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 small rock with mass 0.22 kg is released from rest at point exttip{A}{A}, which is at the top edge of a large, hemispherical bowl with radius exttip{R}{R} = 0.52 m (the figure ). Assume that the size of the rock is small compared to R, so that the rock can be treated as a particle, and assume that the rock slides rather than rolls. The work done by friction on the rock when it moves from point exttip{A}{A} to point exttip{B}{B} at the bottom of the bowl has magnitude 0.22 J.Between points exttip{A}{A} and exttip{B}{B}, how much work is done on the rock by the normal force?What is the speed of the rock as it reaches point exttip{B}{B}?Of the three forces acting on the rock as it slides down the bowl, which (if any) are constant and which are not? Explain.Just as the rock reaches point exttip{B}{B}, what is the normal force on it due to the bottom of the bowl?Between points exttip{A}{A} and exttip{B}{B}, how much work is done on the rock by gravity?
In an auto accident, a car hit a pedestrian and the driver then slammed on the brakes to stop the car. During the subsequent trial, the drivers lawyer claimed that he was obeying the posted 40 mi/h speed limit, but that the legal speed was too high to allow him to see and react to the pedestrian in time. You have been called in as the states expert witness. Your investigation of the accident found that the skid marks made while the brakes were applied were 280 ft long, and the tread on the tires produced a coefficient of kinetic friction of 0.30 with the road.In your testimony in court, will you say that the driver was obeying the posted speed? You must be able to back up your conclusion with clear reasoning because one of the lawyers will surely cross-examine you.If the drivers speeding ticket were $10 for each mile per hour he was driving above the posted speed limit, would he have to pay a fine? If so, how much would it be?
Two identical arrows, one with twice the speed of the other, are fired into a bale of hay.Assuming the hay exerts a constant "frictional" force on the arrows, the faster arrow will penetrate how much farther than the slower arrow?
A baggage handler throws a 15 kg suitcase along the floor of an airplane luggage compartment with a speed of 1.2 m/s. The suitcase slides 2.1 m before stopping.Use work and energy to find the suitcase’s coefficient of kinetic friction on the floor.
In a truck-loading station at a post office, a small 0.200-kg package is released from rest at point exttip{A}{A} on a track that is one-quarter of a circle with radius 1.60 m (the figure ). The size of the package is much less than 1.60 m, so the package can be treated as a particle. It slides down the track and reaches point exttip{B}{B} with a speed of 4.60 m/s . From point exttip{B}{B}, it slides on a level surface a distance of 3.00 m to point C, where it comes to rest.What is the coefficient of kinetic friction on the horizontal surface?How much work is done on the package by friction as it slides down the circular arc from exttip{A}{A} to exttip{B}{B}?
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?
A smooth circular hoop with a radius of 0.500 m is placed flat on the floor. A 0.400-kg particle slides around the inside edge of the hoop. The particle is given an initial speed of 8.00  m/s. After one revolution, its speed has dropped to 6.00 m/s because of friction with the floor.(a)  Find the energy transformed from mechanical to internal in the particle–hoop– floor system as a result of friction in one revolution.(b) What is the total number of revolutions the particle makes before stopping? Assume the friction force remains constant during the entire motion.
A sled of mass m is given a kick on a frozen pond. The kick imparts to the sled an initial speed of 2.00 m/s. The coefficient of kinetic friction between sled and ice is 0.100. Use energy considerations to find the distance the sled moves before it stops.
A uniform board of length L is sliding along a smooth, frictionless, horizontal plane as shown in Figure P8.79a. The board then slides across the boundary with a rough horizontal surface. The coefficient of kinetic friction between the board and the second surface is µk. (a) Find the acceleration of the board at the moment its front end has traveled a distance x beyond the boundary. (b) The board stops at the moment its back end reaches the boundary as shown in Figure P8.79b. Find the initial speed v of the board.