A12000-n car is raised using a hydraulic lift, which consists of a u-tube with arms of unequal areas, filled with oil with a density of and capped at both ends with tight-fitting pistons. the wider arm of the u-tube has a radius of and the narrower arm has a radius of the car rests on the piston on the wider arm of the u-tube. the pistons are initially at the same level. what is the force that must be applied to the smaller piston in order to lift the car after it has been raised? for purposes of this problem, neglect the weight of the pistons.

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?

The field between two charged parallel plates is kept constant. if the two plates are brought closer together, the potential difference between the two plates either a) decrease b) does not change c) increase?