Question

Review Part A A small puck (450 g ) on an air hockey table is attached to a spring with spring constant 11.0 N/m. The puck sits at rest before another puck (400 g ) is pushed towards it from the other end of the track at 162 cm/s. The second puck collides with and sticks to the first. After the two pucks collide, what is the amplitude of their oscillation? Express your answer with the appropriate units. Value Units Submit Request Answer Part B What is their period? Express your answer with the appropriate units. Value Units Submit Request Answer

Answer 1

$m_1=450\,g=0.450\,kg$ is at rest $u_1=0\,m/s$ (initially) ,

$m_2=400\,g=0.400\,kg$ is moving with $u_2=162\,cm/s=1.62\,m/s$ (initially)

After collision, both masses move with same velocity $v$.

Conserving the momentum of the two masses before and after collision,

$m_1u_1+m_2u_2=(m_1+m_2)v$

$0.450*0+0.400*1.62=(0.450+0.400)v$

$v=0.7624\,m/s$

Part A)

When the spring is compressed to its maximum displacement, $\frac{1}{2}kA^2=\frac{1}{2}(m_1+m_2)v^2$

$A=\sqrt{\frac{(m_1+m_2)v^2}{k}}$

$A=\sqrt{\frac{(0.850)(0.7624)^2}{11}}=0.212\,m=21.2\,cm$

Part B)

Time period $T=2\pi\sqrt{\frac{(m_1+m_2)}{k}}$

$T=2\pi\sqrt{\frac{(0.850)}{11}}=1.75\,s$