A solid block of mass m2 = 9.6 kg, at rest on a horizontal frictionless surface,

Question

A solid block of mass m2 = 9.6 kg, at rest on a horizontal frictionless surface, is connected to a relaxed spring. The other end of the spring is fixed, and the spring constant is k = 90 N/m. Another solid block of mass m1 = 13.4 kg and speed v1 = 9.4 m/s collides with the 9.6 kg block. The blocks stick together, and compress the spring.

A)What is the maximum compression of the spring?

B)What is the magnitude of the acceleration of the two blocks when the spring is at maximum compression?

*A) is not 7.66m

*B) is not 30m/s

Explanation / Answer

m1 = 13.4 kg

m2 = 9.6 kg

u1 = initial velocity of m1 = 9.4 m/s

u2 = initial velocity of m2 = 0

k = spring constant = 90 N/m

a) initial momentum = final momentum

[ here V = common velocity by which blocks move after stick to each other]

m1*u1 + m2*u2 = ( m1+m2)*V

13.4*9.4 + 0 = (13.4+ 9.6) *V

V = 5.47 m/s

K.E of block = P.E of spring

(1/2)*(m1+m2)*V2 = (1/2)*K*x2   [ x = maximum compression]

( 13.4+9.6) * (5.47)2 = 90*x2

x = 2.76 m

b) now after compression final velocity (V) of blocks = 0

u ( initial velocity ) of blocks = 5.47 m/s

from V2 - u2 = 2*a*S

0 - (5.47)2 = 2*a * 2.76

a ( acceleration) = - 5.42 m/s2

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