You are playing croquet with some friends. assume the mass of the mallet is 3m and the mass of the ball is m. the time of impact between the mallet and the ball is 1.00ms. you give your mallet head an initial velocity of 2.00 m/s.

a. with what velocity does your ball roll away after you hit it if the collision is elastic? assume the final velocity of the mallet head is 1.00m/s.

b. if m=0.454kg, what force did the mallet head exert on the ball?

c. if the mallet stuck to the ball, what is the final velocity of the mallet-ball combination?

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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