The potential energy for a certain mass moving in one dimension is given by U(x)=(2.0J/m3)x3−(15J/m2)x2+(36J/m) x−23JU(x)=(2.0J/m3)x3−(15J/m2)x2+(3 6J/m)x−23JU(x) = (2.0 {\rm J/m}^{3})x^{3}- (15 {\rm J/m}^{2})x^{2}+ (36 {\rm J/m})x - 23 {\rm J}. Find the location(s) where the force on the mass is zero.

Experiment scenario 2: a biology student wants to conduct a study of how the amount of food affects the weight gain for mice. i have set up four cages with a mouse in each cage. fill in the boxes that would allow the biology student to complete the study correctly

The first law of thermodynamics states that heat added to a system is neither created nor destroyed but is transformed ⇒ as it changes into other forms of energy.

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.