PHY 317K 1st EditionExam 1 Study Guide: Lecture 7 - 11Work and Conservation of EnergyLecture 7- Work is equal to force times distance- Work done at an angle is equal to F cosine theta times delta x- Conservation of energy:There are two types of energy:- Potential Energyo Position of the object in a force fieldo PE = mgh- Kinetic Energyo KE = ½ mv^2o Depends on the motion or speed of an object- Non-Conservative Force: Work depends on the path when friction is involved (friction can be air resistance or anything that is an opposing force)- Conservative Force: Work does NOT depend on the path, so regardless of the path that the object takes, the work is the sameo KEi + PEi = KEf + PEf o The summation of the initial kinetic and potential energy is equal to the final kinetic and potential energyPractice Problems:1.A cart loaded with bricks has a total mass of 21.6 kg and is pulled at constant speed by a rope. The rope is inclined at 27.8 ◦ degrees above the horizontal and the cart moves 31.7m on a horizontal floor. The coefficient of kinetic friction between ground and cart is 0.329. The acceleration of gravity is 9.8 m/s2 .How much work is done on the cart by therope? 2. A weight lifter lifts a mass m at constant speed to a height h in time t. How much work W is done by the weight lifter? 3.A block of mass 4 kg, which has an initial speed of 5m/s at time t=0, slides on a horizontal surface. Find the magnitude of the work that must be done on the block to bring it to rest.4.If a constant friction force of magnitude 14 newton’s is exerted on the block by the surface, find the magnitude of the acceleration of the block. 5. How far does the block slide before it comes to rest? Answers:1.1.88133 kJ.2.W= mgh3.50J4.3.5 m/s^25.3.57143 m.Conservation of Energy RevisitedLecture 8Work at an Angle:- If an object is pulled at an angle, the work is given by W = F d sin theta (if the object is being pulled at 30 degrees above the horizontal)- Work is force times distance, therefore the force is calculated by the tension pulled by the ropePotential Energy:- Potential energy depends on the height and the mass of an object- PE = mgh- The higher an object is above the ground, the more potential energy it has- The larger an object is, the more potential energy it has- Potential energy can translate to kinetic energy- Since potential energy and kinetic energy are conserved, an object with a larger potential energy will have more kinetic energyKinetic Energy:- Kinetic energy depends on the mass and velocity of an object- This is the energy given by motion- The larger the mass of an object, the more kinetic energy it has- The larger the velocity of an object, the more kinetic energy- KE = ½ mv^2Practice Problems:1.A 0.50 kg rubber ball has a speed of 2.6 m/s at point A and kinetic energy 7.8 J at point B. Find the balls kinetic energy at A.2.Find the balls speed at B. 3.Find the total work done on the ball as it moves from A to B. 4.A 0.321 kg mass is attached to a spring with a spring constant 199 N/m so that the mass is allowed to move on a horizontal frictionless surface. The mass is released from rest when the spring is compressed 0.184 m. Find the maximum force on the mass. 5.Find the maximum acceleration.6. A 0.2 kg bead slides on a curved wire, starting from rest at point A as shown in the figure. The segment from A to B is frictionless, and the segment from B to C is rough. The point Aisatheight6.1mandthepointCisat height 2.3 m with respect to point B. Find the speed ofthe bead at B. The acceleration due to gravity is 9.8 m/s^2. 7.If the bead comes to rest at C, find the change in mechanical energy due to friction as it moves from B to C. Answers:1.1.69 J2.5.5857 m/s3.6.11 J4.36.616 N5.114.069 m/s26.10.9343 m/s7.−7.448 JPower and MomentumLecture 9Power:- Power is energy divided by time- P = w/t- P = Fx/t - P = Fv (force times velocity)The Force of Gravity:- F = G m1 m2 / r^2- M1 = large mass- M2 = small mass- So the acceleration of the small mass can equal a = GM/ r^2 by rearranging the equation- G is the universal constant of gravitation - G = 6.67 x 10^-11 Nm^2/Kg^2Center of Mass:- The point on an object where the mass is evenly distributed- This point can be balanced if held up in the air- M1D1 = m2D2- The center of mass on point x is given by the summation of all the masses and the distance on point x divided by the entire massMomentum:- Linear momentum is given by mass times velocity- Linear momentum is conserved - If we have a large and a small ball that collide, the one with a larger mass will have a smaller final velocity than the small ballPractice Problems:1.The linear impulse delivered by the hit of a boxer is 126 N · s during the 0.133 s of contact.What is the magnitude of the average force exerted on the glove by the other boxer? 2.A child bounces a 54 g superball on the side- walk. The velocity change of the superball is from 23 m/s downward to 11 m/s upward. If the contact time with the sidewalk is 1/800 s, what is the magnitude of the average force exerted on the superball by the sidewalk? 3.A 113 g cart moves on a horizontal, frictionless surface with a constant speed of 33.7 cm/s. A 59.5 g piece of modeling clay is dropped vertically onto the cart. If the clay sticks to the cart, find the final speed of the system. 4.A 7 kg mass slides to the right on a surface having a coefficient of friction 0.56 as shown. The mass has a speed of 6 m/s when contact is made with a spring that has a spring constant 129 N/m. The mass comes to rest after the spring has been compressed a distance d. The mass is then forced toward the left by the spring and continues to move in that direction beyond the unstretched position. Finally the mass comes to rest a distance D to the left of the unstretched spring. Find the compressed distance d.Answers:1.947.368 N2.1468.8 N3.22.0759 cm/s4.1.13125 mElastic and Inelastic CollisionsLecture 10 (February 19, 2013)Elastic collision:- Energy is conserved (kinetic)- No loss of kinetic energy- Momentum conservationInelastic collision:- momentum conserved- Perfect inelastic collision: two objects stuck together and lose energyo Momentum conserved- Kinetic energy is changed to some other form of energyConservation of Momentum:- Summation of pf = summation of pi- Momentum is denoted by “P”, so final momentum is Pf and initial momentum is Pi- Vf = (m1-m2)/(m1+m2)