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 Horizontal Springs

Practice: A 4-kg block moving on a frictionless, horizontal surface with 20 m/s strikes a massless, horizontal spring of force constant 600 N/m. Calculate the maximum distance that the block will compress the spring by.  

EXTRA: What maximum acceleration will the block experience? (hint: this happens when it temporarily stops).

Example #2: Springs in Rough Surfaces

Practice: A 4-kg block moving on a flat surface strikes a massless, horizontal spring of force constant 600 N/m with a 20 m/s. The block-surface coefficient of friction is 0.5. Calculate the maximum compression that the spring will experience.

Example #3: Energy in Vertical Springs

Example #4: Energy in Vertical Springs

Additional Problems
A 205 kg block is released at a 6.3 m height as shown. The track is frictionless. The block travels down the track, hits a spring of force constant k = 1285 N/m . The acceleration of gravity is 9.8 m/s2. Determine the compression of the spring x from its equilibrium position before coming to rest momentarily. A. 3.39911 B. 2.46691 C. 3.05595 D. 2.80797 E. 3.4477 F. 3.57838 G. 2.50776 H. 3.66395 I. 3.72911 J. 4.43837
A 1.86-kg block is held in place against the spring by an 81-N horizontal external force (see the figure). The external force is removed, and the block is projected with a velocity v1 = 1.2 m/s upon separation from the spring. The block descends a ramp and has a velocity v2 = 1.9 m/s at the bottom. The track is frictionless between points A and B. The block enters a rough section at B, extending to E. The coefficient of kinetic friction over this section is 0.28. The velocity of the block is v3 = 1.4 m/s at C. The block moves on to D, where it stops. The height h of the ramp is closest to _____. A. 15 cm B. 17 cm C. 11 cm D. 18 cm E. 7.3 cm
It takes 4.36 J of work to stretch a Hooke’s-law spring 7.54 cm from its unstressed length. How much the extra work is required to stretch it an additional 4.8 cm? 1. 27.5923 2. 13.8816 3. 14.269 4. 3.54616 5. 6.58426 6. 5.18114 7. 15.988 8. 17.1564 9. 18.2072 10. 7.31815
A small rock block with mass 0.400 kg is placed against a compressed spring at the bottom of a 37.0° incline. The compressed spring has 50.0 J of elastic potential energy stored in it. The spring is released and the block moves a distance of 12.0 m along the incline before momentarily coming to rest. How much work does the friction force do on the block during the motion? What is the coefficient of kinetic frinction μk between the block and the incline?
In a physics lab experiment, a compressed spring launches a 31 g metal ball at a 35° angle. Compressing the spring 18 cm causes the ball to hit the floor 1.8 m below the point at which it leaves the spring after traveling 5.6 m horizontally. What is the spring constant?
Its your birthday, and to celebrate you're going to make your first bungee jump. You stand on a bridge 120 m above a raging river and attach a 33-m-long bungee cord to your harness. A bungee cord, for practical purposes, is just a long spring, and this cord has a spring constant of 43 N/m . Assume that your mass is 76 kg . After a long hesitation, you dive off the bridge. How far are you above the water when the cord reaches its maximum elongation?
A spring has a spring constant k of 82.0 N/m. How much must this spring be compressed to store 40.0 J of potential energy?
A student places her 410 g physics book on a frictionless table. She pushes the book against a spring, compressing the spring by 7.00 cm, then releases the book. What is the books speed as it slides away? The spring constant is 1650 N/m.
A 1300 kg car moving on a horizontal surface has speed exttip{v}{v} = 80 km/h when it strikes a horizontal coiled spring and is brought to rest in a distance of 2.3 m. What is the spring stiffness constant of the spring?
What should be the spring constant k of a spring designed to bring a 1300 kg car to rest from a speed of 90 km/h so that the occupants undergo a maximum acceleration of 5.5 g?
A 0.160 kg block of ice is placed against a horizontal, compressed spring mounted on a horizontal tabletop that is 1.30 m above the floor. The spring has force constant 2050 N/m and is initially compressed 0.045 m. The mass of the spring is negligible. The spring is released, and the block slides along the table, goes off the edge, and travels to the floor. If there is negligible friction between the block of ice and the tabletop, what is the speed of the block of ice when it reaches the floor?
A box with mass 5.00 kg is placed against a compressed spring. The spring is released and the box slides 4.00 m along a horizontal surface before coming to rest. (At this point the box is no longer in contact with the spring and there is no potential energy left stored in the spring.) The coefficient of kinetic friction between the block and the surface is 0.300. How much energy was initially stored in the compressed spring?