Question

In Fig, block 1 (mass 2.0 kg) is moving rightward at 10 m/s and block 2 (mass 5.0 kg) is moving rightward at 3.0 m/s. The surface is frictionless, and a spring with a spring constant of 571 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 of 5 m/s. Find the maximum compression.

Answer 1

xmax = 0.65m

Step-by-step explanation:

When the spring is maximum compressed all kinetic energy of both masses will be elastic potential energy of the spring. From there we can take apart xmax. Hence we have

`E_(k1)+E_(k2)=(1)/(2)kx_(max)^2`

`x_(max)=\sqrt{(1)/(k)(m_1v_1^2+m_2v_2^2)}\\x_(max)=\sqrt{(1)/(571N/m)[(2.0kg)(10(m)/(s))^2+(5.0kg)(3.0(m)/(s))^2]}\\\\x_(max)=0.65m`

hope this helps!!