Question

A 0.60 kg spike is hammered into a railroad

tie. The initial speed of the spike is equal to

1.8 m/s.

If the tie and spike together absorb 57.8

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

A 0.60 kg spike is hammered into a railroad tie. The initial speed of the spike is equal to 1.8 m/s. If the tie and spike together absorb 57.8 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.

Change in internal energy of the tie and the spike is 0.56 Joules (J).

Step-by-step explanation:

Given:

Mass of the spike, m = 0.60 kg

Its initial speed, u = 1.8 m/s

According to the question:

The tie and spike together absorb 57.8 percent of the spike’s initial kinetic energy as internal energy.

We have to find the increase in internal energy of the tie and spike.

So,

Let the change in internal energy = ΔE

And the kinetic energy is KE :

Then,

⇒
`KE=(mu^2)/(2)`

⇒
`KE=(0.60* (1.8)^2)/(2)`

⇒
`KE=(0.60* 3.24)/(2)`

⇒
`KE=(1.944)/(2)`

⇒
`KE= 0.972` J

Now,

Change in internal energy:

⇒
`\triangle E = 0.578* KE` ...as 57.8 % = 0.578

⇒
`\triangle E = 0.578* 0.972`

⇒
`\triangle E = 0.561816` J

Change in internal energy of the tie and the spike is 0.56 Joules.