When a board with a box on it is slowly tilted to larger and larger angle, common experience shows that the box will at some point "break loose" and start to accelerate down the board.

the box begins to slide once the component of gravity acting parallel to the boardequals the force of static friction. which of the following is the most general explanation for why the box accelerates down the board?

the force of kinetic friction is smaller than that of static friction, butf_gremains the same.
once the box is moving, f_gis smaller than the force of static friction but larger than the force of kinetic friction.
once the box is moving, f_gis larger than the force of static friction.
when the box is stationary, f_gequals the force of static friction, but once the box starts moving, the sliding reduces the normal force, which in turn reduces the friction.

Which term best describes the phrase “something that happens”?

Acoal-fired plant generates 600 mw of electric power. the plant uses 4.8 x 10^6 kg of coal each day, and the heat of combustion of coal is 3.3x 10^7 j/kg. the steam that drives the turbines is at a temperature of 300° c, and the exhaust water is at 37° c. (a) what is the overall efficiency of the plant for generating electric power? (b) how much thermal energy is exhausted each day? (c) what is the change in entropy of the universe for this heat engine? (d) using the same heat reservoirs, what is the maximum possible (carnot) efficiency for a heat engine?

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 ⇒