Question

1. A 30 cm spring with constant 70 N/m is compressed to 10 cm and placed between two carts. Cart A has mass m Skg and mg is unknown. Initially the system is at rest. After it is released it is observed that cart A has three times the velocity of cart B. a) What force must be exerted initially to keep the spring compressed? b) What is the work done to compress the spring? c) By considering conservation of momentum determine the mass m d) By considering conservation of energy find the velocities of the carts A and B after the spring is released.

Answer 1

The ans are, a) 14N, b) 1.4J, c) 15kg, d) 43.20 & 21.60cm/sec

Length of spring l = 300m, K = 70N/m Compared length of spring l^1 = 300m, K = 70 N/m Compared length of spring l^1 = 10Cm delta x = l - l^1 = 20 Cm delta x = 0.2M M_A = 5kg, m_B = ? for u required F = K delta x F = 70 times 0.2 F = 14N (b) Work done required to compress the spring W = Potential energy stored W = 1/2 K K delta x^2 W = 1/2 times 70 times (0.2)^2 W = 1.4J (c) Initially the system at rest V_A = V_B = 0 after it is released V^f_A = 3V^f_B m-A V_a + M_B V_B = m_A V^f_A + m_B V^f_B 0 + 0 = 5 times 3V^f_B + m_B V^f_B man can not br negative so m_B = 15 kg \r\n (d) A/c to Law of conservation of energy energy stored in the spring (initially) = kinetic energy after releasing the system