SME
Statics · Problem type
Slip or tip: which happens first
Use this for “A 300 N crate 0.6 m wide is pushed level at 1.2 m above the floor (μₛ = 0.4). Does it tip or slide first, and at what push?”
Diagram
To
tip,
about
the
ringed
edge:
Pₜᵢₚ
×
h
=
W
×
b
2,
so
Pₜᵢₚ
=
Wb
2h
=
300
×
0.6
2 × 1.2
=
75
N
To slip: Pₛₗᵢₚ = μₛW = 0.4 × 300 = 120 N
75 N < 120 N: it tips first, at 75 N, with N and f at the edge.
This is an example. Type your own values to start a new problem.
Pₜᵢₚ (N)
=
W (N)
×
b (m)
2
×
h (m)
Pₛₗᵢₚ (N)
=
μₛ
×
W (N)
P
Push that moves it
worked out (not typed)
Formulas
Pₜᵢₚ
=
W
×
b
2 ×
h
75
=
300
×
0.6
2 × 1.2
Pₛₗᵢₚ
=
μₛ
×
W
120 = 0.4 × 300
P
=
Pₜᵢₚ
75 = 75
Assumptions
•
The push P is level, at height h above the floor; W acts at the crate’s center.
•
About to tip, the floor’s N and friction move to the front bottom edge, so take moments there.
•
About to slide, friction is at its limit μₛN, and N = W.
•
Whichever needs the smaller push happens first.
Step-by-step
WE KNOW
W = 300 N, b = 0.6 m, h = 1.2 m, μₛ = 0.4
FIND
push to tip it (Pₜᵢₚ), push to slide it (Pₛₗᵢₚ), push that moves it (P)
Step 1 · Find push to tip it (Pₜᵢₚ)
Use Pₜᵢₚ = W × b ÷ (2 × h)
Moments
about
the
front
edge:
P
×
h
tips
it,
W
×
b
2
holds
it
down;
they
balance
as
it
starts
to
tip.
Pₜᵢₚ
=
300
×
0.6
2 × 1.2
Pₜᵢₚ
=
300
×
0.6
2.4
Pₜᵢₚ
=
180
2.4
Pₜᵢₚ = 75 N
Step 2 · Find push to slide it (Pₛₗᵢₚ)
Use Pₛₗᵢₚ = μₛ × W
About
to
slide,
the
push
equals
friction
at
its
limit,
μₛN,
and
N
=
W
on
a
level
floor.
Pₛₗᵢₚ = 0.4 × 300
Pₛₗᵢₚ = 120 N
Step 3 · Find push that moves it (P)
Use P = Pₜᵢₚ
The push grows from zero, so it reaches Pₜᵢₚ first: the crate tips.
75 < 120: it tips before it slides
P
=
75
N
Check
Put the numbers back in. Both sides should match.
75
=
300
×
0.6
2 × 1.2
✓
120 = 0.4 × 300 ✓
75 = 75 ✓
Topic check
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