A mass m₁ = 7.0 kg is at rest on a frictionless horizontal surface and connected to a wall by an ideal spring with a spring constant of k = 50 N/m as shown in the figure.A second mass m₂ = 3.0 kg is moving to the left at v_O = 8.0 m/s.The two masses then collide and stick together.What is the maximum compression of the spring? A)0.48 m B)1.1 m C)2.0 m D)2.4 m E)16 m

Question

Quizplus · Accepted Answer

Using the conservation of momentum: 
m1v1 + m2v2 = (m1 + m2)vf 
(7 kg)(0 m/s) + (3 kg)(-8.0 m/s) = (10 kg)(vf) 
vf = -2.4 m/s

Using conservation of energy: 
(0.5)(k)(x^2) = (0.5)(m)(vf^2) 
(0.5)(50 N/m)(x^2) = (0.5)(10 kg)((-2.4 m/s)^2) 
x = 1.1 m

A Mass M1 = 7

A Mass M₁ = 7