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PHYSICS 231 Lecture 9: More on forces

PHYSICS 231 Lecture 9: More on forces. Remco Zegers. Newton’s Laws.

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PHYSICS 231 Lecture 9: More on forces

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  1. PHYSICS 231Lecture 9: More on forces Remco Zegers PHY 231

  2. Newton’s Laws • First Law: If the net force exerted on an object is zero the object continues in its original state of motion; if it was at rest, it remains at rest. If it was moving with a certain velocity, it will keep on moving with the same velocity. • Second Law: The acceleration of an object is proportional to the net force acting on it, and inversely proportional to its mass: F=ma • If two objects interact, the force exerted by the first object on the second is equal but opposite in direction to the force exerted by the second object on the first: F12=-F21 PHY 231

  3. General strategy for problems with forces • If not given, make a drawing of the problem. • Put all the relevant forces in the drawing, object by object. • Think about the axis • Think about the signs • Decompose the forces in direction parallel to the motion and perpendicular to it. • Write down Newton’s first law for forces in the parallel direction and perpendicular direction. • Solve for the unknowns. • Check whether your answer makes sense. PHY 231

  4. quiz! • A homogeneous block of 10 kg is hanging with 2 ropes • from a ceiling. The tension in each of the ropes is: • 0 N • 49 N • 98 N • 196 N • don’t know PHY 231

  5. Horizontal Vertical Due to tide: 3000 N 0 N Due to wind: 6000cos(135)=-4243 6000sin(135)=+4243 Sum: -1243 N 4243 N N 6000N Magnitude of resulting force: Fsum=[(-1243)2+(4243)2]=4421 N Direction: angle=tan-1(4243/-1243)= 1060 (calc: -730, add 1800) F=ma so a=F/m=4421/2000=2.21 m/s2 W E 3000N S A 2000 kg sailboat is pushed by the tide of the sea with a force of 3000 N to the East. Because of the wind in its sail it feels a force of 6000 N toward to North-West direction. What is the magnitude and direction of the acceleration? PHY 231

  6. TVerL horizontal Vertical left rope Tsin(45) Tcos(45) right rope -Tsin(45) Tcos(45) gravity 0 -1*9.81 Sum: 0 2Tcos(45)-9.81 TVerR 450 450 ThorL Object is stationary, so: 2Tcos(45)-9.81=0 so, T=6.9 N Fg T T 900 1kg A mass of 1 kg is hanging from a rope as shown in the figure. If the angle between the 2 supporting wires is 90 degrees, what is the tension in each rope? ThorR PHY 231

  7. Fs,k n=-FgL Fg//=mgsin FgL=mgcos   Fg=mg Problem A)If s=1.0, what is the angle  for which the block just starts to slide? B)The block starts moving. Given that k=0.5, what is the acceleration of the block? A) Parallel direction: mgsin-sn=0 (F=ma) Perpendicular direction: mgcos-n=0 so n=mgcos Combine: mgsin-smgcos=0 s=sin/cos=tan=1 so =45o B) Parallel direction: mgsin(45o)- smgcos(45o)=ma (F=ma) g(½2-¼2)=a so a=g¼2 PHY 231

  8. n T T Fk Fg Fg All the forces come together... If a=3.30 m/s2 (the 12kg block is moving downward), what is the value of k? For the 7 kg block parallel to the slope: T-mgsin-kmgcos=ma For the 12 kg block: Mg-T=Ma Solve for k PHY 231

  9. A lawsuit… A passenger in a bus files a lawsuit claiming that when the driver suddenly pushed the brakes a suitcase came flying toward her from the front of the bus and she got injured. You are in the jury; will you award damages? • No, this could not have happened • Yes, this is plausible PHY 231

  10. puck on ice • After being hit by a hockey-player, a puck is moving over • a sheet of ice (frictionless). The forces working on the • puck are: • No force whatsoever • the normal force only • the normal force and the gravitational force • the force that keeps the puck moving • the normal force, the gravitational force and the force • that keeps the puck moving PHY 231

  11. 20 100 • force Horizontal vertical • person 100 0 • wind 20cos(45) 20sin(45) • sum 100+14.1=114.1 14.1 • Total force: (114.12+14.12)=115 N • F=ma 115=50a a=2.3 m/s2 • Ffriction=n=0.05*m*g=0.05*50*9.8=24.5N • F=ma 115-24.5=50a a=1.8 m/s2 A person is pushing an ice-sledge of 50kg over a frozen lake with a force of 100N to the east. A strong wind is pushing from the south-west and produces a force of20N on the sledge. a) What is the acceleration of the sledge? b) if the coefficient of kinetic friction is 0.05, what is the acceleration? PHY 231

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