A worker drives a 0.509 kg spike into a rail tie
with a 2.08 kg sledgehammer. The hammer
hits the spike with a speed of 63.3 m/s.
If one fifth of the hammer’s kinetic energy
is converted to the internal energy of the hammer and spike, how much does the total internal energy increase?
Answer in units of J
To find the increase in total internal energy, we need to calculate the change in kinetic energy and convert it to joules.
First, we determine the initial kinetic energy of the sledgehammer. The formula for kinetic energy is KE = (1/2) * mass * velocity^2.
Let's denote the mass of the sledgehammer as m_hammer and the velocity as v_hammer.
m_hammer = 2.08 kg (given)
v_hammer = 63.3 m/s (given)
Now we can calculate the initial kinetic energy:
KE_initial = (1/2) * m_hammer * v_hammer^2
Next, we need to calculate the change in kinetic energy. Since one fifth of the hammer's kinetic energy is converted to internal energy, we can calculate the change in kinetic energy as follows:
Change in KE = (1/5) * KE_initial
Finally, we convert the change in kinetic energy to joules:
1 Joule (J) = 1 kg * (m/s)^2
Therefore, to get the change in kinetic energy in joules:
Change in KE (in joules) = Change in KE (in units of kg * (m/s)^2) / 1
Now we can calculate the change in kinetic energy:
Change in KE = (1/5) * KE_initial
Change in KE (in joules) = (1/5) * KE_initial / 1
Substituting the value of KE_initial into the formula:
Change in KE (in joules) = (1/5) * ((1/2) * m_hammer * v_hammer^2) / 1
Let's plug in the given values and calculate the answer in joules.