Module 4 Work and Energy Part 1 PDF

Module 4 Work and Energy Work Kinetic Energy Potential Energy Conservation of Energy Force and Potential Energy Curves Power  ENERGY Ability to do work scalar Unit: Joules Work →Area of force vs position graph...

Module 4 Work and Energy Work Kinetic Energy Potential Energy Conservation of Energy Force and Potential Energy Curves Power  ENERGY Ability to do work scalar Unit: Joules Work →Area of force vs position graph Work, W amount of ENERGY transferred by a FORCE scalar F = force r = position Note: “Dot product”  If Force is constant F θ Δ r Only the component of force |F| cos θ (F) parallel with the displacement (Δr) does work Zero Work Negative Work Positive Work cos 90° = 0 opposite direction same direction  Example #1 The gravitational force exerted by the Sun on the Earth holds the Earth in an orbit around the Sun. Let us assume that the orbit is perfectly circular. What is the work done by this gravitational force during a short time interval in which the Earth moves through a displacement in its orbital path? 6  v ANSWER Δr Fnet 7  As a simple pendulum swings back and Example #2 forth, the forces acting on the suspended object are the gravitational force (W), the Swinging tension in the supporting cord (T), and air resistance (R). Pendulum (a) Which of these forces, if any, does no work on the pendulum? Ans: Tension T (b) Which of these forces does negative work at all times during its motion? Ans: Air Resistance R W (c) Describe the work done by the Example #2 gravitational force while the pendulum is swinging. Swinging Pendulum R T T R W W Negative during upswing Positive during downswing Work →Area of force vs Example # 3 position graph Calculate Work from Graph W = A1 + A2 F (3,2) Area of triangle : A1 (4,0) A2 r (2,-1) W=3-1=2 Calculate the work done by a constant force Example # 4 given the following: F=3 Ni+2Nj Δr = 4m i - 5m j 11 A tugboat pushes an Example # 5 ocean liner with a force of Stuck cruise ship 830 kN, moving it 0.38 km and doing 290 MJ of work. What is the angle between the direction of the tugboat’s push and the motion of the ship? 12 F = 830 kN; Δd = 0.38 km; Example # 5 W = 290 MJ Stuck cruise ship 13  Example #6 A farmer hitches his tractor to a sled loaded with wood and pull it a distance of 20 m along level ground. The total +y weight of the sled and load is 14,700 N. The tractor exerts a constant N FT 5000-N force at an angle of 36.9° f 36.9° above the horizontal. There is a 3,500N friction force opposing the +x sled’s motion. W (a) Find the work done by each force acting on the sled (b) the total work done by all the forces Work done by the tractor: Example # 6 WFT = FΔx cos θ +y WFT = (5000 N) (20 m) cos (36.9°) WFT = 80,000 J N FT f 36.9° Work done by the friction: +x Wf = (3500N) (20 m) cos (180°) W Wf = -70,000 J Work done by the Normal force: Work done by the Weight: WN = 0 J WW = 0 J Total Work Done: Example # 6 WT = WFT + Wf + WN + WW +y WT = 80,000 J + -70,000 J + 0J + 0J N FT f 36.9° WT = 10,000 J +x W Hooke’s Law Hooke’s Law Force k → spring constant Hooke’s Law Force Restoring Force → tends to bring back to equilibrium → Force is opposite the direction of displacement Work done by a spring: Hooke’s Law Force Final Initial Work done on a spring:  Kinetic Energy, KE Is the energy associated to particles and systems that are moving. 2 KE = ½ mv m = mass v = speed resources.yesican-science.ca  Work-Kinetic Energy Theorem When work is done by a net force on an object and the only change in the object is its speed, the work done is equal to the change in the object’s kinetic energy Speed will increase if work is positive Speed will decrease if work is negative An object’s kinetic energy can also be thought of as the amount of work the moving object experienced starting from rest (KEi=0)  Example # 7 Suppose the sled’s initial speed v1 is 2.0 m/s. What is the speed of the sled after it moves 20 m? (mass is 1,500 kg) WT = 10,000 J 22 Suppose the sled’s initial speed v1 is 2.0 m/s. What is the speed of the sled after it moves 20 m? Example # 7 (mass is 1,500 kg) WT = 10,000 J WT = KEf - KEi vf= 4.2 m/s 23 ▪Two iceboats hold a race on a Example # 8 frictionless horizontal lake. The two iceboats have masses m and 2m respectively. Each iceboat has an identical sail, so the wind exerts the same constant force F on each iceboat. The two iceboats start from rest and cross the finish line a distance s away. Which iceboat crosses the finish line with greater kinetic energy? 24  Answer Same force, same displacement, therefore same kinetic energy However, the one with smaller mass has higher speed.  Example # 9 Work Done on a Spring Scale A woman weighing 600 N steps on a bathroom scale containing a stiff spring. In equilibrium the spring is compressed 1.0 cm (0.01 m) under her weight. Find the force constant of the spring and the work done on it during the compression. Assume that the mass of spring is negligible. force constant , k = ? Example # 9 Work Done on a Spring Scale 600 N Work done, W Example # 9 Work Done on a Spring Scale 600 N An air-track glider of mass 0.100 kg is attached to the end Example # 10 of a frictionless horizontal air Spring and track by a spring with force Glider constant 20.0 N/m. When the spring is in its equilibrium position, the glider is moving at 1.50 m/s to the right. Find the maximum distance that the glider can move to the right. m = 0.100 kg, k = 20.0 N/m Example # 10 At x= 0 → v = 1.50 m/s Maximum Δx ? max Δx Δx = 0 v= 0 The 200-kg steel Exercise hammerhead of a pile driver Hammerhead is dropped from rest 3.00 m above the top of a vertical I-beam. The vertical guide rails exert a constant 60-N friction force on the hammerhead. Calculate the speed of the hammerhead just as it hits the I-beam 31  Exercise Hammerhead m = 200-kg H = 3.00 m vo = 0 m/s f = 60-N speed = ? +y  Exercise Hammerhead m = 200-kg H = 3.00 m vo = 0 m/s f = 60-N speed = ? V = 7.55 m/s The interplanetary probe is attracted Example #11 to the Sun by a force given by Work Done by the Sun on a probe in SI units, where x is the Sun-probe separation distance. Determine how much work is done by the Sun on the probe as the probe–Sun separation changes from X1 to X2 m. 34  Example #11 Work Done by the Sun on a probe 35