s in procedure 1: a pair of carts sit on a frictionless track. Assume the mass o
ID: 1695780 • Letter: S
Question
s in procedure 1: a pair of carts sit on a frictionless track. Assume the mass of the larger cart is 4.2 times the mass of the small cart, In this system, however, there is a spring between the carts which can "explode", pushing on the two carts at once..NOTE: Every velocity needs magnitude and direction (given by the sign).
a) Suppose the carts are initially at rest, and after the "explosion" the smaller cart is moving at velocity +6.45 m/s.
- Find the velocity of the larger cart. m/s
- If the mass of the smaller cart is 7.96 kg, find the energy supplied by the spring to the carts. J
- If the spring has spring constant k = 971 N/m, find the distance the spring was compressed before the "explosion". m
HINT: Think conservation of energy!
b) Suppose the carts are initially moving together at constant velocity +3.96 m/s. After the "explosion", the smaller cart is moving at velocity +6.45 m/s. Find the velocity of the larger cart.
m/s
Explanation / Answer
Let mass of the smaller cert be m Then the mass of the larger cart is 4.2*m a) As the carts are initially at rest: The total momentum of the system before explosion of the spring is zero. The velocity of the smaller cart is vs = +6.45 m/s According to the principle of conservation of linear momentum, 0 = m*+6.45 m/s + 4.2*m*v' v' = -1.54 m/s negative sign indicates that the larger cart moves opposite the direction of the smaller cart. The total energy of the system after the collision is the energy supplied by the spring.(conservation of energy) The energy supplied by the spring is E = 0.5*7.96*6.45^2 + 0.5*33.432*1.54^2 = 205.22 J If the spring constant is k then the potential energy of the spring is E = 0.5*kx^2 x is the amount of compression before explosion 0.5*971*x^2 = 205.22 x = 0.65 m b) As the carts are initially moving together at constant velocity u = +3.96 m/s, The total momentum of the system before explosion is (m+4.2m)u = mv + 4.2mv' 5.2*3.96 = 6.45 + 4.2*v' v' = 3.36 m/s Positive sign indicates that the larger cart is moving in the direction of the smaller cart
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