3 more posts in this thread. [Missing image file: an-odd-balance-puzzler.jpg]
You have a balance beam, the kind of scale that tips from one side to the other, depending on the weight on each side. On each side is a beaker, half-filled with water. The sides are in balance. Now, on the left side, you submerge a ping-pong ball suspended by a string. On the right side, you submerge a steel ball of the same volume as the ping-pong ball suspended from a crane.
Does the balance beam tip to the right, to the left, or does it remain unchanged?
4 more posts in this thread. [Missing image file: ha.jpg]
Working on a symbolic problem dealing with translational kinematics in 1 dimension. Not sure I've done it right.
"At time t=0, a student throws a set of keys vertically upward to her sorority sister, who is in a window at distance h above. The second student catches the keys at time t. With what initial velocity were the keys thrown? What was the velocity of the keys just before they were caught?"
Being thrown straight up, the keys are affected by gravity, so we can use a particle under constant acceleration model to analyze this.
x(f) = x(i) + 1/2( V(i) + V(f) ) * t
where x(f) is the the final position, x(i) is the initial position, V(i) is the initial velocity, V(f) is the final velocity and t is the time.
h = 1/2( V(i) + V(f) ) * t,
2h/t = V(i) + V(f),
V(i) = 2h/t - V(f),
V(f) = 2h/t - V(i).
V(i) = ( 2h/t - V(i) ) - a*t,
2*V(i) = 2h/t - 9.8m/s^2 * t,
V(i) = h/t - 4.9m/s^2 * t,
Which is the answer to the first question. For second question,
V(f) = 2h/t - (h/t - 4.9m/s^2 * t)
V(f) = h/t + 4.9m/s^2 * t
That's the anwers I've arrived at. Any way I could refine these answers? Or have I made a mistake?