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Chapter 5

# Chapter 5 - Chapter5 Addi-onalApplica-onsofNewtons Laws...

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Chapter 5 Addi-onal Applica-ons of Newton’s Laws October 1 and October 6, 2009

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Fric-on Fric-on Opposes mo-on between systems in contact Parallel to the contact surface Depends on the force holding the surfaces together (the normal force N) Sta-c fric-on Force required to move a sta-onary object f s is less than or equal to μ s N Kine-c fric-on Fric-onal force on an object in mo-on Can be less than sta-c fric-on f k = μ k N
Proper-es of Surface Fric-on These relations are all useful APPROXIMATIONS to messy reality.

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Newton’s laws: example T=50 N M = 5 kg μ k = 0.2 Find acceleration of block
Newton’s laws: example T=50 N M = 5 kg μ k = 0.2 Find acceleration of block Frictional force: f = μ k Mg opposes the tension T Net force: F net = T - f = T - μ k Mg Acceleration: a = F net / M = ((50 - 0.2 x 5 x 9.8) / 5) m/s 2 Answer: 8.04 m/s 2

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Newton’s laws: another example T=50 N M = 5 kg μ k = 0.2 Find acceleration of block θ =50 0
Newton’s laws: another example T=50 N M = 5 kg μ k = 0.2 Find acceleration of block θ =50 0 Hints: Resolve T in x and y components: T x =T cos θ , T y =T sin θ Draw free body diagram Solve for y-component of force, and note that y-acceleration is zero (Obtain relationship between T and N) Solve for x-component of force, then use a x =F x /m Answer: acceleration of block is 6.0 m/s 2 in +x direction a = F net M = T x μ k N M = T x μ k Mg T y ( ) M = T cos θ μ k Mg T sin θ ( ) M

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Rolling Fric-on: Car Tires Fric-on keeps the car wheels from spinning in place You want the -res to roll You want the fric-on to be high The contact point is at rest ‐ although the car is in mo-on » What maXers is the coeﬃcient of sta-c fric-on! weight Maximum Static friction ( > F car on road for car not to spin in place!) F car on road F road on car Consider Newton’s 3rd law: F road on car is the actual force ON the car. Static Friction μ s N is its maximum value
Surface Fric-on… Fric-on is caused by the “microscopic” interac-ons between the two surfaces:

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Ques-on 1 You are pushing a wooden crate across the floor at constant speed. You decide to turn the crate on end, reducing by half the surface area in contact with the floor. In the new orientation, to push the same crate across the same floor with the same speed, the force that you apply must be about a) four times as great b) twice as great c) equally as great e) one-fourth as great as the force required before you changed the crate orientation.
Ques-on 1 You are pushing a wooden crate across the floor at constant speed. You decide to turn the crate on end, reducing by half the surface area in contact with the floor. In the new orientation, to push the same crate across the same floor with the same speed, the force that you apply must be about a) four times as great b) twice as great c) equally as great e) one-fourth as great as the force required before you changed the crate orientation.

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