Ch 08: Conservation of EnergyWorksheetSee all chapters
All Chapters
Ch 01: Units & Vectors
Ch 02: 1D Motion (Kinematics)
Ch 03: 2D Motion (Projectile Motion)
Ch 04: Intro to Forces (Dynamics)
Ch 05: Friction, Inclines, Systems
Ch 06: Centripetal Forces & Gravitation
Ch 07: Work & Energy
Ch 08: Conservation of Energy
Ch 09: Momentum & Impulse
Ch 10: Rotational Kinematics
Ch 11: Rotational Inertia & Energy
Ch 12: Torque & Rotational Dynamics
Ch 13: Rotational Equilibrium
Ch 14: Angular Momentum
Ch 15: Periodic Motion (NEW)
Ch 15: Periodic Motion (Oscillations)
Ch 16: Waves & Sound
Ch 17: Fluid Mechanics
Ch 18: Heat and Temperature
Ch 19: Kinetic Theory of Ideal Gasses
Ch 20: The First Law of Thermodynamics
Ch 21: The Second Law of Thermodynamics
Ch 22: Electric Force & Field; Gauss' Law
Ch 23: Electric Potential
Ch 24: Capacitors & Dielectrics
Ch 25: Resistors & DC Circuits
Ch 26: Magnetic Fields and Forces
Ch 27: Sources of Magnetic Field
Ch 28: Induction and Inductance
Ch 29: Alternating Current
Ch 30: Electromagnetic Waves
Ch 31: Geometric Optics
Ch 32: Wave Optics
Ch 34: Special Relativity
Ch 35: Particle-Wave Duality
Ch 36: Atomic Structure
Ch 37: Nuclear Physics
Ch 38: Quantum Mechanics

Concept #1: Conservation of Total Energy

Concept #2: Conservation of Mechanical Energy

Example #1: Conservation of Energys

Concept #3: The Conservation of Energy Equation

Example #2: Using the Energy Equation

Concept #4: Using the Energy Equation

Example #3: Using the Energy Equation

Additional Problems
The potential energy between two identical atoms has the form U(x) = A / x 10 − B / x5 where x is the separation distance between the atoms and A and B are constants with appropriate units. The two atoms, initially very far apart, are released from rest. What is the maximum kinetic energy that each of the two atoms can have? 1. Kmax = (A2 / 2B) 2. Kmax = (B2 / 4A) 3. Kmax = (A2 / 8B) 4. Kmax = (A / 4) 5. Kmax = (B2 / 2A) 6. Kmax = 0 7. Kmax = (B / 8) 8. Kmax = (B2 / 8A) 9. Kmax = (A2 / 4B) 10. Kmax = (B)
Is it possible for a system to have negative potential energy? A. Yes, as long as the total energy is positive. B. Yes, since the choice of the zero of potential energy is arbitrary. C. No, because this would have no physical meaning. D. Yes, as long as the kinetic energy is positive. E. No, because the kinetic energy of a system must equal its potential energy.
When an object moves from A to point B, gravity does positive work on the object. When the object from point A to point B, its gravitational potential energy A) stays the same B) increases C) decreases
A 150 g object starts on the ground, is moved 1.2 m in the +x direction over a frictionless surface, is then moved upwards 50 cm, then moved in a straight line back to its starting position. How much work does gravity do during this motion?
Swimmers at water park have a choice of two frictionless water slides, as shown in the figure. Although both slides drop over the same height h, slide 1 is straight while slide 2 is curved, dropping quickly at first and then leveling out. How does the speed v1 of a swimmer reaching the bottom of slide I compare with v 2, the speed of a swimmer reaching the end of slide 2? A) v1 > v2 B) v1 < v2 C) v1 = v2 D)  The heavier swimmer will have a greater speed than the lighter swimmer, no matter which slide he uses. E) No simple relationship exists between v1 and v2.
You and your friend, who weighs the same as you, want to go to the top of the Eiffel Tower. Your friend takes the elevator straight up. You decide to walk up the spiral stairway, taking longer to do so. Compare the gravitational potential energy of you and your friend, after you both reach the top. A) It is impossible to tell, since the times you both took are unknown. B) It is impossible to tell, since the distances you both traveled are unknown. C) You friend's gravitational potential energy is greater than yours, because he got to the top faster. D) Your gravitational potential energy is greater than that of your friend, because you traveled a greater distance getting to the top. E) Both of you have the same amount of gravitational potential energy at the top.
A 12 kg mass is moving down a frictionless incline under the influence of gravity. If the incline has a height of 1 m, and an incline angle of 35°, how much work is done by gravity as the mass slides down the surface? What is the kinetic energy of the mass at the bottom of the incline?
At time t i, the kinetic energy of a particle is 30.0 J and the potential energy of the system to which it belongs is 10.0 J. At some later time tf, the kinetic energy of the particle is 18.0 J.(a) If only conservative forces act on the particle, what are the potential energy and the total energy of the system at time tf?(b) If the potential energy of the system at time tf is 5.00 J, are any nonconservative forces acting on the particle?(c) Explain your answer to part (b).
A 6.0 kg monkey swings from one branch to another 1.5 m higher. What is the change in gravitational potential energy?
A system loses 660 J of potential energy. In the process, it does 660 J of work on the environment and the thermal energy increases by 160 J. Find the change in kinetic energy K.
(a) How much work is done by the environment in the process shown in the figure?(b) Is energy transferred from the environment to the system or from the system to the environment?
Consider the process shown in the figure below. Suppose E1 = 3 J. What is the final kinetic energy of the system for the process shown in the figure?
In one day, a 85 kg mountain climber ascends from the 1520 m level on a vertical cliff to the top at 2420 m. The next day, she descends from the top to the base of the cliff, which is at an elevation of 1310 m.(a) What is her change in gravitational potential energy on the first day?(b) What is her change in gravitational potential energy on the second day?