Wednesday 6/3PHYS 2010

Nathalie HoffmannUniversity of Utah

Spring Force

• Hooke’s Law

• k is the spring constant• x > 0 for extension, x < 0 for compression

• Spring force is a restoring force• It acts in the opposite direction of displacement, trying to restore the spring

to its equilibrium position

Spring Potential Energy

• k is the spring constant• X is the displacement from the spring’s equilibrium position

Momentum

• Momentum is a vector, (has components!)

• Conservation of momentum?

Conservation of momentum

• Total momentum of the system is conserved in collisions

Collisions

• Elastic collision• Momentum is conserved• Kinetic energy is conserved

• Inelastic collisions• Only momentum is conserved

Notes

• Proton & neutron have essentially the same mass: 1.67 x 10-27

Practice Problems

• A spring that has a spring constant of 200 N/m is oriented vertically with one end on the ground. (a) What distance does the spring compress when a 2.00-kg object is placed on its upper end? (b) By how much does the potential energy of the spring increase during the compression?

• You may have noticed runaway truck lanes while driving in the mountains. These gravel-filled lanes are designed to stop trucks that have lost their brakes on mountain grades. Typically such a lane is horizontal (if possible) and about 35.0 m long. We can think of the ground as exerting a frictional drag force on the truck. If the truck enters the gravel lane with a speed of 55.0 mph (24.6 m/s), use the work-energy theorem to find the minimum coefficient of kinetic friction between the truck and the lane to be able to stop the truck.

Practice Problems

• In 2006, NASA’s Mars Odyssey orbiter detected violent gas eruptions on Mars, where the acceleration due to gravity is 3.7 m/s2. The jets throw sand and dust about 75.0 m above the surface. (a) What is the speed of the material just as it leaves the surface? (b) Scientists estimate that the jets originate as high-pressure gas speeds through vents just underground at about 160 km/h. How much energy per kilogram of material is lost due to nonconservative forces as the high-speed matter forces its way to the surface and into the air?

• A spring that is compressed 12.5 cm from its equilibrium position stores 3.33 J of potential energy. Determine the spring constant.

Answers

• P1.1: x = 9.80 cm, U = 0.960 J• P1.2: μ = 0.882• P1.3: • P2.1: v = 24 m/s, E = 710 J/kg lost to non-conservative forces• P2.2: k = 426 N/m• P2.3: