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: Non-Conservative Problems

Example #2: Non-Conservative Problems

Practice: Your hand moves a horizontal distance of 1.6 meter while you throw a 0.140-kg baseball horizontally. If the ball leaves your hand at 35 m/s, calculate: (a) the work done by you, and (b) the average force you exert on the ball.

Practice: A 500-kg load is originally at rest on the floor. A crane pulls the load vertically up on the box with a constant 7,500 N until it reaches a height of 20 m. Calculate the speed of the load once it reaches 20 m.

Practice: A 800-kg car leaves a skid mark of 90 m in stopping from 30 m/s. Calculate the car-road coefficient of friction.

Example #3: Energy with Resistive Forces

Practice: A 10-g bullet hits a wooden wall with a horizontal 300 m/s. If the bullet penetrates the wall by 5 cm, calculate: 

(a) the amount of energy lost by the bullet. 

(b) the average frictional force that stops the bullet.

Example #4: Energy with Resistive Forces

Additional Problems
A 30 g object is dropped from a height of 50 cm and bounces off the ground. If after the bounce, the ball leaves the ground with 50% of the speed it hit with, how high will the ball bounce?
A sled of mass m is given a kick on a frozen pond. The kick imparts to the sled an initial speed of v. The coefficient of kinetic friction between sled and ice is µk. Use energy considerations to find the distance the sled moves before it stops.
A 11.0 kg box is pulled by a horizontal wire in a circle on a rough horizontal surface for which the coefficient of kinetic friction is 0.300.(a) Calculate the work done by friction during one complete circular trip if the radius is 2.00 m.(b) Calculate the work done by friction during one complete circular trip if the radius is 4.00 m.(c) On the basis of the results you just obtained, would you say that friction is a conservative or nonconservative force?
A 62.0-kg skier is moving at 6.60 m/s on a frictionless, horizontal, snow-covered plateau when she encounters a rough patch 4.60 m long. The coefficient of kinetic friction between this patch and her skis is 0.300. After crossing the rough patch and returning to friction-free snow, she skis down an icy, frictionless hill 2.50 m high.(a) How fast is the skier moving when she gets to the bottom of the hill?(b) How much internal energy was generated in crossing the rough patch?
You drop a ball from a height of 2.1 m, and it bounces back to a height of 1.3 m.(a) What fraction of its initial energy is lost during the bounce?(b) What is the balls speed just before the bounce?(c) Where did the energy go?(d) What is the balls speed just after the bounce?
A 2.3 kg piece of wood slides on the surface shown in the figure. The curved sides are perfectly smooth, but the rough horizontal bottom is 33 m long and has a kinetic friction coefficient of 0.26 with the wood. The piece of wood starts from rest 4.0 m above the rough bottom.(a) Where will this wood eventually come to rest?(b) For the motion from the initial release until the piece of wood comes to rest, what is the total amount of work done by friction?
A small block with mass 0.0425 kg slides in a vertical circle of radius 0.525 m on the inside of a circular track. During one of the revolutions of the block, when the block is at the bottom of its path, point A, the magnitude of the normal force exerted on the block by the track has magnitude 3.90 N. In this same revolution, when the block reaches the top of its path, point B, the magnitude of the normal force exerted on the block has magnitude 0.680 N. How much work was done on the block by friction during the motion of the block from point A to point B?