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
Use work and energy to find an expression for the speed of the block in the following figure just before it hits the floor.Find an expression for the speed of the block if the coefficient of kinetic friction for the block on the table is k.Find an expression for the speed of the block if the table is frictionless.
Two blocks are connected by a very light string passing over a massless and frictionless pulley (Figure ). The 20.0-N block moves 75.0 cm to the right and the 12.0-N block moves 75.0 cm downward.Find the total work done on 20.0-N block if there is no friction between the table and the 20.0-N block.Find the total work done on 20.0-N block if s=0.500 and k=0.325 between the table and the 20.0-N block.Find the total work done on 12.0-N block if there is no friction between the table and the 20.0-N block.Find the total work done on 12.0-N block if s = 0.500 and k = 0.325 between the table and the 20.0-N block.
Consider the system shown in the figure . The rope and pulley have negligible mass, and the pulley is frictionless. Initially the 6.00-kg block is moving downward and the 8.00-kg block is moving to the right, both with a speed of 0.600 m/s . The blocks come to rest after moving 6.00 m .Use the work-energy theorem to calculate the coefficient of kinetic friction between the 8.00-kg block and the tabletop.
At a construction site, a 66.0 kg bucket of concrete hangs from a light (but strong) cable that passes over a light friction-free pulley and is connected to an 83.0 kg box on a horizontal roof (see the figure ). The cable pulls horizontally on the box, and a 48.0 kg bag of gravel rests on top of the box. The coefficients of friction between the box and roof are shown. The system is not moving.Find the friction force on the bag of gravel.Suddenly a worker picks up the bag of gravel. Use energy conservation to find the speed of the bucket after it has descended 2.10 m , from rest. (You can check your answer by solving this problem using Newtons laws.)Find the friction force on the box.
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.
As shown in Figure P8.46, a light string that does not stretch changes from horizontal to vertical as it passes over the edge of a table. The string connects m1, a 3.50-kg block originally at rest on the horizontal table at a height h = 1.20 m above the floor, to m2, a hanging 1.90-kg block originally a distance d = 0.900 m above the floor. Neither the surface of the table nor its edge exerts a force of kinetic friction. The blocks start to move from rest. The sliding block m1 is projected horizontally after reaching the edge of the table. The hanging block m2 stops without bouncing when it strikes the floor. Consider the two blocks plus the Earth as the system.(a) Find the speed at which m1 leaves the edge of the table.(b) Find the impact speed of m1 on the floor.(c) What is the shortest length of the string so that it does not go taut while m1 is in flight?(d) Is the energy of the system when it is released from rest equal to the energy of the system just before m1 strikes the ground?(e) Why or why not?
Two objects are connected by a light string passing over a light, frictionless pulley as shown in Figure P8.7. The object of mass m1 is released from rest at height h above the table. Using the isolated system model, (a) determine the speed of m2 just as m1 hits the table and(b) find the maximum height above the table to which m2 rises.
The system shown in Figure P8.11 consists of a light, inextensible cord, light, frictionless pulleys, and blocks of equal mass. Notice that block B is attached to one of the pulleys. The system is initially held at rest so that the blocks are at the same height above the ground. The blocks are then released. Find the speed of block A at the moment the vertical separation of the blocks is h.