Lotte leans on a refrigerator, and it does not move. She leans harder. Still nothing.
Then a little more force, and it suddenly gives way.
What decides the exact moment an object starts to slide?
The last two lessons give the answer. One number belongs to the object and its floor: the maximum static friction, μ_s N. The other number is whatever force is applied.
The decision is a comparison between those two numbers.
Earlier in this topic you saw the rule: static friction adjusts to match the applied force up to a maximum of μ_s N, and only beyond that maximum does sliding begin.
So the question to ask is: is the applied force bigger than the maximum static friction, μ_s N?
If the applied force is no bigger than the maximum, static friction matches it exactly, and the object stays at rest.
If the applied force is bigger than the maximum, static friction cannot match it, and the object starts to slide.
Here is one crate, tested four times. Its maximum static friction is 50 N, because μ_s = 0.25 and N = 200 N, and 0.25 × 200 = 50.
The comparison decides it every time: the applied force against μ_s N.
The maximum static friction on a cabinet is 70 N. Lotte applies a 55 N horizontal force to the cabinet. Does the cabinet start to slide?
A 35 N horizontal force is applied to a packed suitcase. μ_s = 0.50 and N = 90 N. Does the suitcase start to slide?
Write down the values in the question:
applied force = 35 N
μ_s = 0.50
N = 90 N
Find the maximum static friction:
f_s,max = μ_s N
f_s,max = 0.50 × 90
f_s,max = 45 N
Compare the two forces:
35 N is less than 45 N.
Static friction matches the 35 N applied force, and the suitcase stays at rest.
A 120 N horizontal force is applied to a workbench. μ_s = 0.35 and N = 260 N. Does the workbench start to slide?
Write down the values in the question:
applied force = 120 N
μ_s = 0.35
N = 260 N
Find the maximum static friction:
f_s,max = μ_s N
f_s,max = 0.35 × 260
f_s,max = 91 N
Compare the two forces:
120 N is bigger than 91 N.
Static friction cannot match the applied force, and the workbench starts to slide.
Gideon applies a 95 N horizontal force to a stone planter. μ_s = 0.30 and N = 300 N. Does the planter start to slide?
A washing machine stands on a kitchen floor. μ_s = 0.35 and N = 220 N. Enter the largest horizontal applied force, in N, at which the machine still stays at rest.
A packed footlocker rests on a gym floor. μ_s = 0.44 and N = 250 N. Enter the maximum static friction on the footlocker in N.
June applies a 40 N horizontal force to a desk, and the desk stays at rest. Its maximum static friction is 65 N. Enter the static friction force on the desk right now, in N.
A 130 N horizontal force is applied to a planter box. μ_s = 0.42 and N = 200 N. Enter how many newtons the applied force exceeds the maximum static friction by.