Consider three force vectors F~ 1 with magnitude 43 N and direction 38◦ , F~ 2 with magnitude 26 N and direction −140◦ , and F~ 3 with magnitude 27 N and direction 110◦ . All direction angles θ are measured from the positive x axis: counter-clockwise for θ > 0 and clockwise for θ < 0. What is the magnitude F of the net force vector F~ = F~ 1 + F~ 2 + F~ 3? Answer in units of N.

Which of the following explains why it took so long for the public to accept the negative health effects of smoking? a)people were waiting for counter reasons, and those were presented.b)scientists had not completely finalized their results, which took 30 years.c)cigarettes were cheaply available and media channels were very inefficient.d)cigarette manufacturers were trying hard to bring an alternative into the market

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 ⇒

In a heat engine if 1000 j of heat enters the system the piston does 500 j of work, what is the final internal energy of the system if the initial energy was 2000 j? 1. write the equation 2.list out your known variables 3.plug the numbers into the equations 4.solve 5.write your solution statement that includes initial energy and final