Static Friction 𝐹 𝑓𝑠 ≤ 𝜇 𝑠 𝐹 𝑛 Static friction varies depending on what is happening Has a maximum value based on an equality This is the maximum value of static friction that must be overcome in order to “slide” or move into kinetic friction. Most problems work with the maximum but you must be careful. Mathematically: 𝜇 𝑠 is the coefficient of static friction Higher values than kinetic friction 𝐹 𝑓𝑠 ≤ 𝜇 𝑠 𝐹 𝑛

Sample Block A weighs 1.5 N and block B weighs 4.0 N. The coefficient of static friction between the blocks is 0.35. What is the greatest force F that can be applied without the blocks sliding past each other?

Sample A block is placed against the vertical front of a cart as shown. The coefficient of static friction between the block and cart is 0.45. What is the minimum acceleration of the cart such that the block does not fall?

Sample You’re dragging your little brother up the 25° wheelchair ramp at the doctor’s office. If he has a mass of 40 kg and the coefficient of static friction, µs is 0.15, how much force will you need to apply to get him moving?

Hooke’s Law 𝐹 𝑒𝑙 =𝑘∆𝑥 One more force we haven’t talked about Elastic Force ( 𝐹 𝑒𝑙 ) – forces that cause a change in shape or deformation (think springs) For small ‘deformations’, the this force can be described by Hooke’s Law: ∆𝑥 is the change in length of the spring (or rubber band, etc.) 𝑘 is the spring constant (N/m) – property of the spring 𝐹 𝑒𝑙 =𝑘∆𝑥

Sample What is the force required to stretch a spring whose constant value is 100 N/m by an amount of 0.50 m?

Sample It is weigh-in time for the local under-85-kg rugby team. The bathroom scale used to assess eligibility can be described by Hooke’s law and is depressed 0.75 cm by its maximum load of 120 kg. What is the spring’s effective spring constant? A player stands on the scales and depresses it by 0.48 cm. Is he eligible to play on this under-85 kg team?