Question

A $4.0kg$ mass moving with a speed of $2.0m/s$ collides with a spring bumper of negligible mass and having a force constant $100N/m$. The maximum compression of the spring bumper will be:

• A. $1.6m$
• B. $0.4m$
• C. $2.0m$
• D. $1.0m$

Answer 1

The correct option is B $0.4m$

The kinetic energy of the sliding block is$=1/2\times m\times v^2$ $=1/2\times 4\times 2^2=8J$

Now since there is no friction on the surface then it is a conservative system. So all the energy of the block will be used to compress the spring. Suppose the maximum compression of the spring will be $x$ m. So the potential energy needed will be equal to $1/2\times k\times x^2$.

Equating there two energies and solving for $x$, we get $1/2\times k{x}^2=8$

Or $0.5\times \left(100\right)x^2=8$

Thus we get $x=0.4m$