Potential energy defined; proof of conservation of mechanical energy.

Example of ball in rollercoaster; proof that h ≥ 2.5R for ball to make it around.

Conservation of mechanical energy demonstrated by swinging wrecking ball across room.

Derivation of differential equation for SHM from conservation of energy in a spring.

Setup and calculations for system of bullet hitting pendulum to measure speed.

Numerical calculations for ballistic pendulum experiment; kinetic energy loss approximated.

Work-Energy Theorem and conservation of mechanical energy restated.

Calculation of acceleration and descent time for this system from dynamics and from conservation of energy.

Calculation of θ_max for pendulum moving upwards along arc, using conservation of energy.

Kinetic energy of a particle; gravitational potential energy; the law of conservation of mechanical energy. Includes several examples.

Definition of the law of conservation of energy, with examples; definition of conservative forces and the potential energy of conservative forces.

Spring potential energy and gravitational potential energy, with several examples; superposition of conservative forces; definition of non-conservative forces; conversion between forces and resultant potential energies.

Kinetic energy of a particle; gravitational potential energy; the law of conservation of mechanical energy. Includes several examples.

Definition of the law of conservation of energy, with examples; definition of conservative forces and their potential energy.

Spring potential energy and gravitational potential energy, with several examples; superposition of conservative forces; definition of non-conservative forces; conversion between forces and resultant potential energies.

Work done by a force (W = F*d); conservation of energy.

Energy transformations and conservation of energy; energy of system and surroundings; definition of kinetic energy, with equation (K = 1/2*m*v²); definition of work done by a constant force, with equation (W_applied = F_x*δ x).

Class problems.

Definition of conservative force; change in potential energy and conservation of mechanical energy; energy curves; potential energy for gravity and springs; energy changes for conservative and non-conservative forces.

Definitions of kinetic energy and work; work-energy relationship; work done along an arbitrary path; instantaneous power; potential energy and force; potential energy of a spring; potential energy due to gravity; conservation of mechanical energy.

3-part problem; finding normal force from wire and height the bead attains on the way back up.

Solution (PDF)^#

Changes in momentum and kinetic energy of two objects. Solution not included.

Momentum and kinetic energy of a baseball bat; simple harmonic motion of two mass-spring systems. Solution not included.

Motion of an object along a frictionless loop-the-loop track.

Solution (PDF)

Forces acting on a suspended ring with sliding beads.

Solution (PDF)

Linear speed of a streetcar on a circular track. Solution not included.

Velocity of a ball thrown downward in comparison to velocity of a ball dropped from rest. Solution not included.

Combined kinetic and potential energy of a ball dropped into a jar of oil. Solution not included.

Defining a mass-spring system such that energy is conserved. Solution not included.

Defining a system of a falling ball such that energy is conserved. Solution not included.

Energy and work with respect to a ball lifted at constant velocity. Solution not included.

Energy and work with respect to a ball lifted at constant velocity and the earth. Solution not included.

Work done on a system of a cup of water and the earth. Solution not included.

Work done on a system of a falling ball and the earth. Solution not included.

Compression of a spring resulting from collision with a moving object. Solution not included.

Conversion of the kinetic energy of the earth-sun system to potential energy. Solution not included.

Work done on a ball launched vertically by a spring. Solution not included.

Velocity and acceleration of a cart compressing a spring on an inclined track. Solution not included.

Acceleration of a cart as it moves up an inclined track. Solution not included.

Collision of a cart with a fixed spring on a track.

Solution (PDF)

Motion of a small object that slides down a large sphere and hits the ground.

Solution (PDF)

Fitting data from Experiment 6.

Solution (PDF)

4-part problem; free-body diagram and tension while hanging; speed and tension after one rope is cut. Solutions are included after problems.

Finding the spring constant of a spring from the maximum height of a ball shot by the spring.

Solution (PDF)

Motion of a small mass launched from the surface of the earth.

Solution (PDF)

Motion of a mass propelled by a spring along a frictionless loop.

Solution (PDF)

Motion of a mass that slides down an inclined plane and compresses a spring.

Solution (PDF)

Cart rolling down an inclined plane and compressing a spring.

Solution (PDF)^#

5-part problem involving Hooke's Law, friction, and conservation of energy.

Solution (PDF)

3-part work problem; pendulum swings 90°; finding work by gravity and tension, and v_final.

Solution (PDF)