Question

Constants Periodic Table Correct A 1.10 kg block is attached to a spring with spring constant 17.0 N/m . While the block is sitting at rest, a student hits it with a hammer and almost instantaneously gives it a speed of 46.0 cm/s What are ▼ Part B The block's speed at the point where x= 0.100 A? Express your answer with the appropriate units. Value Units Previous Answers Request Answer X Incorrect; Try Again; 5 attempts remaining

Answer 1

Mass of block $m=1.10\,kg$

Spring constant $k=17.0\,N/m$

Initial velocity of block (at equilibrium position) $v_0=46.0\,cm/s$

Conserving energy of block spring system, $\frac{1}{2}mv^2_0=\frac{1}{2}kA^2$

Amplitude of oscillation is $A=v_0\sqrt{\frac{m}{k}}$

When displacement $x=0.100A$,

Conserving energy,  $\frac{1}{2}mv^2_0=\frac{1}{2}kx^2+\frac{1}{2}mv^2$

$\frac{1}{2}mv^2=\frac{1}{2}mv^2_0-\frac{1}{2}kx^2$

$mv^2=mv^2_0-k(0.100)^2A^2$

$mv^2=mv^2_0-k(0.100)^2\left(v_0\sqrt{\frac{m}{k}}\right)^2$

$mv^2=mv^2_0-k(0.100)^2v^2_0\frac{m}{k}$

$v^2=v^2_0-(0.100)^2v^2_0=(1-0.01)v_0^2$

$v=v_0\sqrt{1-0.01}=0.994987v_0=0.4577\,m/s$