At the beach, kate collects sea shells of mass 100 g and places them in a bucket. she swings the bucket in a large circle (radius 0.4 m), vertical with the ground, so that the bucket swings over her head. when the bucket is at the top of the circle, upside down, the tangential velocity of the shells is 4 m/s. the sea shells do not fall out of the bucket. what is the net force on the sea shells inside the bucket at this poin
a. the net force is the same as the force of gravity.
b. the net force is the same as the centripetal force.
c. the net force is zero because the force of gravity cancels the centripetal force and the shells do not fall out of the bucket.
d. the net force is the centripetal force plus the force of gravity since both are acting downward when the bucket is at the top of the circle.

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 ⇒