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: Projectile Motion with Energy

Example #2: Projectile Motion with Energy

Practice: You are practicing jumping as far as you can. In one attempt, you run and leave the floor with 7 m/s directed at an unknown angle. What maximum height do you reach if your speed at that point is 5 m/s? Ignore air resistance.

Practice: When you launch a 3-kg object from the ground with unknown initial speed directed at 37° above the x-axis, it hits the building shown below at 15 m above the ground with 25 m/s. Calculate the object’s launch speed.

Practice: A 3-kg box is nudged off the top of the path shown below, slides down, and is launched form the lower end of the path. The path is frictionless and its highest point is 10 m above the ground. The lower end is 2 m above the ground and makes 53° with the horizontal. Calculate the box’s speed: 

(a) at the lowest point in the path; 

(b) just before it leaves the path; 

(c) at its highest point; 

(d) just before it hits the ground.

Additional Problems
An archer performs 20.0 J of work to stretch a bow, storing elastic potential energy in it (much like a spring). The archer then loads an arrow of mass 100 g into the stretched bow, and fires it at an angle of 30.0° above the horizontal. What is the horizontal component of the arrow’s velocity as it leaves the bow A. 20.0 m/s B. 0.63 m/s C. 17.3 m/s D. 10.0 m/s E. 0.55 m/s
A 7 kg projectile is fired at an initial speed of 43 m/s, with a launch angle of 32°. What is the initial kinetic energy of the projectile? What is the kinetic energy of the projectile at its maximum height?
It's been a great day of new, frictionless snow. Julie starts at the top of the 60° slope shown in the figure. At the bottom, a circular arc carries her through a 90 m turn, and she then launches off a 3.0-m { m m}high ramp. How far horizontally is her touchdown point from the end of the ramp?
A projectile is fired at an upward angle of 48.0° from the top of a 130-m-high cliff with a speed of 180 m/s m m/s. What will be its speed when it strikes the ground below? (Use conservation of energy. Neglect air resistance.)
A projectile is fired at an initial speed of v 0 at a launch angle of  θ. Using energy conservation, find the maximum height of the projectile.
A boy starts at rest and slides down a frictionless slide as shown in the figure. The bottom of the track is a height h above the ground. The boy then leaves the track horizontally, striking the ground at a distance d as shown. Using energy methods, determine the initial height H of the boy above the ground in terms of h and d.