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

Concept #1: Conservative Forces are Path Independent

Practice: A 3 kg block is initially moving on a flat surface when it reaches the bottom of an inclined plane with 20 m/s. If the plane is smooth and makes 53° with the horizontal, how far up the plane will the block slide?

Example #1: Energy Problems in Inclines

Example #2: Energy Problems in Inclines

Example #3: Energy Problems in Inclines

Practice: When a 4-kg block is released from rest from the top of an inclined plane, it reaches the bottom with 4 m/s. The incline is 5 m long and makes 37° with the horizontal. Calculate the magnitude of the frictional force acting on the block.

Practice: When a block of unknown mass is released from the top of an inclined plane of length L meters, it slides down. The incline makes an angle of Θ degrees with the horizontal, and the coefficient of kinetic friction between the block and the plane is µ. Derive an expression for the speed of the block at the bottom of the plane.

Practice: A block of unknown mass is released from a distance D1 from the bottom of an inclined plane, then slides on a horizontal surface, and up a second inclined plane, as shown. Both planes make an angle of Θ degrees with the horizontal. The horizontal surface is smooth, but the coefficient of friction between the block and the two inclines is µ. Derive an expression for the maximum distance D2 that the block will reach on the second incline.

Additional Problems
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).
You are designing a ski jump ramp for the next Winter Olympics. You need to calculate the vertical height h from the starting gate to the bottom of the ramp. The skiers push off hard with their ski poles at the start, just above the starting gate, so they typically have a speed of 2.0 m/s as they reach the gate. For safety, the skiers should have a speed of no more than 30.0 m/s when they reach the bottom of the ramp. You determine that for a 83.0 kg skier with good form, friction and air resistance will do total work of magnitude 4000 J on him during his run down the slope. What is the maximum height h for which the maximum safe speed will not be exceeded?
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 sled is initially given a shove up a frictionless 23.0° incline. It reaches a maximum vertical height 1.27 m { m { m m}}higher than where it started. What was its initial speed?
What height does a frictionless playground slide need so that a 35 kg child reaches the bottom at a speed of 5.7 m/s?