Question

A 0.70 kg spike is hammered into a railroad tie. The initial speed of the spike is equal to 2.6 m/s. If the tie and spike together absorb 38.1 percent of the spike’s initial kinetic energy as internal energy, calculate the increase in internal energy of the tie and spike. Answer in units of J.

Answer 1

To calculate the increase in internal energy of the tie and spike, we first need to find the initial kinetic energy (KE) of the spike.

The formula for kinetic energy is given by:

\[
KE = \frac{1}{2} m v^2
\]

where:
- \( m \) is the mass,
- \( v \) is the velocity.

Here, the mass \( m = 0.70 \, \text{kg} \) and the initial speed \( v = 2.6 \, \text{m/s} \).

Substituting these values into the formula:

\[
KE = \frac{1}{2} \times 0.70 \, \text{kg} \times (2.6 \, \text{m/s})^2
\]

Calculating \( (2.6 \, \text{m/s})^2 \):

\[
(2.6)^2 = 6.76 \, \text{m}^2/\text{s}^2
\]

Now substituting back to calculate KE:

\[
KE = \frac{1}{2} \times 0.70 \times 6.76
\]

Calculating the product:

\[
KE = 0.35 \times 6.76 = 2.366 \, \text{J}
\]

Now, we need to find the increase in internal energy, which is 38.1% of the initial kinetic energy:

\[
\text{Increase in internal energy} = 0.381 \times KE
\]

Calculating this:

\[
\text{Increase in internal energy} = 0.381 \times 2.366 \, \text{J}
\]

Calculating the final value:

\[
\text{Increase in internal energy} \approx 0.900 \, \text{J}
\]

Thus, the increase in internal energy of the tie and spike is approximately **0.90 J**.