Machines: Can You lift a car?
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1 Work=Force x Distance 10 m Units of work Nt-m=joules How much work? Machines: Can You lift a car? The ratio of the input force to the output force is called the Mechanical Advantage MA=5000/50=100 1
2 = 2 Efficiency will be always less than 1 or less than 100% Pulleys Pulley Systems W 2T=W T=W/2 In each of these cases we will need to pull more rope than the height the weight is lifted W 4T=W T=W/4 Pulley Systems mg mg 2T=mg 4T=mg T=mg/2 T=mg/4 Work=Fh=Td 500 (0.1)=250 (d) d=50/250 =0.2 m We want to lift a 500 N weight a distance of h= 10 cm (0.1 m). How much force ideally will we need to use and thru what distance will we move the force? What is the mechanical Advantage of this pulley 2T=W 2T=500 T=250 N (ideally) Ideal MA= Effort Dist/Load Dist=2 Actual MA=Load Force/Effort Force =500/300=1.67 Suppose T=300 Efficiency= 1.67/2=0.85 or 85 % 2
3 W=Fh=Td We want to lift a 500 N weight a distance of h= 10 cm (0.1 m). How much force will we need to use and thru what distance will we move the force? 2T=mg 2T=500 T=250 N Inclined Plane Sliding a load up an inclined plane requires less force than lifting it vertically. In plane below we push five times further. If friction is negligible we need apply only 1/5 load. Mechanical Advantage=5 500 (0.1)=250 (d) d=50/250 =0.2 m MA= 500/250=2 1 m 5 m Efficiency Efficiency will be always less than 1 or less than 100% 60 x x 0.25 Inclined Plane Sliding a load up an inclined plane requires less force than lifting it vertically. In plane below we push five times further. If friction is negligible we need apply only 1/5 load. Mechanical Advantage=5 A child on a sled (total weight 500 N) is pulled up a 10 m slope as shown below. a. What is theoretical MA? b. If there is no friction, what is tension in rope? c. If the tension is 100 N, what is the actual MA? What would be the efficiency? 1 m 10 m T 3
4 Potential Energy An object may have the ability to do work so we say it may store energy because of its position relative to some other object. Energy can be transformed from one form to another Essential to the study of physics, chemistry, biology, geology, astronomy Can be used in place of Newton s laws to solve certain problems more simply Power W=Fh W=mgh A Machine can lift a 1000 N weight a distance of 10 meters. (10,000 Joules of work) P=10,000 Joules/3600 s = P=10,000 Joules/10 s= The potential energy of the 10-N ball is the same (30 J) in all three cases because the work done in elevating it 3 m is the same whether it is (a) lifted with 10 N of force, (b) pushed with 6 N of force up the 5-m incline, or (c) lifted with 10 N up each 1-m stair. No work is done in moving it horizontally (neglecting friction). Check Yourself 1. How much work is done on a 75-N bowling ball when you carry it horizontally across a 10-m-wide room? 2. How much work is done on it when you lift it 1 m? What power is expended if you lift it this distance in 1 s? 3. What is its gravitational potential energy in the lifted position? 4
5 KE=1/2(5000 kg)(20 m/s) 2 = KE=5 x 10 4 kg-m 2 /s 2 = (kg-m/s 2 )-m=n-m= (J) Kinetic Energy If we push on an object, we can set it in motion. More specifically, if we do work on an object, we can change the energy of motion of that object. If an object is moving, then by virtue of that motion it is capable of doing work W=F x =ma x= a x = (v 2- -vo 2 )/ 2 W=m (v 2- -vo 2 )/2 If the speed of an object is doubled, the KE is quadrupled 5
6 Conservation of Energy Suppose you lift a book (which weighs 10 Newtons) at constant velocity through a vertical distance of 1 meter, as shown at left. Work you = Fx = (10 N)(1 m) = 10 Joules Energy cannot be created or destroyed; it may be transformed from one form into another, but the total amount of When you let go of the book, it accelerates toward the Earth - because the Earth is exerting a downward net force on it. As it falls, the Earth (gravity) does work on the book:workearth-down = Fx = (10 N)(1 m) = 10 Joules 6
7 I have developed a very powerful machine. It can lift a 1000 N weight a distance of 10 meters. Would you like to invest in my machine? Example: 60 watt bulb consumes 60 Joules per second of energy P=W/t=Fd/t=Fv 1 hp=750 Watts. If my machine can lift the mass in 0.1 seconds then P=10,000 J/0.1s P=10 5 watts An elevator applying an average force of 1000 N moves at 20 m/s P=Fv=1000N(20 m/s)=20,000 J People can have power rating. Suppose that Ben Pumping iron elevates his 80-kg body up the 2.0 meter stairwell in 1.8 seconds. Work Done by a constant force ( 5N over 6 meters) F F F F 0 1m 2m 3m W= 5 N x 6 m=30 N-m=Area under curve 7
8 Work Done by a Spring Force Slope= F/ x (N/m)=k (spring constant) F=kx =320/0.45 =711 N/m W=Area=1/2 BH=1/2 (x) F=1/2 x kx Example: 320 N stretches a spring 0.45 m. What is k? How much work to compress a spring a distance of 1 cm (0.01 m)? W spring =1/2kx 2 This is also energy stored W spring =1/2kx 2 in spring called W=1/2 (711 N/m)(0.01m) 2 Elastic PE W=0.036 J Suppose that it takes a force of 40 Newtons to hold a spring when it is stretched 1 meter from its normal rest position. How much work was done in stretching the spring k=f/x=40 N/1 m=40 N/m this distance? W spring =1/2kx 2 =1/2(40)(1) 2 =20 J 8
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