Acircular steel axle has a yield stress, \sigma_y=50\: ksiσ y = 50 k s i, and a diameter of 1.5 inches. if this axle is subjected to torsional loading, determine the allowable torque [kip-in] for a factor of safety fs = 1.7 using the maximum distortional energy (von mises) failure theory.

Acup of coffee sits on the dashboard of an automobile. the car goes around a sharp curve. even though you hold the cup still, coffee still splashes out. this can best be explained due to a) density. b) friction. c) gravity. d) inertia.

Acoyote chasing a rabbit is moving 8.00 m/s due east at one moment and 8.80 m/s due south 4.25 s later. let the x axis point due east and the y axis point due north. find the direction of the coyote's average acceleration during that time.

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 ⇒