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 Connected Objects

Example #2: Energy in Connected Objects

Practice: The 4-kg block is 1 m above the floor, and the surface-block coefficient of friction for the 3-kg block is 0.4. If the system is released from rest, find its speed just before the 4-kg block hits the floor. (The string and pulley are massless)

Practice: The system below is released from rest. Calculate the speed of the system after the hanging block has moved 1 meter. (The string and pulley are massless, and you may disregard any effects due to friction)

Additional Problems
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?
Two objects are connected by a light string passing over a light, frictionless pulley as shown in the figure. The object of mass m1 = 5.00 kg is released from rest at a height h = 4.00 m above the table. Using the isolated system model,(a) determine the speed of the object of mass m2 = 3.00 kg just as the 5.00-kg object hits the table(b) find the maximum height above the table to which the 3.00-kg object rises
A block of mass m1 = 20.0 kg is connected to a block of mass m2 = 30.0 kg by a massless string that passes over a light, frictionless pulley. The 30.0-kg block is connected to a spring that has negligible mass and a force constant of k = 250 N/m as shown in the figure. The spring is unstretched when the system is as shown in the figure, and the incline is frictionless. The 20.0-kg block is pulled a distance h = 20.0 cm down the incline of angle θ = 40.0° and released from rest. Find the speed of each block when the spring is again unstretched.
The coefficient of friction between the block of mass m1 = 3.00 kg and the surface in the figure is µk = 0.400. The system starts from rest. What is the speed of the ball of mass m2 = 5.00 kg when it has fallen a distance h = 1.50 m?
Two masses are connected by a string as shown in the figure. mA exttip{m_{ m A}}{m_A}= 3.6 kg rests on a frictionless inclined plane, while mB exttip{m_{ m B}}{m_B}= 4.6 kg is initially held at a height of h exttip{h}{h}= 0.75 m above the floor.(a) If mB is allowed to fall, what will be the resulting acceleration of the masses?(b) If the masses were initially at rest, use the kinematic equations to find their velocity just before mB hits the floor.(c) Use conservation of energy to find the velocity of the masses just before mB hits the floor.
A system of two paint buckets connected by a lightweight rope is released from rest with the 12.0-kg bucket 2.00 m above the floor. Use the principle of conservation of energy to find the speed with which this bucket strikes the floor. You can ignore friction and the mass of the pulley.