Alice and Bob are balancing on top of a board on a rock. The board is two meters

Question

Alice and Bob are balancing on top of a board on a rock. The board is two meters long and has a mass of 5 kg. The rock is 75 cm from the left end of the board. Bob is standing 73 cm from the rock on the left end of the board and his mass is 108 kg. Alice stands 113 cm from the rock on the right side of the board. A) Draw a vector diagram for the board and rock system including all relevant forces and distances B) How much does Alice weigh? C) Calculate the force acting on the board at the pivot point? Assume that the board does not bend. You are running around Lincoln, NE looking for Pikachu! Assume Lincoln is a perfect circle with a radius r_lincoln = 10km and that you are a perfect point mass with m_you = 100kg. A) If you take 2 hours to run around Lincoln, what is your average angular momentum, L_avg, with respect to the center of Lincoln? B) Assuming you pick up a Pikachu, with a mass m_pikachu = 10kg, what is your speed immediately after you pick it up?

Explanation / Answer

2)Let weight of Alice be w

Moment about rock due to Bob weight,board weight and Alice weight should be zero

108*9.8*0.73 = 5*9.8*0.25 + w*1.13

Therefore, w = weight of Alice = 672.9 N=68.66 kg

Total force on rock = (108*9.8)+(5*9.8)+672.9 =1780.3 N

3) radius = r = 10 km = 10000 m

Time taken = t=2hrs = 7200 seconds

Total distance travelled = 2*pi*r = 62831.85 m

Speed = v=62831.85/7200 =8.73 m/s

Angular momentum=mvr=100*8.73*10000 = 8.73*10^6 kgm²/s

Speed just after picking up Pikachu will be such that initial and final angular momentums are equal

Initial angular momentum = 8.73*10^6

Final angular momentum = 110*v*10000

v=8.73*10^6/1.1*10^6 =7.93 m/s

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