A worker drives a 0.460 kg spike into a rail tie
with a 2.16 kg sledgehammer. The hammer
hits the spike with a speed of 64.5 m/s.
If one third of the hammer’s kinetic en-
ergy is converted to the internal energy of the
hammer and spike, how much does the total internal energy increase?
Answer in units of J
internal energy= 1/3*1/2 (2.16*64.5^3)
1.76 J
To calculate the increase in total internal energy, we need to find the amount of kinetic energy that is converted to internal energy.
First, let's calculate the initial kinetic energy of the hammer. The formula for kinetic energy is:
Kinetic Energy = 0.5 * mass * velocity^2
Given:
Mass of the hammer (m_hammer) = 2.16 kg
Velocity of the hammer (v_hammer) = 64.5 m/s
Initial Kinetic Energy of the hammer = 0.5 * 2.16 kg * (64.5 m/s)^2
Now, we need to find one-third of the hammer's kinetic energy:
One-Third of Initial Kinetic Energy = (1/3) * Initial Kinetic Energy
Next, we need to calculate the increase in total internal energy. Since one-third of the hammer's kinetic energy is converted to internal energy, the increase in total internal energy can be calculated as:
Increase in Total Internal Energy = One-Third of Initial Kinetic Energy
Finally, we calculate the increase in total internal energy by substituting the values:
Increase in Total Internal Energy = (1/3) * [0.5 * 2.16 kg * (64.5 m/s)^2]
Simplifying the equation gives us the answer in joules (J).