Question

Problem 9.41 Part A A 3.0-kg block slides along a frictionless tabletop at 8.0 m/s toward a second block (at rest) of mass 4.5 kg. A coil spring, which obeys Hooke's law and has spring constant k = 720 N/m , is attached to the second block in such a way that it will be compressed when struck by the moving block. (Figure 1) What will be the maximum compression of the spring? Express your answer using two significant figures Submit My Answers Give Up Part B What will be the final velocities of the blocks after the collision? Enter your answers numerically separated by a comma. Express your answers using two significant figures. first second m/s Submit My Answers Give Up ure 1 Part C e 8.0 m/s Is the collision elastic? Ignore the mass of the spring 3.0kg ○Yes O No

Answer 1

a) Apply conservation of energy

$\frac{1}{2} m_1v_{i1}^2 = \frac{1}{2} (m_1 +m_2) v_f^2 + \frac{1}{2} kx^2$

From momentum conservation we derive the Vf here

$v_f = \frac{m_1 v_{i1}}{m_1+m_2}$

so the energy equation reduces to

$kx^2 = \frac{m_1 m_2}{m_1+m_2} v_{i1}^2$

$(720)x^2 = \frac{(3) (4.5)}{3+4.5} (8)^2$

b)

using the momentum and energy to find the speed after collision is (spring stretch out)

$V_{f2} = \frac{2m_1 v_{i1}}{m_1 +m_2} = \frac{2 (3)(8)}{7.5} =6.4 m/s$

Speed are

c)

yes the collision is elastic