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

Example #1: Energy in Curved Paths

Example #2: Energy in Curved Paths

Example #3: Energy in Curved Paths

Concept #1: More Rollercoaster Problems

Concept #2: Gravitational Energy is Relative (Pendulums)

Practice: A 60 kg surfer is moving with 3 m/s at a certain point in a wave. Later on, he is moving with 8 m/s at a second point, 2 meters lower. Calculate the work done by the wave on the surfer.

Example #4: More Pendulum Problems

Practice: A pendulum is built from a 3 kg bob and a 4 m-long light rope. It is attached to the ceiling and pulled from its equilibrium position until it makes an angle of 53° with the vertical. It is then given an initial speed of 2 m/s directed down. 

(a) Calculate the maximum speed that the pendulum will attain. 

(b) Calculate the maximum angle that the pendulum will make with the vertical on the other side.

Concept #3: Energy Problems with Bumps (Part A)

Concept #4: Energy Problems with Bumps (Part B)

Concept #5: Energy Problems with Bumps (Part C)

Additional Problems
A pendulum is released from rest at an angle of 40 o. If the pendulum is made of a light, 1 m string supporting a 2.5 kg bowling ball, what is the speed of the bowling ball at its lowest point in the motion? What is the tension in the string at the lowest point?
A 5 kg object undergoes uniform circular motion. If the object has a tangential speed of 15 m/s in a 0.7 m orbit and undergoes a 1/4 revolution, how much work was done on the object by the centripetal force?
A 500 kg car carrying 200 kg of passengers on a rollercoaster encounters a stop on the track shown in the figure below. How high does the car have to start in order to traverse the loop without any passengers being in danger of falling out if their harness broke? Note that the car starts from rest at the top of the slope and that there is no friction between the car and the track.
A small rock of mass m is attached to a strong string and whirled in a vertical circle of radius R. When the rock is at the lowest point in its path, the tension in the string is five times the weight of the rock. At this point the speed of the rock isA) √2gRB) √3gRC) 2√gRD) 3√gRE) √5gRF) √6gRG) None of the above answers
A 240 kg roller coaster car starts from rest at point A and slides down the frictionless loop-the-loop shown in the accompanying figure. Point A is 25.0 m above the ground and point B is 12.0 m above the ground. The height of other points on the track are shown in the diagram.How fast is this roller coaster moving at point B?
A 240 kg roller coaster car starts from rest at point A and slides down the frictionless loop-the-loop shown in the accompanying figure. Point A is 25.0 m above the ground and point B is 12.0 m above the ground. The height of other points on the track are shown in the diagram.What is the magnitude of the normal force that the track exerts on it at point B?
A 5.00 m long light rope is tied to the ceiling. A steel ball with mass 2.00 kg is attached to the lower end of the rope. The ball is pulled to one side and released, and swings back and forth as a pendulum. As the ball passes through its lowest point, with the rope vertical, its speed is 6.00 m/s. As the ball swings through this point, what is the tension in the rope?(a) 34.0 N(b) 26.8 N(c) 19.6 N(d) 14.4 N(e) 12.4 N(f) 5.2 N(g) none of the above answers
One end of a 6.00 m long rope is tied to the ceiling. A small rock with mass 0.500 kg is tied to the other end of the rope. The rock is released from rest with the rope horizontal. What is the tension in the rope when the rock is swinging through its lowest point, where the rope is vertical?A) zeroB) 4.9 NC) 9.8 ND) 14.7 NE) 19.6 NF) None of the above answers