You see two carts connected by a spring and oscillating on ahorizontal air track. You happen to know that the spring constantof the spring is k = 50.0 N/m. You use Newton's second law todetermine that the period of oscillation is the same for each cartand is related to the masses of the carts by
T = 2Ïâ[ (m1m2)/(k(m1 +m2))].
Using a position vector, you determine that the positions of thecarts as functions of time can be expressed as
x1(t) = 2.70[1 - cos(18.0t)] and
x2(t) = 10.70 + 1.29cos(18.0t)
wher the coordinates are in centimeters and the time is inseconds.
a) Use the principle of conservation of momentum to find the massesof the carts.
b) Generate a table of the values of x1,x2 for every 1 s from t = 0 to t = 35 s.
For each of these times, also calculate the position of the centerof mass, the total momentum of the two-cart system, and the forceof the spring on each cart.
Verify that the center of mass does not move, that the totalmomentum is conserved, and that the forces on the carts from thespring have the same magnitude but in opposite directions.
c) Use the table to find the equilibrium length of thespring.
You see two carts connected by a spring and oscillating on ahorizontal air track. You happen to know that the spring constantof the spring is k = 50.0 N/m. You use Newton's second law todetermine that the period of oscillation is the same for each cartand is related to the masses of the carts by
T = 2Ïâ[ (m1m2)/(k(m1 +m2))].
Using a position vector, you determine that the positions of thecarts as functions of time can be expressed as
x1(t) = 2.70[1 - cos(18.0t)] and
x2(t) = 10.70 + 1.29cos(18.0t)
wher the coordinates are in centimeters and the time is inseconds.
a) Use the principle of conservation of momentum to find the massesof the carts.
b) Generate a table of the values of x1,x2 for every 1 s from t = 0 to t = 35 s.
For each of these times, also calculate the position of the centerof mass, the total momentum of the two-cart system, and the forceof the spring on each cart.
Verify that the center of mass does not move, that the totalmomentum is conserved, and that the forces on the carts from thespring have the same magnitude but in opposite directions.
c) Use the table to find the equilibrium length of thespring.
