Question

A 0.45 kg spike is hammered into a railroad tie. The initial speed of the spike is equal to1.9 m/s.If the tie and spike together absorb 22 per- cent of the spike’s initial kinetic energy as internal energy, calculate the increase in in- ternal energy of the tie and spike.Answer in units of J.

Answer 1

Given:

mass of the spike is

`0.45\text{ kg}`

initial speed od the spike is

`v_=\text{ 1.9 m/s}`

if the tie and spike together absorb 22 percent of the spike's initial kinetic energy.

Required:

calculate the increase in internal energy of the tie and spike.

Step-by-step explanation:

here we apply conservation of energy.

`\Delta U+\Delta K+\Delta P=0`

total change in energy is zero.

here potential energy is not given so neglect that part. we have only

`\Delta U+\Delta K=0`
`\Delta U=-\Delta K`

Here,

`\Delta U=-(K_2-K_1)`

K1 is initial kinetic energy and K2 is final kinetic energy that is equal to zero.

now we have

`\Delta U=K_1`

we know that kinetic energy is

`K=(1)/(2)mv^2`

then

`\Delta U=(1)/(2)mv^2`

plugging all the values in the above relation. we get

`\begin{gathered} \Delta U=(1)/(2)*0.45\text{ kg }*(1.9\text{ m/s})^2*0.22 \\ \Delta U=0.18\text{ J} \end{gathered}`

Thus, the change in internal energy is

`0.18\text{ J}`