An 7.9 kg crate is pulled 5.5 m up a 30∘ incline by a rope angled 19 ∘ above the incline. The tension in the rope is 140 N and the crate's coefficient of kinetic friction on the incline is 0.26.

A) How much work is done by tension, by gravity, and by the normal force?

Express your answers using two significant figures. Enter your answers numerically separated by commas.

B) What is the increase in thermal energy of the crate and incline?

Express your answer using two significant figures.

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 ⇒

The rocket is fired vertically and tracked by the radar station shown. when θ reaches 66°, other corresponding measurements give the values r = 32700 ft, r¨ = 85 ft/sec2, and θ˙ = 0.019 rad/sec. calculate the magnitudes of the velocity and acceleration of the rocket at this position.

Assume this car is driven off a cliff . how many arrows of force need to be drawn in the free body diagram? assume no air resistance -five -one -three -four