort divided by the efficiency.
•
A smooth ramp is 100% efficient.
Step-by-step
WE KNOW
FL = 900 N, L = 3 m, h = 1 m, e = 100%
FIND
ideal mechanical advantage (IMA), effort (FE)
Step 1 · Find ideal mechanical advantage (IMA)
Use IMA = L/h
The ramp’s length over its height.
IMA
=
3
1
IMA = 3
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
=
900/(3
×
100
100
)
FE
=
900
3
FE = 300 N
Check
Put the numbers back in. Both sides should match.
3
=
3
1
✓
300
=
900/(3
×
100
100
)
✓
Topic check
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