A 60-kg skier starts from rest at the top of a 80-meter high practice slope (A). He uses his poles to propel himself forward, doing 12000 Joules of positive work from the top of the hill to the halfway point on the hill (B). Use g = 10 m/s/s to perform an energy analysis

Power can be defined as a. the distance over which work was done. b. how much work can be done in a given time. c. all the work in an given area. d. the energy required to do work.

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 ⇒

What is the force that opposes motion and works against the downward pull? a) friction b) gravity c) weight d) acceleration