A block of mass m1 = 1.5 kg initially moving to the right with a speed of 2.2 m/

Question

A block of mass m1 = 1.5 kg initially moving to the right with a speed of 2.2 m/s on a frictionless, horizontal track collides with a spring attached to a second block of mass m2 = 4.4 kg (stationary) m/s as shown in figure (a). The spring constant is 541 N/m.

(a) Find the maximum spring compression in this case. x = m

(b) What will be the individual velocities of the two masses (v1 and v2) after the spring extended fully again? (That is, when the two masses separate from each other after the collision is complete.)

v1 = m/s to the left

v2 = m/s to the right

Explanation / Answer

m1u1 + m2u2 = (m1 + m2)v v = m1u1 + m2u2 / (m1 + m2) v = 2.4(4.0) + 1.3(0) / (2.4 + 1.3) v = 2.59 m/s ½kx² = ½mv² x² = mv²/k x = v(mv²/k) x = v((2.4 + 1.3)(2.59 ²)/110) ?x = 0.475 m or 47.5 cm

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