Consider a system of two particles: ball A with a mass m is moving to the right a speed 2v and ball B with a mass 3m is moving to the left at a speed v. In the time interval before the two balls collide, what is the magnitude and the direction of the velocity of the center of mass of this system?

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 ⇒

In one or two sentences, describe how you did in the balancing game. in a few more sentences, explain one strategy you learned for balancing more complex equations.

Two point charges are separated by a certain distance. how does the strength of the electric field produced by the first charge, at the position of the second charge, change if the second charge is doubled? a. the field does not change b. the field strength decreases by half. c. the field strength doubles d. the field strength quadruples