PHYS 2010 Nathalie Hoffmann University of Utah Tuesday 6/2 PHYS 2010 Nathalie Hoffmann University of Utah

Momentum 𝒑=𝑚𝒗 Momentum is conserved in collisions.

Types of Energy (so far) Kinetic Energy 𝐾= 1 2 𝑚 𝑣 2 Gravitational Potential Energy 𝑈 𝑔𝑟𝑎𝑣 =𝑚𝑔ℎ

Work 𝑊=𝐹𝑐𝑜𝑠𝜃𝑑 where 𝜃 is the angle between 𝑭 and 𝒅 When a force acts to oppose the motion of the object, the value of the work done by that force is negative.

Energy Conservation If there are no non-conservative forces, total energy is conserved ∆𝐸= 𝐸 𝑓 − 𝐸 𝑖 =∆𝐾+∆𝑈=0 1 2 𝑚 𝑣 𝑖 2 +𝑚𝑔 ℎ 𝑖 = 1 2 𝑚 𝑣 𝑓 2 +𝑚𝑔 ℎ 𝑓

Work-Energy Theorem 𝑊 𝑛𝑒𝑡 = 𝐾 𝑓 − 𝐾 𝑖 =∆𝐾 The net work done by all forces on an object, Wnet, equals the difference between its final kinetic energy Kf and its initial kinetic energy Ki

Practice Problems Calculate the final speed of the 2.00-kg object that is pushed for 22.0 m by the 40.0-N force on a level, frictionless floor. Assume the object starts from rest. A water balloon is thrown straight down at 12.0 m/s from a second floor window, 5.00 m above ground level. How fast is the balloon moving when it hits the ground? A bicyclist maintains a constant speed of 4.00 m/s up a hill that is inclined at 10.0° with the horizontal. Calculate the work done by the person and the work done by gravity if the bicycle moves a distance of 20.0 m up the hill. The combined mass of the rider and the bike is 90.0 kg.

Practice Problems An adult dolphin is about 5.00 m long and weighs about 1600 N. How fast must he be moving as he leaves the water in order to jump to a height of 2.50 m? Ignore any effects due to air resistance. 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 non-conservative forces as the high-speed matter forces its way to the surface and into the air?

Answers P1.1: v = 28.8 m/s P1.2: v = 15.6 m/s P1.3: W = +3.06 kJ (rider), W = -3.06 kJ (gravity) P2.1: v = 7.0 m/s P2.2: v = 24 m/s, ΔE = 710 J/kg lost