Consider the situation in which three identical spheres of clay are launched simultaneously, one along each possible path. All three spheres of clay are launched with the same initial linear speed and collide with the rod at the same time. The time of collision with the rod for each sphere is time t0. Which of the following predictions is correct about the motion of the system containing the rod and all three spheres of clay immediately after the collision? a. The system will rotate in the clockwise direction with a constant angular speed.
b. The system will rotate in the counterclockwise direction with a constant angular speed.
c. The system will rotate in the clockwise direction with a changing angular speed.
d. The system will rotate in the counterclockwise direction with a changing angular speed.

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 ⇒

4r-134a enters the condenser of a residential heat pump at 800 kpa and 50°c at a rate of 0.022 kg/s and leaves at 750 kpa subcooled by 3°c. the refrigerant enters the compressor at 200 kpa superheated by 4°c determine (a) the isentropic efficiency of the compressor, (b) the rate of heat supplied to the heated room, and (c) the cop of the heat pump. also, determine (d) the cop and rate of heat supplied to the heated room if this heat pump operated on the ideal vapor-compression cycle between the pressure limits of 200 and 800 kpa. (0.757, 4.37 kw, 5.12, 6.18, 3.91 kw)

Two balls, each with a mass of 0.5 kg, collide on a pool table. is the law of conservation of momentum satisfied in the collision? explain why or why not