ok well this was my homework over the weekend and i think i got an idea of how to solve these but I am not quite sure on my answers... I've scanned the problems because they all require diagrams that must be seen to solve the problems
problem number 1 . x = (Vi)(t)+1/2(a)(t^2)
problem number 2. . no equations necessary
problem number 3 . v = (f)(λ)
The Attempt at a Solution
problem 1 a) 1/4(g)
i couldn't figure out how to even begin with this problem so all i did was take the proportion of the string relative to each mass and then multiplied by the acceleration due to gravity
b) t = [(2h)/(1/4)(g)]
now for this one it really didnt make sense to me because could you really use this equation to find time considering the acceleration would always be changing based on its proportionality to the string... or would the answer simply be t = [(2h)/(a)]^1/2... i really didnt have an idea for this..
c) Sliding across the table to the right
d) Slides across the table to the right until it falls off the table where it'd follow a projectile path til hitting the ground
e) wasnt sure, considering the acceleration dilemma
problem 2 a) i. velocity to the right of ball, acceleration towards center
ii. acceleration down and left, no velocity
b) i. this would follow a projectile path, it'd take the motion of something falling off a cliff
ii. this would also follow a projectile path, but it'd be more parabolic?... it'd take the motion of a ball being thrown up and then later falling.
problem 3 a) λ - .6m
b) v = fλ v = (120 hz) (.6m) = 72 m/s
c) The mass should be decreased because mass is directly proportional to tension according to the formula Ft = ma. Then Tension (decreased) is directly proportional to velocity (as stated in problem). Finally velocity (decreased) is directly proportional to λ according to the formula v = fλ (the tuning forks frequency is constant). So with a shorter wavelength we will have a greater number of "loops."
d) 4cm/3 = 1.33cm