Show that lagrange’s equations in the form of eqs. (1.53) can also be written as ∂t˙ ∂ ˙ q j − 2 ∂t ∂q j = q j . these are sometimes known as the nielsen form of the lagrange equations.

The membrane surrounding a living cell consists of an inner and an outer wall that are separated by a small space. assume that the membrane acts like a parallel plate capacitor in which the effective charge density on the inner and outer walls has a magnitude of 7.0 × 10-6 c/m2. (a) what is the magnitude of the electric field within the cell membrane? (b) find the magnitude of the electric force that would be exerted on a potassium ion (k+; charge = +e) placed inside the membrane.

In which situation has the independent variable for the experiment been changed? check all that apply. changed from counting the number of duckweed at day 0 and day 14 to counting them every day changed from testing duckweed growth in beakers to testing duckweed growth in large outdoor tanks changed from testing the effect of ph on duckweed growth to testing the effect of light levels on duckweed growth changed from testing the effect of acid ph on duckweed growth to testing the effect of basic ph on duckweed growth

In which of the following cases is work being done on an object? question 2 options: pushing against a locked door carrying a box down a corridor pulling a trailer up a hill suspending a heavy weight with a strong chain