The virial theorem of classical mechanics applied to a single 1d particle subject to a force f(x) = −v 0 (x) in the potential v (x) is1 : 2 hti t = − hxf(x)i t = hxv 0 (x)i t , where h. .i t represents an average over time. in this question, you will develop the quantum mechanics analog of the virial theorem. (a) use the following result for an arbitrary state |ψi and matrix q that is not explicitly time dependent ( ∂q ∂t = 0) d hqiψ dt = i ~ h[h, q]iψ to show that d hxpiψ dt = 2 htiψ − hxv 0 iψ , where t = p 2/(2m) is the usual kinetic energy and v 0 = v 0 (x). note that q = xp is not hermitian, but the result above does not assume this

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c. newton's third law of motion

gpe = mass x gravity constant x height or… gpe = mgh

where… mass: measured in kilograms (kg)

gravity: gravity constant on earth = 10.00 m/s2

height: measured in meters (m)

gpe: measured in joules (j) or kilojoules (kj)

how do you solve gpe?

gravitational potential energy (gpe) is the energy an object has because of its position above the. ground.

gpe = mass x gravity constant x height or… gpe = mgh.

mass:

note: to earn full marks when solving science word problems, you must show your work:

formula.

example:

given values:

mass = 0.3 kg.

force required to detach it is given by

charges are taken to be fundamental charge

now we have

so above is the minimum distance at which it will detach