Tipping versus sliding
A pushed object can either slide or tip over. Which happens first depends on its proportions, where you push, and the friction coefficient.
Two ways to fail
When you push a tall object such as a cabinet, it may slide along the floor or rotate about its front bottom edge. Statics predicts which by finding the force needed for each and comparing them; the smaller force wins.
Condition for sliding
Sliding begins when the push equals the maximum friction: P = mu_s N. For an 800 N cabinet on a floor with mu_s = 0.4, that is 320 N, regardless of where the push is applied.
Condition for tipping
Tipping begins when the cabinet is about to pivot on its front edge, so the normal force and friction shift entirely to that edge. Taking moments about the edge, the push's moment equals the weight's restoring moment: P h = W (b/2), for a push at height h on a uniform cabinet of width b.
A cabinet example
A uniform cabinet 0.6 m wide and 1.8 m tall weighs 800 N. Pushed at 1.5 m height, it tips when P x 1.5 = 800 x 0.3, so P = 160 N, half the 320 N needed to slide. It will tip over before sliding, which is how furniture falls on people during earthquakes or careless moves.
Pushing lower
Lowering the push reduces its tipping moment. The tipping force is 240 / h newtons, which equals the 320 N sliding force when h = 0.75 m. Pushing below 0.75 m makes the cabinet slide before tipping, a practical tip for moving tall furniture.
Where the normal force acts
As a push increases, the normal force's effective point moves toward the front edge. At the moment of tipping, it reaches the edge. If the required location would be outside the base, the object tips. This idea also explains why wide-based vehicles and furniture are more stable.
Safety applications
Engineers check tipping for vending machines, bookcases, trucks on slopes, and cranes. Anti-tip straps that anchor tall furniture to walls are recommended in many countries to prevent tip-over injuries to children.
Worked example
A uniform crate 1.0 m wide and 1.0 m tall weighing 1,000 N is pushed at 0.9 m with mu_s = 0.6. Sliding needs 600 N; tipping needs P x 0.9 = 1,000 x 0.5, so P is about 556 N. It tips first. On a slipperier floor with mu_s = 0.4, sliding would need only 400 N, so it would slide instead.
Key takeaways
A pushed object either slides, at P = mu_s N, or tips about its front edge, when the push's moment P h equals the weight's moment W b/2 for a uniform body. Compare the two forces; the smaller one happens first. Tall, narrow objects pushed high tend to tip; pushing lower or reducing friction favours sliding. At tipping, the normal force acts at the edge. Tipping checks matter for furniture, vehicles, and cranes, and anti-tip straps prevent injuries.
Flashcard
P = mu_s N
Check your understanding
An 800 N cabinet 0.6 m wide is pushed 1.5 m above the floor with mu_s = 0.4. What happens first?