Question

Block 1 (mass 2.00 kg) is moving rightward at 10.0 m/s and block 2 (mass 5.00 kg) is moving rightward at 3.00 m/s. The surface is frictionless, and a spring with a spring constant of 1120 N/m is fixed to block 2. When the blocks collide, the compression of the spring is maximum at the instant the blocks have the same velocity. (a) Find the maximum compression. (b) Find the final velocities of the two blocks.

Answer 1

here,

the mass of block1 , m1 = 2 kg

mass of block 2 , m2 = 5 kg

the initial speed of 1 ,u1 = 10 m/s

the initial speed of 2 , u2 = 3 m/s

let the final speed of combination be v

using conservation of momentum

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

2 * 10 + 5 * 3 = ( 2 + 5) * v

v = 5 m/s

the spring constant , K = 1120 N/m

let the maximum compression in the spring be x

using conservation of energy

0.5 * K * x^2 = (0.5 * m1 * u1^2 + 0.5 * m2 * u2^2) - (0.5 * (m1 + m2) * v^2)

1120 * x^2 = (2* 10^2 + 5 * 3^2) - ( (2 + 5) * 5^2)

solving for x

x = 0.25 m

the maximum compression in the spring is 0.25 m

b)

the final velocities of the two blocks is rightwards