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 205 kg block is released at a 6.3 m height as shown. The track is frictionless. The block travels down the track, hits a spring of force constant k = 1285 N/m . The acceleration of gravity is 9.8 m/s2. Determine the compression of the spring x from its equilibrium position before coming to rest momentarily. A. 3.39911 B. 2.46691 C. 3.05595 D. 2.80797 E. 3.4477 F. 3.57838 G. 2.50776 H. 3.66395 I. 3.72911 J. 4.43837
A 50 kg crate is at rest on the floor, and you need to move it across a room. The floor you are moving it across has a coefficient of static friction of 0.5 and a coefficient of kinetic friction of 0.3. In order to move it across the room, first you need to move it 5 m to the left, then 7 m forward, then finally 3 m to the right. How much work do you do on the box in order to move it across the room?
A 1.86-kg block is held in place against the spring by an 81-N horizontal external force (see the figure). The external force is removed, and the block is projected with a velocity v1 = 1.2 m/s upon separation from the spring. The block descends a ramp and has a velocity v2 = 1.9 m/s at the bottom. The track is frictionless between points A and B. The block enters a rough section at B, extending to E. The coefficient of kinetic friction over this section is 0.28. The velocity of the block is v3 = 1.4 m/s at C. The block moves on to D, where it stops. The height h of the ramp is closest to _____. A. 15 cm B. 17 cm C. 11 cm D. 18 cm E. 7.3 cm
A box of mass m = 1.80 kg is at point A, which is at the top of an inclined plane of length ℓ = 2.40 m and inclination angle θ = 36.9°. The inclined angle is greased so that it is frictionless. The box slides down the inclined plane to the point B, where it starts to move horizontally across a surface with coefficient of kinetic friction μk. The box moves a distance d = 4.80 m across this surface before coming to rest at point C. Find the gravitational potential energy of the box at point A (the top of the incline).
An object moves along a floor with some coefficient of kinetic friction. Which of the following statements is true? a. The work done by friction is positive, and doesn’t depend upon the path taken b. The work done by friction is positive, and does depend upon the path taken c. The work done by friction is negative, and doesn’t depend upon the path taken d. The work done by friction is negative, and does depend upon the path taken  
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?
In the following figure, the pulley doesn’t rotate without friction, so it limits how fast the system can move. In this particular case, the 15 kg mass can only drop at a maximum speed of 10 m/s. At this speed, how much work does the pulley need to do every meter the 15 kg mass drops?
A small rock block with mass 0.400 kg is placed against a compressed spring at the bottom of a 37.0° incline. The compressed spring has 50.0 J of elastic potential energy stored in it. The spring is released and the block moves a distance of 12.0 m along the incline before momentarily coming to rest. How much work does the friction force do on the block during the motion? What is the coefficient of kinetic frinction μk between the block and the incline?
A box of mass m = 1.80 kg is at point A, which is at the top of an inclined plane of length ℓ = 2.40 m and inclination angle θ = 36.9°. The inclined angle is greased so that it is frictionless. The box slides down the inclined plane to the point B, where it starts to move horizontally across a surface with coefficient of kinetic friction μk. The box moves a distance d = 4.80 m across this surface before coming to rest at point C.Calculate μk. Hint: if there were no friction, the box would not stop moving. What does this tell you about the work done against friction over the distance d?
A block of mass 10.0 kg slides 16.0 m down a 36.9° incline, from point A at the top of the incline to point B at the bottom. As the block moves from point A to point B, the surface of the incline exerts a constant friction force that has magnitude 42.0 N.If the block has an initial speed of 8.0 m/s at point A, what is the speed of the block when it reaches point B?
A box with mass 5.00 kg is pulled up a 36.9° incline by a constant force  F that has magnitude 75.0 N and that is parallel to the incline. The distance along the incline from the bottom to the top is 6.00 m. During the motion of the box, the surface of the incline exerts a constant friction force fk = 18.0 N on the box, in a direction opposite to the motion.If the box starts froom rest at the botttom of the incline, what is the kinetic energy of the box when it reaches the top of the incline?
A box with mass 5.00 kg is placed against a compressed spring. The spring is released and the box slides 4.00 m along a horizontal surface before coming to rest. (At this point the box is no longer in contact with the spring and there is no potential energy left stored in the spring.) The coefficient of kinetic friction between the block and the surface is 0.300. How much energy was initially stored in the compressed spring?