What is the change in potential energy of a squirrel that jumps from a tree branch that is 4.5 meters off of the ground and lands on a branch 2.1 meters off of the ground if the mass of the squirrel is 1.5 kilograms?

The frequency of vibrations of a vibrating violin string is given by f = 1 2l t ρ where l is the length of the string, t is its tension, and ρ is its linear density.† (a) find the rate of change of the frequency with respect to the following. (i) the length (when t and ρ are constant) (ii) the tension (when l and ρ are constant) (iii) the linear density (when l and t are constant) (b) the pitch of a note (how high or low the note sounds) is determined by the frequency f. (the higher the frequency, the higher the pitch.) use the signs of the derivatives in part (a) to determine what happens to the pitch of a note for the following. (i) when the effective length of a string is decreased by placing a finger on the string so a shorter portion of the string vibrates df dl 0 and l is ⇒ f is ⇒ (ii) when the tension is increased by turning a tuning peg df dt 0 and t is ⇒ f is ⇒ (iii) when the linear density is increased by switching to another string df dρ 0 and ρ is ⇒ f is ⇒

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The average density of the planet uranus is 1.27 103 kg/m3. the ratio of the mass of neptune to that of uranus is 1.19. the ratio of the radius of neptune to that of uranus is 0.969. find the average density of neptune.