Question

ED. 05.39 m/sE. O 0.388 m/s10. An object of mass 16 kg moving with a speedof 26 m/s to the right collides with an objectof mass 9 kg at rest. If the collision is completely inelastic,calculate the kinetic energy lost during the collision. (1 point)A. O-3302.995 JB. O-1703.969 JC. O-1205.975 JD. O-3546.668 JE. O-1946.88 JSubmit Query

Answer 1

Given:

The mass of one object is m1 = 16 kg

The initial speed of the object is

$v_i=\text{ 26 m/s}$

The mass of another object is m2 = 9 kg.

The speed of the object will be zero as it is at rest.

To calculate the kinetic energy lost.

Explanation:

The collision is inelastic.

According to the conservation of momentum, the speed after the collision can be calculated as

$\begin{gathered} m1v_i+m2\times0=(m1+m2)v_f \\ v_f=\frac{m1v_i}{(m1+m2)} \\ =\frac{16\times26}{16+9} \\ =\text{ 16.64 m/s} \end{gathered}$

The loss in kinetic energy during a collision can be calculated as

$\begin{gathered} \Delta K.E\text{ =K.E.}_f-K.E._i \\ =\frac{1}{2}(m1+m2)v_f-\frac{1}{2}m1v_i^2 \\ =\frac{1}{2}\times25\times(16.64)^2-\frac{1}{2}\times16\times(26)^2 \\ =3461.12-5408 \\ =-1946.88\text{ J} \end{gathered}$

Thus, the correct choice is E