Consider four different oscillating systems, indexed using . each system consists of a block of mass moving at speed on a frictionless surface while attached to an ideal, horizontally fixed spring with a force constant of . let denote the displacement of the block from its equilibrium position. order the systems from largest total mechanical energy to smallest. 1) m1= 0.5kg k2=500 n/m amplitude a = 0.02 m

2)m2= 0.6kg k2=300 n/m v2= 1 m/s . when passing through equilibrium

3) m3= 1.2kg k3=400 n/m v3= 0.5 m/s . when passing through x= -0.01 m

4) m4= 2 kg k4=200 n/m v4= 0.2 m/s . when passing through x=-0.05 m

Alinearly polarized electromagnetic wave has an average intensity of 196 w/m^2. this wave is directed towards two ideal polarizers (in real polarizers, transmission is also effected by reflection and absorption). polarizer a is oriented with its transmission axis at an angle of θ_1=20.8∘ with the incident electric field. polarizer b has its axis at an angle of θ_2=63.0∘ with the incident electric field. what is the average intensity of the wave after it passes through polarizer a? what is the average intensity of the wave after it passes through polarizer b? suppose that the two polarizers a and b are interchanged. what would the average intensity be after passing through both polarizers?

As you are trying to move a heavy box of mass m, you realize that it is too heavy for you to lift by yourself. there is no one around to , so you attach an ideal pulley to the box and a massless rope to the ceiling, which you wrap around the pulley. you pull up on the rope to lift the box. use g for the magnitude of the acceleration due to gravity and neglect friction forces. once you have pulled hard enough to start the box moving upward, what is the magnitude f of the upward force you must apply to the rope to start raising the box with constant velocity? express the magnitude of the force in terms of m, the mass of the box.

To practice problem-solving strategy 10.1 for energy conservation problems. a sled is being held at rest on a slope that makes an angle θ with the horizontal. after the sled is released, it slides a distance d1 down the slope and then covers the distance d2 along the horizontal terrain before stopping. find the coefficient of kinetic friction μk between the sled and the ground, assuming that it is constant throughout the trip.