Avery small object with mass 6.90 × 10^−9 kg and positive charge 8.30 × 10^−9 c is projected directly toward a very large insulating sheet of positive charge that has uniform surface charge density 5.90 x 10^-8 c/m^2. the object is initially 0.530 m from the sheet. what initial speed must the object have in order for its closest distance of approach to the sheet to be 0.170 m ? ,

Ablock of mass m = 2.5 kg is attached to a spring with spring constant k = 710 n/m. it is initially at rest on an inclined plane that is at an angle of θ = 23° with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is μk = 0.19. in the initial position, where the spring is compressed by a distance of d = 0.16 m, the mass is at its lowest position and the spring is compressed the maximum amount. take the initial gravitational energy of the block as zero. a) what is the block's initial mechanical energy? b) if the spring pushes the block up the incline, what distance, l, in meters will the block travel before coming to rest? the spring remains attached to both the block and the fixed wall throughout its motion.

The focal length of a relaxed human eye is approximately 1.7 cm. when we focus our eyes on a close up object, we can change the refractive power of the eye by about 16 diopters. (a) does the refractive power of our eyes increase or decrease by 16 diopters when we focus closely? explain. (b) calculate the focal length of the eye when we focus closely.

If gases like carbon dioxide and methane make up less than 1% of the total atmosphere, why is it important for scientists to monitor changes in percentages of these gases?