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PHYSICS 231 Lecture 8: Forces, forces & examples Remco Zegers Walk-in hour: Monday 11:30-13:30 Helproom PHY 231 1 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 2 Forces seen in the previous lecture • Gravity: Force between massive objects • Normal force: Elasticity force from supporting surface n=-FgL FgL=mgcos Fg//=mgsin Fg=mg PHY 231 3 Gravity, mass and weights. Weight=mass times gravitational acceleration Fg(N)=M(kg) g(m/s2) Newton’s law of universal gravitation: Fgravitation=Gm1m2/r2 G=6.67·10-11 Nm2/kg2 For objects on the surface of the earth: •m1=mearth=fixed •r=“radius” of earth=fixed •The earth is not a point object relative to m2 PHY 231 4 Measuring mass and weight. Given that gearth=9.81 m/s2, gsun=274 m/s2, gmoon=1.67 m/s2, what is the mass of a person on the sun and moon if his mass on earth is 70 kg? And what is his weight on each of the three surfaces? • The mass is the same on each of the surfaces • On Earth: w=686.7 N • On the Moon: w=116.7 N • On the Sun: 19180 N PHY 231 5 Jumping! The pelvis has a mass of 30.0 kg. What is its acceleration? Decompose all forces in x and y directions Force x (N) y (N) 300 N -122 -274 690 N 236 648 Weight 0 -249 Resultant 114 N 80.3 N Total Force: F=(1142+80.32)=139 N Direction: =tan-1(Fy/Fx)=35.2o Acceleration: a=F/m=139/30.0=4.65 m/s2 PHY 231 6 Tension T The magnitude of the force T acting on the crate, is the same as the tension in the rope. Spring-scale You could measure the tension by inserting a spring-scale... PHY 231 7 Newton’s second law and tension m1 n T Fg No friction. T What is the acceleration of the objects? m2 Fg Object 1: Object 2: F=m1a, so F=m2a, so T=m1a Fg-T=m2a m2g-T=m2a Combine 1&2 (Tension is the same): a=m2g/(m1+m2) PHY 231 8 Problem What is the tension in the string and what will be the acceleration of the two masses? Draw the forces: what is positive & negative??? T T For 3.00 kg mass: F=ma T-9.813.00=3.00a For 5.00 kg mass: F=ma 9.815.00-T=5.00a T=36.8 N a=2.45 m/s2 Fg Fg PHY 231 9 Friction Friction are the forces acting on an object due to interaction with the surroundings (air-friction, ground-friction etc). Two variants: • Static Friction: as long as an external force (F) trying to make an object move is smaller than fs,max, the static friction fs equals F but is pointing in the opposite direction: no movement! fs,max=sn s=coefficient of static friction • Kinetic Friction: After F has surpassed fs,max, the object starts moving but there is still friction. However, the friction will be less than fs,max! fk=kn k=coefficient of kinetic friction PHY 231 10 PHY 231 11 Problem n=-FgL A)If s=1.0, what is the angle for which the block just starts to slide? F =mgsin g// FgL=mgcos B)The block starts moving. Given that k=0.5, what is the acceleration of the block? Fg=mg Fs,k 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(½2-¼2)=a so a=g¼2 PHY 231 12 All the forces come together... n T T If a=3.30 m/s2 (the 12kg block is moving downward), what is the value of k? Fg For the 7 kg block parallel to the slope: T-mgsin-kmgcos=ma For the 12 kg block: Mg-T=Ma Fk Fg Solve for k M ( g a) m g sin m a k 0.25 m g cos PHY 231 13 General strategy • 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 14 Next Lecture: Revision and go through an exam May the Force be with you! PHY 231 15