SP211 Worksheet 11: 6.1 Static and Kinetic Friction Problem ... - USNA

SP211. Worksheet 11: 6.1 Static and Kinetic Friction. For kinetic friction problems: • fk always points in the opposite direction of the relative moti...

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SP211 Worksheet 11: 6.1 Static and Kinetic Friction For kinetic friction problems: • f~k always points in the opposite direction of the relative motion between the object and the surface. For example, if a block is sliding across the floor, kinetic friction points in the opposite direction from the slide. • the magnitude of the force due to kinetic friction is |f~k | = µk |F~N |.

Problem 1 A block slides down a 27◦ incline. It is observed to be speeding up as it slides. The coefficient of kinetic friction between the block and the incline is µk = 0.14. a)What is the magnitude of the normal force experienced by the block? b) What is the magnitude of the block’s acceleration?

Problem 2 A cord pulls an 8.0 kg block across a horizontal floor at constant velocity. The cord makes an angle of 34◦ above the horizontal. The coefficient of kinetic friction between the block and the coord is µk = 0.21. What is the tension in the cord? HINT: If the block is moving with constant velocity, what is its acceleration?

SP211 Worksheet 11: 6.1 Static and Kinetic Friction For static friction problems: • f~s points parallel with the surface in whichever direction it has to so that the relative motion between the object and surface is zero. • the magnitude of the force due to statice friction has a maximum value given by|f~s,max | = µs |F~N |. In other words |f~s | ≤ µs |F~N |.

Problem 3 You are trying to drag a large box of mass m along the ground by a cord, but the box is not moving yet. The tension in the cord is FT and it makes an angle of θ above horizontal. The coefficient of static friction between the box and the ground is µs . a) Develop an expression for |f~s | in terms of FT , θ, m, and g. HINT: If there was no friction, in which direction would the box want to start accelerating? Your force due to static friction should point in the direction that can cancel out any unbalanced horizontal forces. b) Using your expression from above, assume that the force due to static friction is “maxed out,” such that if you were to pull any harder the box would start moving. Develop and expression for the mass of the box in terms of FT , θ, µs , and g. HEADS UP: This will help you greatly for problem 6.21 in the homework which asks for the maximum mass you could pull. In the homework you can take the expression for mass as a function of θ found here, and use differential calculus to find what value of θ gives the largest m.