A particle of mass m is restricted to move without friction on the x-axis. This particle is connected to a fixed point P a distance d from the x axis by a spring with constant k and length at rest l_0. Working in the two-dimensional plane (x, y), we will denote the coordinates of the particle by (x, 0) while the point P has coordinates (0, d). Find the equilibrium positions of the particle and discuss their stability. In the case where the equilibrium positions are stable, find the period of the small oscillations near equilibrium. Hint: You will want to distinguish the cases d > l_0 , and d < l_0 (ignore the special case d = l_0).

Considering only the earth's rotation, determine how much later the asteroid would have had to arrive to put the explosion above helsinki at longitude 25˚ e? this would have obliterated the city.

Consider a one meter long horizontal pipe with a constant 100 cm^2 cross sectional area. water flows rightward into the pipe at x = 0 with flow velocity 02m/sec at every point within the pipe intake area. at x=1, the rightward flow rate is 0.192 m/sec. assume the water is a conserved quantity in the pipe, so there must be a leak (a sink) somewhere in the pipe. 1. compute net volumetric flow of the source if the system to be in equilibrium. 2. now assume the pipe in the problem has no leaks. compute the net volumetric rate of change for the system.

Cells in the nervous system have a potential difference of 70 mv across the cell membrane separating the interior of the cell from the extracellular fluid. this potential difference is maintained by ion pumps that move charged ions across the membrane. is this an emf? select the correct answer and explanation. 1)no. the ion pumps cannot separate charges; thus, they cannot create a potential difference. 2)yes. the ion pumps cannot separate charges, but they still can create a potential difference. 3)yes. the ion pumps can actively separate charge; thus, they can create a potential difference. 4)no. the ion pumps can separate charges, but they cannot create a potential difference.