Aparallel-plate capacitor is made of two square plates 25 cm on a side and 1.0 mm apart. the capacitor is connected to a 50.0-v battery. with the battery still connected, the plates are pulled apart to a separation of 2.00 mm. what are the energies stored in the capacitor before and after the plates are pulled farther apart? why does the energy decrease even though work is done in separating the plates?

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 ⇒

Two carts, one of mass 2m and one of mass m, approach each other with the same speed, v. when the carts collide, they hook together. assume that positive momentum is to the right. which graph best represents the momentum of both carts over time, before and after the collision?

An athlete swings a ball, connected to the end of a chain, in a horizontal circle. the athlete is able to rotate the ball at the rate of 8.13 rev/s when the length of the chain is 0.600 m. when he increases the length to 0.900 m, he is able to rotate the ball only 6.04 rev/s. (a) which rate of rotation gives the greater speed for the ball? 6.04 rev/s 8.13 rev/s (b) what is the centripetal acceleration of the ball at 8.13 rev/s? m/s2 (c) what is the centripetal acceleration at 6.04 rev/s? m/s2