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Transcript
Chris McWilliams Lab: AP Review Sheet Chapter 07: Energy of a System Summary So far we have been using kinematics equations and force analysis to solve problems. Though these techniques are appropriate for many scenarios, they fall short in others and it is for these that we will use an energy approach. By examining the work done on a system, we can determine the amount of energy transferred from one object to another. We will also review potential and kinetic energy and use these principles to calculate the total energy in a system. Equations Energy Terms Work: a transfer of energy that occurs when a force is applied to an object over a certain distance. ⋅ SI unit for work is newton meter(N ⋅ Work W = FΔr cosθ M) xf W = Dot product Kinetic energy: Energy associated with the motion of a particle. € A • B ≡ ABcos θ Force of a spring € Potential energy: Energy that represents the amount of kinetic energy that a particle has the potential to possess. x xi Spring constant: the spring constant k is a value that is unique to each individual spring. € ∫ F dx € Workkinetic energy theorem: When work is done on a system and the only change in the system is in its speed, the net work done on the system equals the change in kinetic energy of the system. € € Potential energy of a spring 1 U s = kx 2 2 SI unit for energy is joules (J) Conservative force: a force which satisfies the conservative force properties, the most prominent being gravitational force and € spring force. Fs = −kx External Work 1 1 2 2 W ext = ΔK = mv f − mv i 2 2 Chris McWilliams Conservative force properties: 1. The work done by a conservative force on a particle moving between any two points is independent of the path taken by the particle. 2. The work done by a conservative force on a particle moving through any path for which the beginning and endpoint are the same is zero. Practice Problems € € Equations Kinetic energy K= 1 mv 2 2 Potential energy U g = mgh Forceenergy relationship Fx = − € dU dx Problem 1: A man pulls box across the floor with a force of 50.0 N at an angle of 30° with the horizontal. Calculate the work done by the force on the box as the box is displaced 3.00 m to the right. € 30° € Solution: W = FΔr cosθ € W = (50.0N)(3.00m)(cos(30°)) W = 130J Chris McWilliams Problem 2: A spring is hung vertically, and an object of mass m is attached to its lower end. Under the action of the load, the spring stretches a distance d from its equilibrium position. A) If a spring is stretched 2.0 cm by a suspended object having a mass of 0.55 kg, what is the force constant of the spring? B) How much work is done by the spring on the object as it stretches through this distance? Solution: A) Fs − mg = 0 Fs = mg kx = mg mg (0.55kg)(9.80m /s2 ) k= = d 2.0 ×10−2 m k = 2.7 ×10 2 N /m B) € € 1 W s = 0 − kd 2 2 1 W s = − (2.7 ×10 2 N /m)(2.0 ×10−2 m) 2 2 W s = −5.4 ×10−2 J Chris McWilliams Problem 3: A 6.0 kg block initially at rest is pulled to the right along a frictionless, horizontal surface by a constant horizontal force of 12 N. Find the block’s speed after it has moved 3.0 m. Solution: 1 2 W ext = K f − K i = mv f 2 2W ext 2FΔx vf = = m m vf = € 2 ⋅ (12N)(3.0m) 6.0kg v f = 3.5m /s